Citation
Multiresolution processing of satellite images and geographic information systems techniques for land-use classification

Material Information

Title:
Multiresolution processing of satellite images and geographic information systems techniques for land-use classification
Creator:
Tan, Yurong
Publication Date:
Language:
English
Physical Description:
xiii, 224 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Artificial satellites ( jstor )
Canopy ( jstor )
Datasets ( jstor )
Digital images ( jstor )
Image classification ( jstor )
Image contrast ( jstor )
Image enhancement ( jstor )
Image processing ( jstor )
Image resolution ( jstor )
Statistical discrepancies ( jstor )
Agricultural Engineering thesis Ph. D
Dissertations, Academic -- Agricultural Engineering -- UF
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1994.
Bibliography:
Includes bibliographical references (leaves 213-219)
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Yurong Tan.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
002043693 ( ALEPH )
33327857 ( OCLC )
AKN1588 ( NOTIS )

Downloads

This item has the following downloads:


Full Text









MULTIRESOLUTION PROCESSING OF SATELLITE IMAGES AND
GEOGRAPHIC INFORMATION SYSTEMS TECHNIQUES FOR
LAND-USE CLASSIFICATION


















By

YURONG TAN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1994


































Copyright 1994

by

Yurong Tan












ACKNOWLEDGEMENTS


This research was performed using the facilities of the

Remote Sensing Applications Laboratory (RSAL) of the

Department of Agricultural Engineering at the University of

Florida. The author is grateful for the assistance provided

by the RSAL director, Dr. Sun F. Shih; RSAL manager, Orlando

Lanni; and RSAL assistants, Jonathan D. Jordan, Chih-Hung Tan,

and Bruce E. Myhre. The author is also grateful for the

comments and review of this manuscript by Dr. Donald L. Myhre

of the Soil and Water Science Department at the University of

Florida.

The author extends his appreciation to each of the

members of his advisory committee, Dr. Brian J. Boman, Dr.

Edward P. Lincoln, Dr. Allen R. Overman, and Dr. Byron E. Ruth

for their comments and advice rendered during this research,

particularly to the committee chairman, Dr. Sun F. Shih of the

Department of Agricultural Engineering at the University of

Florida, for the guidance and support provided throughout the

course of his graduate study at the University of Florida.

The greatest gratitude of the author goes to his wife,

Siru, who always shared the joy as well as frustrations and

provided unconditional support in every aspect during this

seemingly endless process. The author is in debt to his son,

Guolong, for the patience he undertook while this research was

being actively pursued.


iii








Lastly, the author acknowledges that this research would

not have been completed without the continuous support and

encouragement from his loving parents.












TABLE OF CONTENTS


ACKNOWLEDGEMENTS ...................................... iii

LIST OF TABLES .......................................... vii

LIST OF FIGURES ......................................... ix

ABSTRACT ................................................. xii

CHAPTERS

1 INTRODUCTION .................................. 1
Overview ................. ................. 1
Statement of Research Problem ................. 3
Concept of Multiresolution Processing ....... 8

2 OBJECTIVES OF RESEARCH .......................... 13

3 REVIEW OF LITERATURE .......................... 14
Conventional Image Enhancement .............. 14
Multiresolution Enhancement ................ 20
Color Composite Generation .............. 20
Radiometric Enhancement ................. 27
Other Enhancement Methods ............... 36
Summary: Assessment of Problems ............. 40

4 PRINCIPLE OF MERGING IMAGES ..................... 46
Principle of Merging Images ................. 46
Assumptions ............................. 47
Arithmetic of Random Variables ......... 48
Confining Method ........................... 53
Preserving Method .......................... 63
Differencing Method ........................ 69
Summary: Principle of Merging Images ........ 73

5 DEMONSTRATION OF MERGING METHODS ................ 76
Satellite Image Data ......................... 76
Variance of Merged LAC Images ............. 81
Comparison of Merged LAC Images ............ 91
Ratioing of Satellite Images ................ 106
Multiresolution Enhancement ................. 113
Summary: Appraisal of Merging Methods ....... 116

6 MATERIALS AND METHODOLOGY FOR
MULTIRESOLUTION LAND-USE CLASSIFICATION ........ 119
Data Source and Equipment ................... 119








SPOT Image Data and Study Area .......... 119
ACIR Photography ....................... 122
Image Processing Systems ................ 122
Photogrammetric Stereo Plotter .......... 123
Procedures for Merging SPOT Dataset ......... 124
Pre-merging Processing .................. 124
Generating Merged Dataset ............... 126
Evaluation of Merged Data ............... 129
Image Response and Citrus Canopy Cover ...... 132
Photogrammetric Measurement ............. 132
Canopy Cover Estimation ................. 134
Land-use Classification ..................... 136
Precis and Concept ....................... 137
Extracting Signature Patterns ........... 139
GIS-base Discrete Classification ........ 141

7 DISCUSSIONS AND ANALYSES OF
MULTIRESOLUTION LAND-USE CLASSIFICATION ......... 148
Evaluation of Merged Image ................. 148
Radiometric Quality ..................... 148
Spatial Improvement and Spectral
Integrity .......................... 151
Image Response and Citrus Canopy Cover ...... 157
Estimation of Citrus Canopy Cover ....... 157
Relation of Image response to
Canopy Cover ....................... 159
Differentiation of Canopy Cover ......... 166
Effect of Multiresolution Merging ...... 177
Land-use Classification ..................... 183
Potential for Signature Extraction ...... 184
GIS Discrete Classification ............. 189

8 CONCLUSIONS AND RECOMMENDATIONS ................. 195
Research Conclusions ....................... 195
Recommendations ............................ 199

APPENDICES

A RGB COLOR DISPLAY ............................... 202

B IHS TRANSFORM FOR IMAGE DISPLAY ................ 203

C PROGRAM CODES TO UNPACK AVHRR LAC DATA .......... 206

D CLASSIFICATION DECISION RULES .................. 209

REFERENCES ......... .................................... 213

GLOSSARY ................................................ 220

BIOGRAPHICAL SKETCH .................................. 224












LIST OF TABLES


Table

1-1 Available sources of Landsat and SPOT resource
satellite data and system characteristics ....... 5

4-1 Summary of the characteristics of different
merging approaches ............................ 75

5-1 Wavelength characteristics of NOAA-11
AVHRR LAC images ................................ 77

5-2 standard deviation (a), normalized variance
(g2), mean (A), maximum and minimum values
of NOAA-11 AVHRR LAC images .................... 80

5-3 Offset constant (C) used in the differencing
method for merging LAC images ................... 82

6-1 Standard deviation (a), mean (.), and maximum
and minimum values, and correlation coefficients
(r) of SPOT multiresolution dataset ............. 127

6-2 Multiresolution datasets and corresponding
merging equations .............................. 130

6-3 Parameters used in ERDAS STATCL and ELAS
TMTR modules for signature extraction ........... 142

7-1 Standard deviation (a) and mean brightness
values (I) for multiresolution merged SPOT
images ... .... ................................... 149

7-2 Summary for correlations between a merged image
and its original multispectral counterpart ...... 153

7-3 Between-waveband correlations (r) within
multiresolution merged datasets ................. 154

7-4 Summary for corelations between citrus
canopy size and image response for
multiresolution merged images ................. 178

7-5 Variation of image data correlation (r)
between panchromatic and original
multispectral wavebands among selected groves ... 179


vii








7-6 Standard deviations (a) of merged image
data for selected citrus groves ................. 180

7-7 Summary of spectral signatures unveiled
by ERDAS STATCL module ........................ 185

7-8 Summary of spectral signatures unveiled
by ELAS TMTR module ........................... 188

7-9 Canopy cover for spectral classes by GIS-
based discrete classification technique ......... 190


viii












LIST OF FIGURES


Figure Bue

1-1 Schematics of merging multiresolution
satellite images ............................... 9

3-1 Schematics of principal component analysis
for multispectral datasets .................... 18

4-1 Relation of radiometric variance to merging
coefficient (B) and correlation coefficient
(r) for the confining method .................... 57

4-2 Effect of variance difference on the
radiometric quality of merged images
for the confining method ........................ 61

4-3 Relation of radiometric variance to merging
coefficient (B) and correlation coefficient
(r) for the preserving method ................... 66

4-4 Effect of variance difference on the
radiometric quality of merged images
for the preserving method ....................... 68

5-1 Location of clipped NOAA-11 AVHRR LAC images .... 79

5-2 Comparison between actual and estimated
radiometric variance for merged LAC
images (case I) ............................... 83

5-3 Comparison between actual and estimated
radiometric variance for merged LAC
images (case II) ................................ 84

5-4 Comparison between actual and estimated mean
digital count for merged LAC images (case I) .... 85

5-5 Comparison between actual and estimated mean
digital count for merged LAC images (case II) ... 86

5-6 Original clipped NOAA-11 LAC images of
red and NIR wavebands .......................... 93

5-7 Merged LAC images by the preserving
method (case I) ................................. 94








5-8 Merged LAC images by the preserving
method (case II) ................................ 96

5-9 Merged LAC images by the confining
method (case I) ................ ................. 97

5-10 Merged LAC images by the confining
method (case II) ............................... 98

5-11 Merged LAC images by the differencing
method (case I) ................................ 100

5-12 Merged LAC images by the differencing
method (case II) ............................... 101

5-13 Summary (mosaic) of merged LAC images for
three methods (case I) .......................... 104

5-14 Summary (mosaic) of merged LAC images for
three methods (case II) ......................... 105

6-1 Location of clipped SPOT multiresolution
dataset and study area ......................... 121

7-1 Comparison of SPOT 20-m NDVI and 10-m
NDVIp images .................................... 156

7-2 Effect of citrus canopy cover on SPOT green
waveband response .............................. 160

7-3 Effect of citrus canopy cover on SPOT red
waveband response ............................... 161

7-4 Effect of citrus canopy cover on SPOT
panchromatic waveband response .................. 163

7-5 Effect of citrus canopy cover on SPOT NIR
waveband response .............................. 164

7-6 Coincident plot of SPOT green waveband
response for select citrus groves ............... 168

7-7 Coincident plot of SPOT red waveband
response for select citrus groves .............. 169

7-8 Coincident plot of SPOT NIR waveband
response for select citrus groves ............... 170

7-9 Effect of tree crown variations on SPOT
green waveband response variability for
partial canopy groves .......................... 172








7-10 Effect of tree crown variations on SPOT
red waveband response variability for
partial canopy groves ......................... 173

7-11 Effect of tree crown variations on SPOT
NIR waveband response variability for
partial canopy groves ....................... 174

7-12 Relation of citrus tree variations to
canopy cover difference ........................ 176












Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

MULTIRESOLUTION PROCESSING OF SATELLITE IMAGES AND
GEOGRAPHIC INFORMATION SYSTEMS TECHNIQUES FOR
LAND-USE CLASSIFICATION

By

Yurong Tan

December, 1994


Chairman: Dr. Sun Fu Shih
Major Department: Agricultural Engineering

Combining multiresolution images to improve land-use

information assessment is an important subject in remote

sensing applications. The problem in finding effective

methods for multispatial processing must be resolved through

the development of new procedures for merging satellite

images. The effect of combining image data on the quality of

merged datasets must also be assessed toward land-use

classification applications and multispectral analyses.

In digitally merging satellite images, the statistical

variation analyses for combining random variables can be used

to understand the various forms of image data merging and

assess the radiometric quality of pre-merged images. The

selection of an effective merging approach must be made with

consideration of both the correlation and radiometric variance

difference between the combining images and the merging

coefficients. Merging images is a radiometric transformation


xii








among the various land-use types in a scene. This principle

can be used to collaborate Landsat MSS, Landsat TM, SPOT, and

other satellite data for broader applications.

To generate enhanced datasets, the preserving approach

should be used for non-negatively correlated images, and the

differencing approach for those with negative correlations.

The commonly used, but ineffective confining method should be

avoided. The efficacy of waveband ratioing is limited to the

land-use elements with weak/negative correlations and larger

values in the numerator image.

The preserving method with a B=0.5 coefficient was

effective in generating both spatially and radiometrically

enhanced SPOT multiresolution merged datasets which

consistently rendered significantly more spectral signatures

from a satellite scene. This enhanced differentiation

provides a greater amount of information for applications

including land-use classification and image interpretation.

The photogrammetric estimation of citrus canopy cover is

feasible and accurate. Except for the NIR waveband, citrus

canopy cover is inversely related to SPOT image spectra of

partial canopy groves, suggesting a strong influence of soil

substrate on satellite image response. The canopy-size

classification of citrus groves was improved through the

combined use of merged SPOT dataset and GIS-based

classification techniques. Citrus groves with a higher

percentage of canopy cover had more uniform trees and less

variable spectral responses.


xiii












CHAPTER 1
INTRODUCTION


Overview


Information about land use plays an increasingly

important role in the management and preservation of natural

resources. For instance, land-use data are used in the

operations of water resources management which range from

water-use permitting to the development and implementation of

regional planning and management strategies. In environmental

and water quality monitoring, land-use activities are often

indicative of the source and type of pollutants (Novotny and

Chesters, 1981; Fukushima and Muraoka, 1988), particularly

from agricultural and urban lands (USEPA, 1984; Pionke and

Urban, 1985). In many cases, it is the change of land use

that creates immense environmental concerns. Agricultural

land-use data are needed to forecast and monitor production as

well as to assess damage caused by diseases and natural

catastrophic events. Also, land-use data are used in many

other ways including forest management (Coleman et al., 1990),

urban development and planning (Colwell and Poulton, 1985),

hydrological investigations, and applications of geographic

information systems (Ehlers, 1989; Piwowar et al., 1990; Tan

and Shih, 1991a). Therefore, the availability of quality and

timely land-use information becomes an indispensable factor

1








2

which prescribes our efforts in better managing natural

resources.

Traditionally, land-use data are collected through aerial

photography, ground surveys, and existing maps. While these

methods are reliable and accurate, they are expensive and

time-consuming. In addition, the process of traditional

methods is tedious, and therefore often provides land-use data

that are years out of date, while data availability becomes a

limiting factor in some cases. When a large coverage area is

needed, the difficulties involved increase in magnitude as

well as in complexity. Fortunately, the synoptic coverage and

periodic availability of satellite remote sensing data provide

an excellent opportunity for the acquisition of timely land-

use data and the monitoring of extensive land-use activities.

This significantly amplifies our ability to understand the

effects of land use types and to manage the impacts and

consequences resulting from the change of land use activities.

With increasing environmental awareness, more careful planning

and monitoring of land-use activities becomes an important

consideration in all levels of resources management.

To derive land-use information from satellite data, a

land-use classification procedure is used within an automated

computer image processing system. Such procedures generate

statistically similar spectral classes which are then related

to different land-use types (Lillesand and Kiefer, 1979;

Thomas et al., 1987) through a ground-truthing process. To










improve the acquisition of land-use information from space,

continuous research efforts are underway in the development of

both new sensing systems (Engel, 1986; Spotlight, 1991; EOSAT,

1992a, 1992b) and image processing techniques.


Statement of Research Problem


Obtaining land-use data or land-use information by

satellite remote sensing requires a significant improvement

both in accuracy and in specificity in order to be used

operationally in many applications (Lo et al., 1986; DeGloria

et al., 1986). For instance, day-to-day operations in water

resources management seldom use satellite-based land-use data,

mainly because of the lack of desired specificity or details.

One facet to the solution of this problem is to improve the

quality of raw data through advanced sensing technology and

sensor system design. This has been initiated by the

development of new sensing systems which will be onboard

Landsat-7 (EOSAT, 1992a, 1992b) and the French Systeme Probatoire

de 1'Observation de la Terre (SPOT) resources satellite four

referred to as SPOT-4 (Spotlight, 1991). Equally important is

the development of data processing techniques to analyze and

classify the remotely sensed data so that improved land-use

information becomes feasible in practical applications.

Combining multispectral satellite data that have

different spatial resolutions to extract more subtle land-use

information has become an important component in image








4

processing techniques. In the process, the spectral and

spatial advantages rendered by different sensing systems

(Table 1-1) are combined complementarily into a merged

dataset. This provides an unparalleled opportunity that

expands our ability beyond using any of the original

individual datasets to acquire land-use information. Because

of the challenge of future sensor systems which will provide

multiresolution sensing as well as onboard registration

capabilities (Spotlight, 1991; EOSAT, 1992a, 1992b) and the

tremendous amount of image data already captured by satellite

sensors operating over a wide range of spatial resolutions and

spectral wavebands (Shih, 1984; Moore, 1989; Ehlers, 1989),

merging multiresolution satellite images creates an immense

opportunity to make contributions to the improvement of

current land-use data acquisition from space. As a result,

multiresolution processing is anticipated to be a very

powerful image processing technique in future remote sensing

applications.

To date, much research work remains to be done in order

to effectively use multiresolution satellite imagery for

resources management. For instance, finding effective methods

to digitally merge multiresolution datasets continues to be

the central problem in multiresolution processing. A good

merger will be able to take full advantage of the spectral and

spatial benefits of multiresolution images so that resultant

merged datasets will have incomparable radiometric quality















0
C

0

4-I
,,a
CO 4
^i


t)
>1
CIn


41
0


4)


0




E43






U)


In







(4
0)










I


0






*4
U)
S(



to
(0







*oI










44
0









I








rO
0,








I$
*1* 1


ar o o




















k 54 4
O I 00 $4 (
$4 $4 4
HI WW rW Id
1 o 0-I- g









t- CO) 0000 I




w C 0000 1
SC1 4 orW)o i) %D I


moo











r4(4CI I


4.4
0 W
0
O


o t-r-o ld to I
S 4I4 4
V I













a


k .--I r

0 r. r- VI

4- r4 to

$0
k 4) 4 ) 1

4 9 ZZZ E-4 4)
0
I



0
LOI

0 000 HCN I
I H I
0

0 00000 1
H I
(d0
ku
CC 4 IC
O ##94


000

























0 4 10
S1 W
(Q U O


00
I I



0 0
00
















Eu -v.4
O 3
(v .-I 4
10 6
0)
w w'--


0000 D0 0DD0D0
NI










0 0


$.4 -4


0 4) $4 4) 4) ) )


44 #0 4O t-l 4


$4 4) EQ) ) k M
A 9 4 9 k ) 4) 4) 1
Z HE(W-4 H .
c-4 0 0 0
0 1II










0 r- NOD 0000 1
*... L n~orco I
1-4* *0 O H I

4909 0000
-W tnqo %am q I
OrION 0000 I


ON
0 *
00


000


I I I I I I


o 00
* *
o o


(N CO
888Ol


I I



-ON
1-4


M0000000
i-inmmmn




M -4



o to


SMd
r 4) )

0 4) 4 4) 4Q)

f *il rq) *r4


44 MV V


0PMOIPZHE-4H


0 M
O
0

E-C


0000
-B N N VN


















o )4




O! C
S0 9
C00 I
9 Wuo 0


O % coo

000


0 -1 0

000


Hi N m -q i 0 r














0

WH
toH 0
mO (
me B


M' co(A Ln

0 00 r-


o C--i co
*OO O


0 0000
















SV
(0










4 00)
U 4 ) Qa J
( 0)C
0< UK SSHi


**rl

A)
0
00

43
4.)

44




o i
i> oco 3JO> *A
SC 0C M\COC
\\\' 0) Q0 0 0 0 W-C

O\\\ 0I NM LV
c-l N Ln OD 04 -0 H D0



0% ON 0%0 ON (A Or4t
0t 0
1I IV 1 I 4J I I I U
NtncO W HwOO u



N eqO 0 0 0 E NN-4
*\S.\Ns5%.\ <0 V s.NN. 0





0090000r,222
4M44444HNOW









$H







0
o




fz


8
0

o E
0 0
4 OW


o 4


0)



4 4
a


o









t o
rI --
t >

0

UC 4







.r m ) .c
-04


> C0 -4
0 C b--1



to U pI 4 4
4 U U CH
>R a) )U^-



0 L-i 040 c4



43 o al U -p 0
Li-lo N 0

0I 0 E- E-4 -H

W .Q C 0 *o 40


4-I
ONi
0
0
O
4)
tO








8

and enhanced spatial information. These quality factors of

image data are vital not only to the utility of the merged

datasets for potential applications, but also to any remote

sensing efforts that attempt to improve our capability in

monitoring land-use resources. Therefore, this research was

focused on the techniques for combining multiresolution

satellite images as well as on the utility of multiresolution

processing for land-use classification and image

interpretation.


Concept of Multiresolution Processing


Multiresolution processing is an image processing

technique used to combine or merge multispectral images that

have different spatial resolutions. One of the images to be

combined will have a high spatial resolution or a smaller size

of picture element (pixel), and a panchromatic waveband, while

the others will be multispectral (or multi-waveband), but with

a relatively lower spatial resolution, or a larger pixel.

These images of different spatial resolutions are digitally

merged to reconstruct a new set of images that can inherit the

spectral and spatial characteristics of both the multispectral

and panchromatic images. The process is schematically

illustrated in Figure 1-1.

The purpose of multiresolution processing is to generate

a new set of images with enhanced spectral and spatial

qualities by taking the spectral and spatial advantages of the




















r-4


-0
M
U



-0
a









a,


E
0


CM

0.


I.


z
C-


z
0.


0


-,4
't




4.
ta






0




(0
4
DC


z
a->


I








10

images to be combined. The spatial and spectral virtues of

the original multiresolution image data are utilized

complementarily. As a result, the merged dataset becomes

spectrally as well as spatially more powerful for remote

sensing applications.

One example of multiresolution processing is to merge the

SPOT high resolution visible (HRV) panchromatic and

multispectral images that have respective 10-m and 20-m

spatial resolutions (Cliche et al., 1985; Carper et al.,

1990). The panchromatic image with a 10-m resolution can

reveal subtle spatial details of scene objects, but its usage

for multispectral analyses (land-use classification) is

hampered by its very broad spectral waveband. The 20-m

multispectral data with three spectral wavebands are more

useful for land-use classification, however a high spatial

resolution multispectral dataset is more desirable for

extracting subtle information from the scene. When such

multiresolution images are merged, the spectral and spatial

advantages are combined into a new set of images which are

multispectral and with a 10-m spatial resolution. As a

result, the new merged dataset will have a greater potential

for remote sensing applications.

There are two major steps involved in the process of

multiresolution processing. The first deals with the co-

registration of the multiresolution images. This can be done

with two different approaches. The first one is to simply







11

project all images to a mutual geographic reference system

which can be either the latitude-longitude system, or the

universal transverse mercator (UTM) system, or the state plane

coordinate (SPC) system. The second approach is to treat one

of the images as a master and the rest as slaves. After

selecting a number of tie points that are mutual to all images

including the master one, the slave images are rectified to

the master image. In the second approach, no actual

geographical coordinate system (e.g. UTM) is utilized and the

slave images are referenced relative to the master image.

Usually, this relative approach produces a smaller error of

co-registration because transitional reference (e.g. maps) and

digitizing operations for map data entry are not involved. To

register multiresolution images, it is also necessary to

invoke an image resampling procedure before or during the

registration process. Virtually all image processing software

packages provide the facilities for image resampling and

registration operations.

The second step involves the use of mathematical

manipulations to digitally combine, pixel by pixel, the

numerical image data. This is a very critical step because

the spectral, radiometric, and spatial qualities of the merged

dataset depend on the selection of a good combining algorithm.

At the end, a new set of multispectral images are generated

which are radiometrically, spatially, and spectrally enhanced.

While the combining algorithms reported in the literature vary








12

considerably, their introduction is the results of

speculations and arbitrary elaborations because the basic

principle of digitally merging satellite images is not well

understood. Therefore, it has become essential to explore and

to understand the principle of image data manipulations so

that the techniques of multiresolution processing can be

developed to effectively enhance satellite remote sensing

applications including land-use classification.











CHAPTER 2
OBJECTIVES OF RESEARCH


The main objective of this research was to study the

principle of digitally merging satellite images and to develop

techniques for combining multiresolution satellite datasets,

as well as to evaluate the utility of multiresolution

processing for satellite-based land-use classifications. The

specific objectives included:

1. To formulate the principle of digitally combining

multispectral satellite images including those with different

spatial resolutions.

2. To develop techniques and methods for digitally

merging multiresolution satellite images.

3. To study the effects of multiresolution processing

on the spectral, spatial, and radiometric qualities of merged

multispectral datasets.

4. To study the effects of canopy sizes of citrus trees

on the spectral responses of SPOT satellite data as well as to

investigate the feasibility of a canopy-size differentiation

of citrus crops on satellite images.

5. To investigate the utility and benefits of combining

multiresolution satellite images for land-use classifications,

particularly for citrus crops.












CHAPTER 3
REVIEW OF LITERATURE


Because of the multispectral capabilities of contemporary

satellite sensing systems, a geographic area can be imaged

simultaneously with a number of spectral wavebands, resulting

in a multi-image scene or dataset. In the discussions

throughout this dissertation, a scene includes all the images

acquired for one geographic area at one time, while an image

is meant to represent the numerical data of only one spectral

waveband.


Conventional Image Enhancement


Over the years that remote sensing data have become

widely used, many techniques for image enhancement have been

well developed and standardized in image processing software

systems. Therefore, an in-depth discussion for each of these

techniques seems inappropriate. However, a brief review of

those techniques which were involved or used in many previous

research efforts to combine multiresolution satellite images

would be useful to the understanding of continued discussions.

Those techniques included the contrast stretching, spatial

filtering, and principal component analysis.

A contrast-stretching procedure is an image processing

procedure used to arbitrarily rescale a set of image gray








15

shades to a larger range or to a full range (0-255) for

increasing image contrast. The gray shades of an original

satellite image of Landsat, SPOT, and other satellites usually

spread over a portion of the available 0-255 dynamic range (or

sometimes called data depth). As a result, such images with

cramped gray shades do not have conspicuous tonal gradations.

After a contrast-stretching process, the image values (often

called image digital counts) of relatively dark pixels are

scaled back further, while those of bright pixels are scaled

up. As a result, original dark pixels will become darker

while the bright ones become brighter in a contrast-stretched

image (Gonzalez and Wintz, 1987). Very often, this simple

procedure can produce satisfactory results for image

interpretation. Note that the increase in image tonal

contrast by a contrast-stretching procedure gives a false

sense that the procedure can improve the image radiometric

quality.

The contrast-stretching procedure can be applied to a

portion of the existing image gray shades (Thomas et al.,

1987) or to a subimage area (Gonzalez and Wintz, 1987) for a

selective enhancement. Also, there are linear and nonlinear

contrast stretching methods (Lillesand and Kiefer, 1979;

Thomas et al., 1987) and the procedure is performed for each

image or waveband independently.

A spatial filtering procedure includes both the high-pass

and low-pass filters which are often used to remove or to








16

emphasize certain visual effects of a digital image. For

instance, a low-pass filter is used for image smoothing and

noise elimination while a high-pass filter is for edge

enhancement (Lillesand and Kiefer, 1979). The simplest form

of a low-pass filter is to replace the value of a pixel by the

average computed from its neighborhood (e.g. 3 x 3 pixel

array). By replacing a pixel's value with its neighborhood

average, the large values (such as noises) will be compressed

while the small values are inflated or exaggerated (Lillesand

and Kiefer, 1979). As a result, a low-pass filtered image

will appear smoother and have less contrast. In the case of

a high-pass filter, the value of a pixel will be added to or

subtracted from by its deviation from the average of its

neighborhood (e.g. 3 x 3 array), depending on its relative

magnitude with respect to the defined neighborhood average.

Therefore, boundary pixels which usually have the largest

deviations will become either much darker or brighter. Often,

the deviations are doubled or even tripled in order to make

edges or linear features more conspicuous (Lillesand and

Kiefer, 1979). The operation of a spatial filtering procedure

(high-pass or a low-pass) is performed independently for each

image or waveband. An important point in spatial filtering is

that the resultant image data are radiometrically altered by

such filtering procedures.

As compared to the methods of both contrast stretching

and spatial filtering, principal component analysis (PCA) is








17

a procedure which involves a multi-dimensional transformation

for a set of multispectral images. In the process, the multi-

waveband data are transformed from the original coordinate

system formed by the spectral wavebands into one defined by

new synthesized wavebands. There are several usages for a PCA

procedure. First, it can be used to reduce the dimensionality

of multi-waveband datasets (Thomas et al., 1987). For

instance, when a PCA transform is applied, the image data of

a two-waveband dataset can be effectively represented by the

first principal component (PC1) as shown in Figure 2-1, thus

reducing the dataset to essentially one dimension (or one

synthesized waveband). The second usage is to increase the

image contrast as well as the separability for land-use

elements (Lillesand and Kiefer, 1979). For instance, the

image data variance encompassed by the PC1 component (Figure

2-1) is greater than either of those for the two original

wavebands. Therefore, the image of the PC1 component will

have more contrast as well as greater separation among the

different land-use elements in the image. The third usage of

a PCA procedure is for the decorrelation of multispectral

images (Gillespie et al., 1986). In such a case, a PCA

transform is followed by a contrast-stretching procedure

applied to the PC components, particularly the PC2 component

as shown in Figure 2-1. Then, the first (PC1) and second

(PC2) components are together retransformed back to their

original multispectral space. In a decorrelated dataset, the












a









Sto
r(0
0


.0

AV U
p4 0


















-'-4



.r4
@ e 0*



*.w 0



0 \* o ,








.o; o
3 0


4.-)
-" U







H *
3 ^ *A "*-**0
h V ^ '.4








19

identities for the various types of spectral elements may be

significantly different from those of the original images

(Gillespie et al., 1986).

If the PCA procedure is applied to a multispectral image

dataset with n wavebands, the image data transformation will

take place within a n-dimensional space. The results are that

the amount of radiometric information represented by the

first, the second, ... and the nth component will be in a

decreasing order. Also, the transformed components can each

be contrast-stretched (Lillesand and Kiefer, 1979) to further

enhance the tonal gradations of transformed images. The PCA

transform is usually carried out before initiating land-use

classification procedures to reduce data dimensionality as

well as to enhance the radiometric separability of spectral

classes. Thomas et al. (1987) presents in-depth discussions

about PCA transforms which are exemplified by using a Landsat

multispectral scanner (MSS) dataset.


Finally, it is worthwhile to point out that the

procedures of contrast stretching, spatial filtering, and

principal component analysis will not enhance or improve the

spatial resolution of the original images. In addition, a

contrast-stretching procedure will not increase the actual

number of gray shades in an image, even though the radiometric

variance of stretched image data is increased.









Multiresolution Enhancement


Combining the spatial and multispectral advantages of

multiresolution satellite images for various resource

management applications has inspired great interests in the

remote sensing community. To merge satellite images with

different spatial resolutions, both image co-registration and

arithmetical data manipulations are required. If the images

are already co-registered, the primary methods to manipulate

the image data can be summarized into two broad approaches

which include the generation of color composites and the

enhancement of radiometric quality of merged images. Note

that to generate a color composite usually requires three

images for the blue, green, and red primary colors of a

display device.


Color Composite Generation


The most commonly used methods for generating color

renditions from image datasets are the well-known RGB (red,

green, and blue) color display system (Appendix A) and the

intensity-hue-saturation (IHS) color transform (Appendix B).

For multiresolution datasets, the RGB system is simple and

easy to use, but the resultant color composites often have a

blocky appearance, particularly when the spatial resolution

difference is large. Recently, the IHS transform has gained

popularity mainly because of its effectiveness to produce more

balanced color products for a wide range of datasets. To








21

generate a color composite from a multiresolution dataset, the

IHS method first takes a forward transformation from the low

spatial resolution images of three wavebands into the

intensity (I), hue (H), and saturation (S) components

(Appendix B). Then, a reverse transformation is carried out

to convert the I, H, and S components to the RGB values in

order to generate color composites through a RGB color display

device. The high spatial resolution image is merged in the

process by replacing the I component during the reverse

transformation (Haydn et al., 1982; Carper et al., 1990).

Note that a color composite by either the RGB system or the

IHS transform uses a maximum of only three spectral channels

and successful results often depend on a tedious trial-and-

error process.

Daily et al. (1979) were among the first to recognize the

importance of multiresolution processing of satellite data for

remote sensing applications. An airborne radar image with a

10-m spatial resolution was co-registered with Landsat 80-m

MSS images in an effort to improve geological interpretation

for a desert environment. The superior textural variations of

the radar image along with a 10-m spatial resolution were

utilized to complement the low contrast as well as the low

spatial resolution of Landsat MSS data which, in turn,

compensated for the drawbacks of radar shadows. Through a

direct RGB color display method, color composites generated

from the co-registered dataset were able to delineate subtle







22

geologic units through a visual image interpretation. Using

a similar approach, Wong and Orth (1980) also generated useful

color composites from Seasat synthetic aperture radar (SAR)

and Landsat MSS images which have 40-m and 80-m spatial

resolutions, respectively. These two early studies underlined

the benefits in the unified use of satellite data acquired by

completely different sensing systems multispectrall vs. radar)

for improving the interpretability of remote sensing images.

When the RGB color display system is used, satellite

images do not readily define or fit into the red, green, and

blue primary colors (Harris et al., 1990). In other words,

the images can not simply substitute the red, green, and blue

primaries in the RGB display system because of the spectral

incompatibility which could lead to serious color distortions

and poor-quality composites (Haydn et al., 1982; Harris et

al., 1990; and Carper et al., 1990). As a result, the IHS

color perception system has become the widely adopted approach

to resolve the color distortion problems encountered in the

RGB display of multispectral images. The entire process of an

IHS transform for multiresolution processing takes four steps

which include (i) co-registration of multiresolution images,

(ii) a forward transformation from three multispectral images

to the three IHS components, (iii) a reverse transformation

from the IHS components to RGB values, usually with the

replacement of the intensity component by the high spatial

resolution image, and (iv) display the results through a RGB








23

color display system. For the IHS system, the intensity or

brightness of a scene is a function of illumination (Boynton,

1979). Therefore, the intensity component should encompass a

broader range of wavelength (Haydn et al, 1982) and is

extensively associated with the spatial relations of scene

objects (Judd and Wyszechi, 1975). For this reason, the

intensity component is always assumed to be replaced by the

high spatial resolution panchromatic image in the reverse IHS

transformation.

Zobrist et al. (1979) were among the first to apply the

IHS transform to satellite data for image enhancement. In the

study, Landsat MSS 80-m and meteorological Seasat 25-m radar

images were used. The intensity component transformed from

the Landsat MSS data was simply replaced by the 25-m radar

image. Then, an IHS reverse transformation was taken to

create color composites.

Haydn et al. (1982) further demonstrated the utility of

the IHS transform for image enhancement. Landsat MSS, Landsat

return beam vidicon (RBV), and the Heat Capacity Mapping

Mission (HCMM) thermal infrared (TIR) images with respective

spatial resolutions of 80 m, 30 m, and 600 m were merged

between the RBV and MSS and between the MSS and HCMM images.

A direct replacement of the transformed intensity component by

the corresponding high spatial resolution image was employed

in the reverse transformation for each case. Also, ratioed

data between spectral wavebands was demonstrated for the use








24

of the IHS transform. For example, while the intensity

component was transformed from Landsat MSS wavebands four,

five, and seven (denoted respectively as MSS4, MSS5, and

MSS7), the H and S components were substituted, respectively,

by the MSS5/MSS4 and MSS5/MSS6 ratioed data. Substantial

enhancement in color composites was observed. The IHS color

transform was adopted in the entire study because the direct

RGB color model produced confusing and low quality image

presentations. Using a similar methodology, Welch and Ehlers

(1987) were able to produce enhanced color composites from

Landsat (30 m) thematic mapper (TM) and SPOT HRV 10-m

panchromatic images.

Very different approaches for using the IHS transform

have also been reported. A color composite was created from

a Seasat mono-band radar image (Daily, 1983). Both the strong

and weak radar responses related to sloping targets and

vegetation features were extracted, respectively, by high-pass

and low-pass filters, and then used as the hue and saturation

components while the original radar image was used directly as

the intensity component for the IHS transform. The color

composite was able to reveal major structural features

invisible in the original black-and-white radar image. Harris

et al. (1990) took a step further when combining Landsat 30-m

TM and 10-m airborne radar images. In two instances, the high

spatial resolution image was used directly as the intensity

component, while the hue components were created from a








25

combination of Landsat TM wavebands two, four, and seven

(denoted as TM2, TM4, and TM7) or of Landsat TM wavebands two,

five, and seven (denoted as TM2, TM5, and TM7). However, the

saturation component was held at a constant value (150). In

another instance of the same study by Harris et al. (1990),

the radar image was used as the intensity component and the

geological units (numerical codes) in a digitized map as the

hue component, while the saturation component was held at a

constant (150). Based on a visual assessment, the study

concluded that the color composites were able to define

lithological and structural features that were absent from

existing geological maps. These two studies by Daily (1983)

and Harris et al. (1990) not only opened a new dimension in

the use of the IHS transform for remote sensing applications,

but also demonstrated the effectiveness and compatibility of

the IHS transform for a broad range of data characteristics

including satellite images and digital maps.

The use of the IHS transform can be extended to include

the imagery digitized from an aerial color infrared (ACIR)

photography (Grasso, 1993). In the study, a digitized ACIR

high spatial resolution (10 m) image was merged with Landsat

MSS and Landsat TM data to enhance geological interpretation.

The intensity components transformed from either Landsat MSS

or Landsat TM images were directly replaced by the ACIR image

during the IHS reverse transformation. The color composites,

which had a 8x linear spatial resolution factor, were still








26

useful for geological mapping. Also in the study, a different

approach in utilizing the IHS transform was demonstrated in

which the digitized ACIR image was used as the intensity

component, the Landsat TM ratio data (TM5/TM7) as the

saturation component while the hue component was held at a

constant value (96). The results were very useful for

delineating the high and low clay content areas. Note that

the high and low TM5/TM7 ratios were essentially used to

regulate the level of color saturation (S component) so that

high clay content areas would show more vivid colors than its

counterparts. However, results also showed that the colors of

these composites could change very rapidly by just varying the

hue component with a moderate magnitude. Though the concept

of the latter example is somewhat different from the previous

one by Harris et al. (1990) who emphasized the color diversity

(H component) rather than the color purity (S component), good

quality color composites can still be produced by the IHS

transform. This indicates that the IHS color transform has

tremendous flexibilities in adapting to a wide variety of

geographic data.

In summary, when applying the RGB and IHS methods to

generate color composites, it has been demonstrated that image

interpretability can be significantly improved through a

unified use of multiresolution datasets. This is particularly

evident for the IHS transform which is capable of producing

quality color composites under a broad range of circumstances.








27

Also, several studies have illustrated that the IHS transform

seems to possess a virtually universal adaptability to

geographic data. The multiresolution merged results in the

form of color composites are indispensable for many remote

sensing applications which involve image interpretation.

However, to generate color composites is not the ultimate goal

of multiresolution processing of satellite imagery data. The

radiometric quality of merged images is far more important

than a color display and vital to the potential of post-

merging applications such as land-use classification. In

addition, a severe disadvantage for color composites is that

tremendous efforts are needed to extract quantitative land-use

information from the color products while a maximum of only

three spectral wavebands can be handled at one time.


Radiometric Enhancement


In the radiometric enhancement approach, arithmetical

algorithms are used to digitally combine the multiresolution

image data in order to generate merged images which can

achieve the purpose of multiresolution processing. Direct

substitution of the high spatial resolution image for the RGB

color display system often created color composites with

blocky appearances because of the spatial resolution

differences. To overcome such a weakness, digital

manipulations of the image data have become necessary. In a

study by Cliche et al. (1985), simulated SPOT HRV panchromatic







28

and multispectral images from an airborne dataset, which had

11 spectral wavebands, were digitally merged, pixel by pixel,

using the following methods


I. MIi = Ai (PAN HRVi)W + Bi [3-1]


II. MIi = Ai (PAN HRV,) + Bi [3-2]


III. MI1 = Al (PAN HRV,)1 + B, [3-3a]

MI2 = A2 (PAN HRV2) 2 + B2 [3-3b]

MI3 = A3 (0.25PAN + 0.75HRV3) + B3 [3-3c]


where MIi is the merged multispectral images, i (in methods I

and II and subscripts 1-3 in method III) is waveband index,

PAN and HRV are, respectively, the simulated SPOT panchromatic

and multispectral images, and Ai and B, are coefficients or

scaling factors to maintain the merged data within the 0-255

dynamic range.

From the color composites generated through the use of

the RGB color display system, the study concluded that, while

the improvement on spatial resolution was apparent for all

three methods, method (III) produced the best color composite.

The improvement by method (III) was attributed to the use of

different merging algorithms which helped preserve the SPOT

HRV3 near infrared information. For method (II), the pixel

values were low and concentrated, resulting in dark and no-

contrast merged images. Because of the high correlations in

the merged images between the near infrared and visible








29

wavebands, method (I) produced wash-out images. Even though

all these merging methods were based on arbitrary speculations

and the results were displayed using the RGB system, the

potential benefits of digitally merging image datasets were

indicated with improved spatial information.

In digitally merging multiresolution images, speculations

for a combining approach do not bring about consistent

results. In an effort to find a general approach that does

not depend on arbitrary elaborations, Price (1987) contended

that the high correlations between the panchromatic and both

the multispectral green and red wavebands within a SPOT

multiresolution dataset could be utilized to estimate the

corresponding high spatial resolution multispectral merged

images. In the study, the original SPOT 10-m panchromatic and

20-m multispectral images were artificially degraded, by

averaging, to 20-m panchromatic (P20) and 40-m multispectral

(M40) images, respectively. Then, the whole approach took two
steps. The 20-m multispectral merged images (MI) were first

estimated from the degraded panchromatic P20 data by a

regression equation


MIi = Ai P20 + Bi + D [3-4]


where MIi is the estimated multispectral image i based on the

degraded (20-m) panchromatic image, A, and Bi are regression

coefficients determined from the degraded panchromatic P20 and

the original 20-m spatial resolution multispectral image, and








30

D is a correction factor to balance the numerical sum of

estimated subpixels with the recorded value of a low

resolution pixel (M40). If the sum of the estimated digital

counts of subpixels did not equal the recorded value of the

low resolution pixel in question, a correction was applied.

The estimated 20-m images from the degraded (40-m)

panchromatic waveband were able to retain 99% of the variances

of the original 20-m images of the green and red wavebands.

However, a potentially serious problem could have existed with

a high correlation between the two estimated images because

they both depended on the same identical panchromatic data.

In fact, the multispectral images were used only as

complementary information through a correction procedure.

A different approach was undertaken to estimate the SPOT

near-infrared (NIR) image which in general does not correlate

well with the panchromatic waveband. The (estimated) merged

20-m NIR image (MI3) was first obtained from a lookup table

created by both the degraded 20-m panchromatic (P20) and the

original 20-m NIR images. Then correction was applied similar

to those used for the green and red wavebands. Results

indicated that only 75% of the radiometric variance of the

original NIR image was retained during the merging process.

Though the broad spectral bandwidth of the panchromatic image

encompasses part or even the entire range of the multispectral







31

green and red wavebands, it is impossible that the portion of

image digital count for a merged high spatial resolution image

can be separated from a panchromatic pixel. The difficulty is

analogous to isolating from a jar of oil the part that came

from a particular peanut. In addition, the process of spatial

degradation (by averaging pixels) could smooth out or compress

the radiometric information in the original image data.

To explore the utility of digital manipulations for

datasets acquired by multiple sensors, Landsat MSS and Shuttle

imaging radar A-band (SIR-A) images were digitally merged in

a lithological mapping study (Chavez et al., 1983). However,

the high spatial resolution of the 40-m radar image was not

utilized to its advantage for enhancing the spatial resolution

of the Landsat 80-m MSS images. Instead, the spatial

resolution of the radar image was artificially degraded for

compatibility with that of the Landsat MSS data. From the

results of various arithmetical manipulations including

addition, subtraction, ratioing, and difference-ratioing of

the co-registered SIR-A and Landsat MSS image data, it was

concluded that the addition and ratioing methods were useful

for discriminating some geologic units while the applicability

of the subtraction method is limited only to negatively

correlated images. The results by Chavez et al. (1983) have

two important implications. First, digital manipulations of

image data can be extended to include those images acquired by

different sensing systems. Second, the arithmetical








32

manipulations of image data can be applied to images with

different spatial resolutions as well as those which have the

same spatial resolution.

Digital merging multiresolution images has been used in

efforts to further enhance the results of an IHS transform.

In order to more effectively use the IHS transform, the

selection of a proper intensity or brightness component is

very critical to the quality of color display (Boynton, 1979).

A low intensity component could result in severe image

degradations (Judd and Wyszechi, 1975; Haydn et al., 1982).

In the case of a low intensity value, corrections are needed

for the hue and saturation components (Judd and Wyszechi,

1975) or for the intensity component (Boynton, 1979; Haydn et

al., 1982; Gillespie et al., 1986). However, by applying such

correction procedures, the final image is very difficult to

interpret because the original colors can be altered

significantly (Zobrist et al., 1979).

The importance of finding the most effective method to

generate the intensity component for the IHS transform for

merging multiresolution datasets has been recognized by some

researchers, including Carper et al. (1990). Instead of

adopting the direct replacement of the panchromatic image for

the intensity component, Carper et al. (1990) conducted some

experiments on different merging methods in order to find the

best intensity component. In addition to many previous

studies that relied on imagery data acquired on different








33

dates or even in different years, simultaneously-acquired SPOT

10-m panchromatic and 20-m multispectral images were used.

This was done to eliminate the contribution of temporal

information which could introduce some difficulty to the

assessment of the benefits of an IHS transform. Carper et al.

(1990) proposed the following set of merging algorithms to

calculate the intensity components.


Ia = (PAN + RHV3)/2 [3-5]

Ib = (PAN PAN HRV3)1/3 [3-6]


Ic = (2 PAN + HRV3)/3 [3-7]


Id = (PAN HRV) 1/2 [3-8]

I0 = (HRV, + HRV2 + HRV3)/3 [3-9]

where I, with alphabetical subscripts for method index, is the

calculated intensity component to replace the original

intensity component Io transformed from the 20-m multispectral

images, PAN is the SPOT panchromatic image, and HRV is the

multispectral data with numerical subscripts for waveband

index. The study concluded that the weighted average method

(Ic) consistently produced results as good as or better than
the others. The effectiveness of this weighted average method

(Ic) was attributed to the greater histogram similarity
between the calculated (Ic) and the original (I) intensity

components. However, some points in the results were left








34

undiscussed. For instance, while the histogram of Ic

correlated extremely well to that of the panchromatic image

except with a moderate shift to higher values, it did not have

any resemblance to that of the original HRV3 image. This

indicated that the coefficient (2/3) for the PAN image in

equation [3-7] significantly exaggerated the effect of the

panchromatic image in the Ic component, implying not only a

duplication of the panchromatic information, but also a

significant loss of radiometric information for the HRV3 image

in the merging process. In addition, the great similarity

between the histograms of intensity Ic and the panchromatic

image suggested that a direct replacement of the intensity

component (Io) by the panchromatic image, as used in many

other studies, is workable in an IHS transform.

In response to a broad array of diverse approaches which

have been used to merge multiresolution datasets, several

methods to combine multiresolution images were evaluated by

Chavez et al. (1991) using statistical, visual, and graphical

comparisons. More specifically, those different combining

methods included the IHS transform, the PCA method, and the

high-pass (spatial) filtering (HPF). For the Landsat TM and

SPOT panchromatic datasets used in the study, a contrast-

stretching procedure was applied to the SPOT panchromatic

image in an attempt to increase (arbitrarily scale up) the

radiometric variance. Then, in the IHS method, the intensity

component transformed from Landsat TM images was simply








35

replaced by the contrast-stretched panchromatic image during

the IHS reverse transformation. In the PCA method, the

stretched panchromatic image was assumed to be similar to the

first principal component transformed from the Landsat TM

images of all six wavebands (excluding the TIR waveband),

while in the HPF method, a high-pass filter was applied to the

contrast-stretched panchromatic image to extract the high

frequency spatial information which was merged to each of the

six Landsat TM images through a pixel-by-pixel addition

method.

Color composites generated by all three methods were

subjected to visual comparisons. Statistical correlation

analyses were conducted between the first principal component

of Landsat TM six-waveband data, the IHS intensity component

and the contrast-stretched panchromatic image. Spectral

signatures from five selected land-use types were graphically

compared between the original Landsat TM data and the merged

datasets by the IHS transform and HPF method. Chavez et al.

(1991) concluded that, though the IHS method produced the best

color composite among the three methods, it distorted the

spectral characteristics of the merged images the most. For

the HPF method, the merged images possessed the spectral

characteristics comparable to those of the original Landsat TM

data. The distortion of spectral information by the IHS

method was attributed to the fact that the customary

assumption of similarity between the IHS intensity component








36
and the panchromatic image is not always valid. When one

examines the implicit spectral requirements (in a decreasing

order of spectral bandwidth for the I, H, and S components) by

the IHS transform as discussed by Haydn et al. (1982), it is

not surprising to recognize that the distortions of spectral

integrity would be inevitable in the transformed I, H, and S

components. Note that the requirement for decreasing spectral

bandwidths for the I, H, and S components would generally

result in the numerical values of those components being in

the same order. In using the IHS transformed data for post-

merging applications other than color composites, these

distortions of spectral information cause a serious concern

about the utility and effectiveness of a merged dataset for

multispectral analyses.


Other Enhancement Methods


There were some other cases in which multiresolution

merging was used for purposes other than image enhancement.

It is worthwhile to discuss these methods because of their

pertinence to the subject of merging multiresolution datasets.

The practical importance of digitally merging multiresolution

datasets for image data compression purpose was investigated

by Schowengerdt (1980). He contended that the data volume for

storage and transmission can be significantly reduced if a

high spatial resolution multispectral dataset can be

constructed by combining a high spatial resolution image with








37

a relatively low spatial resolution multispectral dataset.

With that argument in mind, the spatial resolution of the

Landsat MSS images of wavebands four (green), six (NIR), and

seven (NIR) with the original 80-m spatial resolution was

artificially degraded by a linear factor of three to a 240-m

spatial resolution dataset. The original 80-m resolution

image of waveband five (red) remained unchanged and was used

as the high spatial resolution image. Assuming that an image

consists of both spectral and spatial components, the

following merging equations were proposed


MIi = MSSi + ki H5 [3-10]


and


ki = ac / as [3-11]


where MIi is the reconstructed image, i (and subscript 5) is

waveband index, H5 is the high frequency spatial information,

and a is the image-wide standard deviation. The high

frequency spatial component (Hs) was obtained by a subtraction

between the low-pass and the high-pass filtered images of

waveband five. New images with a 80-m spatial resolution were

reconstructed through pixel-by-pixel manipulations using

equations [3-10] and [3-11]. Visual evaluation of the

reconstructed images indicated that a great deal of high

frequency information (edges) could be restored except for

vegetation-dominated areas where a reverse tonal appearance








38
was indicated. Waveband five was selected as the high spatial

resolution image because it had the greatest contrast. This

selection of waveband five would make the ki values by

equation [3-11] smaller than 1.0 because a5 is the largest.

Consequently, equation [3-10] implicitly emphasizes the

multispectral images, making it possible for the merged

datasets to maintain the spectral characteristics of the

original multispectral data.

The utility of an IHS transform for image data

compression was also studied by Haydn et al. (1982) using

Landsat MSS wavebands four (green), five (red), and seven

(NIR). The hue and saturation components transformed from the

three Landsat MSS images were each arbitrarily degraded. The

spatial resolution was reduced by linear factors of two, four,

and six which corresponded to data compression factors of

four, sixteen, and thirty-six, respectively. Color composites

were regenerated for each data compression factor using the

degraded H and S components along with the original I

component. Visual comparisons of the regenerated color

composites to that of the three original wavebands did not

indicate substantial quality deterioration except for the case

which had a data compression factor of thirty-six or a 6x

linear resolution factor.

A half-pixel shifting method to improve the effective

spatial resolution of remote sensing data was studied by Dye

and Wood (1989). They argued that, for a given pixel in a








39
scene imaged twice over a time period, both its numerical

value and geographic location would not be identical because

of the potential offset (error) in sampling the pixel by the

sensor. Therefore, if one of the two images in a dataset is

artificially offset half a pixel before the two images are

combined together, the resultant merged image will increase

its spatial resolution by a linear factor of two. From the

viewpoint of data sampling technique, this method is very

interesting. However, in the remote sensing monitoring of

land-use activities, the concept may not be valid or even

logical when considering the time lapse in image acquisition

and the spectrally dynamic changes in natural environments.

In a study using artificial as well as satellite images,

Albertz and Zelianeos (1990) pointed out the following

requirements necessary for this half-pixel shifting method to

be successful: (1) the scene must be imaged several times--

preferably more than four; (2) there will be no significant

changes in the scene environments (spectrally static objects);

and (3) image geo-referencing or co-registration must be very

accurate in order to have the precise half-pixel offset.

With the advent of geographic information systems (GIS)

techniques, various types of geographical data including

existing map data and multi-date imagery data have been

integrated during an image processing scheme. However, the

main purpose of such image processing efforts is to detect

changes rather than to improve the spatial and radiometric








40

qualities of the final results. To improve agricultural land-

use classification, Lo et al. (1986) combined two Landsat MSS

scenes acquired in different growing seasons. The two scenes

were co-registered and some waveband ratioing was undertaken

before invoking land-use classification procedures. Using

this multitemporal approach, the land-use classification by an

unsupervised classification scheme was improved from 84% to

86%. However, it is arguable that the information accumulated

from the two scenes and the use of more spectral wavebands

would definitely be a factor contributing to the improvement

of classification results. A similar study for corn-soybean

field classifications was conducted by Badhwar et al. (1982)

using Landsat MSS data.

There are many other examples that involved the use of

satellite imagery data and thematic overlay techniques. For

instance, the study by Walsh et al. (1990) combined Landsat TM

images with digital elevation model (DEM) data to study the

hydrological processes in rugged terrain environments, and

that by Shih (1988) who combined Landsat MSS data with the

digitized version of the United States Geological Survey

(USGS) land use/land cover maps within a GIS environment for

land-use classification comparisons.


Summary: Assessment of Problems


Many studies have been made to develop image processing

techniques to combine multiresolution images for remote








41

sensing applications. Opportunities exist to improve the

interpretability of satellite image datasets for the

management and monitoring of natural resources and the

environment. In summary, these efforts have demonstrated the

following aspects.

1. The IHS transform is a powerful and effective method

for generating true color composites of good quality under a

broad range of data characteristics. The effectiveness of the

IHS transform has indicated a virtually universal adaptability

to any geographic datasets. As compared to the direct RGB

color display system, the IHS transform is superior because it

can overcome the incompatibility of spectral information

content of satellite multispectral images. This makes the IHS

transform more likely to produce well balanced color

composites that are more suitable for image interpretation.

However, the effectiveness of the IHS transform has misled

many to believe that it is a powerful image processing

technique that can actually sharpen the image data.

Unfortunately, it is not. The process is only for the display

of colors for human aesthetic pleasure. The merged images by

the IHS transform are not useful for multispectral analyses

because of the inferior radiometric quality and corrupted

spectral integrity.

2. Many combining methods have been developed that vary

significantly in the basic principle as well as in the

complexity of merging algorithms. These methods can be








42

categorized as: (1) linear combination of images, (2)

principal component analysis, (3) regression technique which

is similar to linear combination, and (4) multiplication or

product (including square-root of product). Though arbitrary

and largely dependent on speculation, these methods provide

knowledge about merging multiresolution images. The studies

by Schowengerdt (1980), Cliche et al. (1985), Price (1987),

Carper et al. (1990), and Chavez et al. (1991) suggest that

combining multiresolution images by linear combination of

images would have a greater potential for multiresolution

processing. The multiplication and principal component

analysis methods are perceived as ineffective.

3. The lack of understanding of the principle of

multiresolution processing is ubiquitous, resulting in wide

speculation for merging algorithms. The fundamental problem

is that the effects of combining multiresolution images on the

radiometric, spatial, and spectral qualities of a merged

dataset were not well understood when a merging algorithm was

introduced. Frequently, efforts resulted in radiometrically

inferior and spectrally corrupted merged datasets. A good

merger should take full advantage of the spatial and spectral

benefits of the multiresolution images to create a merged

dataset.

4. The main attention of research efforts was given to

image color display rather than to the radiometric and spatial

enhancement and, the spectral integrity of merged datasets.








43

In remote sensing applications, achieving the best color

display is necessary and often very useful for many

applications, but it is not the ultimate nor the only goal of

combining multiresolution datasets. Instead, the merged

images should be sharpened radiometrically while the spectral

integrity is preserved to enhance the utility of merged

datasets.

5. Visual assessment, which is necessary for evaluating

the quality of color composites, is adopted in most cases as

the only technique for determining the qualities of merged

datasets. However, the subjectivity and great variability of

the technique make many of the efforts inconclusive.

6. One other problem not discussed in the literature is

the accuracy of image co-registration. In order to merge

multiresolution images correctly, an accurate co-registration

is required, particularly for high spatial resolution datasets

as well as for images which are not taken simultaneously. For

instance, if two images are not co-registered accurately, a

pixel of one land-use type will be merged with a different

land-use type and the merged pixel belongs to neither of the

original land-use elements. This makes the merged dataset

very difficult or even impossible to interpret and analyze.

Therefore, both the precision of intermediate references (e.g.

maps) and the methods of entering (or digitizing) reference

coordinates must also be addressed (ASPRS, 1990; Bolstad et

al, 1990; and Tan and Shih 1991b). For the current map







44

standard, which is 0.5 mm (1/47 inch) times the reciprocal of

map scale (APSRS, 1990; Bolstad et al., 1991), the

geographical error for the USGS 7.5 minute series maps

(1:24,000) is about 13 m and the digitizing process could

introduce additional errors of significant magnitude (Tan and

Shih, 1991b). Therefore, it will be necessary to utilize

high-precision techniques such as the global positioning

system (GPS) to bypass the intermediate reference (map) as

well as manual digitizing operations in order to achieve a

high accuracy registration or to use datasets acquired by a

satellite sensor equipped with onboard co-registration

capability.

7. To merge multi-date images creates another problem in

evaluating the techniques of multiresolution processing.

Because of the dynamic change of scene environments, it is

difficult to analyze the merged data due to the intermingling

of image spectral information with the temporal effects. This

is particularly important for agricultural lands, as well as

natural environments, because they can change rapidly within

a short period of time. When multi-date scenes are combined,

the merged dataset will naturally contain more information

than any of the original ones. Therefore, it will be

difficult to objectively assess the possible improvement as

well as to evaluate the processing techniques. While the

temporal effects could be used for improving land-use








45

classifications (Badhwar et al. 1982; Lo et al., 1986), it

does create difficulties in evaluating the technique.

Fortunately, future satellite sensor systems can provide

simultaneous multiresolution sensing capabilities as well as

onboard image co-registration techniques (Spotlight, 1991;

EOSAT, 1992a; 1992b). Therefore, the problems with multidate

merging and image co-registration will no longer be a concern

to the user community of future satellite remote sensing data.





CHAPTER 4
PRINCIPLE OF MERGING IMAGES


This chapter is focused on the principle of merging

satellite remote sensing images. After the fundamental

principle is presented and discussed, three merging methods

are examined. However, the demonstrations and discussions of

the effectiveness of the merging methods are provided in

chapter 5 using actual satellite images.


Principle of Merging Images


Merging multiresolution images requires the use of

arithmetical manipulations to digitally combine the image

data. An effective merging approach will take full advantage

of the spectral, spatial, and radiometric merits of the images

to be combined to generate merged image data with enhanced

qualities. To develop successful merging methods for remote

sensing applications of multiresolution image datasets, an

adequate understanding of the fundamental principle for

digital manipulations of image data is essential. Therefore,

to assist such efforts in exploring this principle, it is

advantageous to conceptualize remote sensing image data so

that the factors affecting the spatial, radiometric, and

spectral qualities of merged images can be identified,

evaluated, and assessed.










Assumptions


A digital image can be considered as a set of repetitive

digital numbers that are constrained to a spatial arrangement

which is determined by the relations of objects present in the

scene. In virtually all image processing efforts, this

spatial arrangement is not important because it serves only to

reveal where an object or activity is identified rather than

to indicate how and why the decision is made in the process.

Therefore, a digital image is similar to a random variable.

The numerical values of a remote sensing image, which are

often called digital counts (DC), have a distribution depicted

by the image histogram.

The radiometric variance of an image is an important

indicator of the image radiometric quality, and like a random

variable, it can be assessed by the variance of image data.

For a given scene environment, a larger radiometric variance

indicates that scene activities are recorded in more detail.

Throughout this dissertation, the term "radiometric variance"

will exclusively refer to those image data that have not been

subjected to procedures such as spatial filtering and

contrast-stretching discussed in chapter 3.

The assumption that an image is similar to a random

variable will allow the statistical variation analyses of

random variable manipulations to be applicable to image data.

From previous research efforts by Cliche et al. (1985); Price

(1987); and Carper et al. (1990), the method of linear








48
combination of images was considered to have the greatest

potential for multiresolution processing. Therefore,

attention will be given to these combining methods, which will

include summation and differencing of image data. To better

understand the benefits as well as to assess the drawbacks

from manipulating remote sensing images, the arithmetical

functions of summation and differencing of random variables

for statistical variation analyses will be briefly reviewed.

Such a review is necessary in order to understand the existing

merging techniques as well as to develop new merging methods

so that remote sensing images can be manipulated more

productively. For the purpose of clarity, continuing

discussions will be limited to the circumstance of merging two

random variables or images, though three or more variables can

be manipulated at one time. Also, images with the same

spatial resolution will be examined first before proceeding to

the discussion of multiresolution merging.


Arithmetic of Random Variables


It is necessary to examine the arithmetical functions of

random variables to effectively investigate the various forms

of digital manipulations of image data and to assess the

results of such manipulations. According to Mood et al.

(1974) and Mendenhall et al. (1986), combining (both summing

up and differencing) two random variables X, and X2 with means

I, and U2 and variances a12 and a22, respectively, will create







49

a merged variable (Y) which is expressed in a general form of

Y = a X1 B X2. [4-1]

This new variable Y will have a mean value (AY)


y = a A B 42 [4-2]

and a variance (a 2)

oy = a22 +2 B2 2 a B cov(X1, X2) [4-3]

where a (>0) and B (>0) are numerical constants and cov(X1, X2)

is the covariance between X1 and X2. In digitally combining

images, Y is the merged image, X, and X2 represent images one

and two to be combined, and the corresponding constants a and

B are often called weighting factors or merging coefficients.

The covariance cov(X1, X2) term in equation [4-3] can be

written as (Mendenhall et al., 1986)


cov(X,, X2) = r aC a2 [4-4]

where al and 02 are the standard deviations and r is the

correlation coefficient for X1 and X2. The value of r can be

negative or positive depending on the actual relationship

between variables X, and X2. Substituting the covariance of

equation [4-4] into equation [4-3] will yield

a =a2 a12 + B2 a22 2 a B r 01 a2 [4-5]


which is the equation for calculating/estimating the variance

of a merged variable based on the merging coefficients, the








50

variances (or standard deviations), and the correlation

coefficient for X1 and X2.

For a merged image, the quality factor of greatest

concern is the contrast (or gray shades), and the contrast of

an image is directly related to the variance of image

radiometric data. For instance, an image will have no

contrast if its radiometric variance is zero. Therefore,

attention in the continuing discussion will be given to the

variance (a2) of merged variable Y. From equation [4-5], the

factors that collectively affect the radiometric variance or

contrast of a merged image are the weighting coefficients a

and B, the correlation coefficient (r), and the variances (a12

and o22) of the two images to be combined.

To assist the efforts in examining the effects of these

various factors on the variance (ay2) of merged variable Y, it

would be advantageous to reduce the number of the involved

elements in equation [4-5]. One method to achieve that is to

normalize the variances of X, and X2 to unity (1.0) using the

following equation


f 2 + 222 = 1 [4-6]

where a,2 and .22 are the normalized variances for X, and X,

respectively. If the condition a12+ 220 is satisfied, a2 and

922 are defined, respectively, as


a2
12 [4-7]
a12+ 22










and

2
2 2 = [4-8]
a 2+a 2


For easy comparisons, let a 2 also be normalized to (o02+o 2) by

the following equation


02
2= a [ 4-9]
-Y 02 2


where o2 is the normalized variance of Y. Note that the

normalized values are a relative measure for the variances of

X,, X2, and Y. Dividing equation [4-5] by (012+022) and making

rearrangements through the use of equations [4-6], [4-7], [4-

8], and [4-9] will yield


2 = a2 a12 + 2 (1-a 2)

2 a B r 1a j(1-_al) [4-10a]


Because the variances of X1 and X2 are normalized to unity,

equation [4-10a] can also be written as


l2Z = a2 (1-_,2) + B2 a22

2 a B r o2 J(l-az) [4-10b]


where


= J('-7) [4-11a]


2z = J(-- ) [).


[4-11b]







52

Three benefits result from normalizing the variances of X1 and

X2. These benefits are (1) reduction of the number of the

involved factors in equation [4-5]; (2) relief from getting

involved with actual image data for conceptual discussions;

and (3) easy comparison of the variance of the merged variable

with those of the original variables. It becomes clear that

equation [4-10a] (or [4-10b]) is the basic relation that

reflects the effects of the various factors (a, B, r, and a)

on the radiometric variance or contrast (a2) of a merged

image.

A comparison of the relations between equations [4-1] and

both [4-10a] and [4-10b] reveals that the only distinction

between summation and differencing of two variables is the

sign for the last terms in equations [4-10a] and [4-10b].

Therefore, in the context of evaluating the variance of the

merged variable, differencing two negatively correlated

variables (r<0) is technically identical to summing up two

positively correlated ones (r>0). Because merged image data

must be positive, differencing two images may require the

addition of a positive constant (C) to the end of equation [4-

1] such that


Y = a X, B X2 + C [4-12]


in order to avoid negative image data. However, from the

relations of equation [4-10], the constant C in equation [4-

12], which is usually determined by a pre-merging scanning of







53

the given image data, will not affect the radiometric variance

of the difference image.

In practical applications where two images are given, the

radiometric variances (a 2 and a22) and the correlation

coefficient (r) are known. The only factors that need to be

determined for equation [4-1] are the merging coefficients a

and B. From the relations of equation [4-10] and based on the

given factors a12, a22, and r, the selection of appropriate

merging coefficients a and B for equation [4-1] is the key

factor that affects the radiometric variance of merged image

data. To assess the impacts of these merging coefficients (a

and B) on the radiometric variance of merged images, three

approaches for digitally combining images will be discussed.

In addition, of the two images (X1 and X2) to be combined, X1

will be denoted as the primary image and X2 as the secondary

image in order to distinguish their relative importance in the

merging process. When actual image data are used, the primary

image (X1) will be assumed to contain primary information

while the secondary image (X2) is used as the supplementary

data for improving the primary image.


Confining Method


The first method to be discussed is the confining method

which is defined mathematically as


[4-13]


Yc = a X1 + B X2








54

where YC is the merged image by the confining method, X, and

X2 are, respectively, the primary and secondary images, and a

and B are weighting coefficients. An unique aspect in

combining images is to keep the merged image data within the

0-255 dynamic range (or 8-bit data depth). One approach to

accomplish that requirement is to choose the weighting

coefficients a and B in equation [4-13] such that


a + B = 1 [4-14a]


which can be written alternatively in the following forms of


a = 1 B [4-14b]


and


B = 1 a. [4-14c]


Because the merged image data is automatically confined to the

0-255 dynamic range, this merging method is called the

confining approach.

Let o 2 and o22 denote the normalized radiometric

variances for the primary (X1) and secondary (X2) images,

respectively. Because the general purpose to combine images

is to use the complementary secondary image data for improving

the primary image, the weighting coefficient B for the

secondary image will be of greater interest. For this reason,

the relation of equation [4-14b] is preferred and by

substituting it into equation [4-13], the following relation









is obtained as


YC = (1-B) X, + B X2. [4-15]

In comparing equation [4-15] with the relations between
equations [4-1] and [4-10a] (or [4-10b]), the normalized

variance (a2) of merged image Yc can be estimated by the

following equation

2 = (1-B)2 a12 + B2(1-, 2)
+ 2r(l-B)B a, J(1--0). [4-16a]

Since the variances of X1 and X2 are normalized to unity,

equation [4-16a] can also be written as


gZ = (1-B)2(1-022) + B2 22
+ 2r(1-B)B 02 J/(1-2) [4-16b]

The following relations for the normalization of variances are

also needed in order to use equation [4-16a] or [4-16b]


ai2 + 22 = 1 [4-17]


S1, = T(9) [4-18]


_z = (Z2'). [4-19]

From equations [4-16a] and [4-16b], the radiometric variance

(af2) of an image merged by the confining method is influenced
only by the secondary image coefficient 8. The value B will








56

have a direct impact on _2 -- a measure of the radiometric

quality of a merged image by the confining method. In

combining multiresolution images, selecting an appropriate B

value is particularly important because it not only affects

the radiometric variance, but also indirectly impacts the

spectral information of the entire merged dataset. For

instance, if a large B is used to merge a panchromatic image

to each image in a multi-waveband dataset, all the images in

the resultant merged dataset will be very similar to each

other.

Assuming that the variances of the primary (X,) and

secondary (X2) images are equal or close to each other, the

relation of g2 as a function of weighting factor B is depicted

in Figure 4-1 for the confining method. Although the graphs

in Figure 4-1 can tilt somewhat from one side to the other in

response to the variance difference between the primary and

secondary images, four important observations can be made for

the confining method.

First, the radiometric variance of a merged image by the

confining method is likely to be smaller than that of either

the primary and secondary image data. A smaller radiometric

variance implies that the merged image by the confining method

will have low contrast and inferior radiometric data.

Second, the state (positive or negative) as well as the

strength of correlation between the primary and secondary

image images also has a strong effect on the radiometric










57






I I I ,





OO *
oo


000




41







.4 O 4q.1
C1 m 44
-,-
o 40

+ H



.- 00

\0 0V-




4 O











S IV 0
,o p4o







-,,
o 0 4
\ <0 0
S* 2 go











0 |40









4) 0
0 -I00 I .- 0 0 r-4 0
I f l II I I I









S A o o r) 0c






-H
o E: U








58

variance of a merged image. If the primary image is

negatively correlated to the secondary image, the loss of

radiometric information in the merged image (Yc) will be even

more detrimental as shown in graphs (4) and (5) of Figure 4-1.

The negative correlation (r<0) creates a negating effect on

the variances of the primary image when the secondary image

data is digitally merged. Consequently, the resultant merged

image will have low or even no contrast depending on the

strength of the correlation as well as the use of B values

(Figure 4-1). As mentioned earlier, adding up negatively

correlated images is similar to subtracting positively

correlated ones or vice versa. If two negatively correlated

images are difference instead of summed together as done by

Chavez et al. (1983), the loss of radiometric information in

the merged image can be alleviated. In this circumstance, the

results of graphs (4) and (5) will be changed to those of

graphs (2) and (1) in Figure 4-1, respectively.

Third, a Bc exists at which the radiometric variance of

merged data will be at minimum. That is, the merged image

with Bc value will have least contrast. Therefore, the use of

such a B value must be avoided when using the confining

method. The value of BS can be obtained by first taking the

derivative of equation [4-16a] (or [4-16b]) with respect to B


d (c2)
-= -2(1-B)g,2 + 2B(1-a,2)
dB


+ 2r a1 .(1-a/ ) (1-2B)


[4-20]








59
and then setting the first derivative to equal to zero such as


0 = -2 (1-B)a,2 + 2Bc(1-Ol2)

+ 2ra1 J(1-g4) (1-2B) [4-21]

Through the use of equations [4-7], [4-8], [4-9], and [4-17],

the BS value can be estimated by the following equation


0a, ra, a2
c = [4-22]
C, + 02 -2 r 0, 02


where a,2 and a 2 are the variances (a, and o2 are the standard

deviations) of the primary and secondary images, respectively.

Note that the range of valid values for B is 0 to 1. If Bc is

outside the 0-1 range, the minimum radiometric variance of a

merged image will not exist within that range. Obtaining the

Bc value before merging the images will give a first

assessment on the variance of a merged image. For instance,

if BC 5 0, the radiometric variance of merged data is an

increasing function with B, implying that an improvement for

image contrast is possible. If Bc 1.0, the variance of

merged data will decreases as B increases. As a result, the

contrast of the merged image will deteriorate. By

substituting BS into equation [4-15a] (or [4-15b]) and by

using the relations of equations [4-7], [4-8], [4-9], and [4-

17], the minimum variance (o,2) for an image merged by the

confining method can be estimated as










ol2 a22 (1 r2)
S= [4-23]
o12 + 022 2 r 0 a2


Caution should be exercised in using equation [4-23] to

estimate the minimum radiometric variance of a merged image.

If BC is not within the 0-1 range, the estimated minimum

radiometric variance is a false value that cannot exist for a

merged image.

Fourth, as B continues to increase beyond the Bc value,

the variance of merged image YC is approaching that of the

secondary image data. This will make the merged image more

and more similar or even identical to the secondary image as

a result of large B values, which has been indicated by Carper

et al. (1990). In the case of merging a high resolution

panchromatic image to a set of multispectral images, all the

resultant merged images will be highly correlated among each

other because of the excessively redundant panchromatic data.

Consequently, the spectral integrity (or signatures) of the

merged dataset will be corrupted and the effectiveness of the

merged multispectral data for differentiating land-use

elements will be reduced.

The variance difference between the primary and secondary

images can also have an effect on the radiometric variance of

a merged image as shown in Figure 4-2. For instance, if the

primary image has a larger variance relative to that of the

secondary image, the merged image will have less contrast

regardless of the state of correlation. This is illustrated






































































r-i \ CO b-



p^Bp pabxemu


o 0

0O aOUPT2IA


*o
04










a)
44I








0




.r4
a
0
*4
ra

a,

4J

0
04.4
4)0
c




4 -I
CO






'U
c *

0 0
CO
4 )



eO
'.4


404
SW4


Eal *4


paZTu r-4lN

paT"euHi>








62

by graphs (1) and (3) of Figure 4-2. If the primary image has

a smaller variance, the radiometric information in the merged

image will either increase or decrease depending on the

magnitude of the variance difference as well as the state of

correlation between the two images as shown by graphs (2) and

(4) in Figure 4-2. Note that only when the primary image has

a very small variance relative to that of the secondary image

and the correlation between the two images to be combined is

high and positive, will an image merged by the confining

method have an enhanced contrast. This indicates that (1) the

confining method is not an effective merging approach for

digitally combining images and (2) the determination of a B

value for the confining method can not be arbitrary nor

independent of the factors such as the variance difference and

the correlation between the two combining images.

The way by which the merging coefficients are determined

(a+B=l) for the confining method has one important implication

of the compromising effect on the quality of the primary and

secondary images. The use of a larger B value to emphasize

the effect of the secondary image is made at the concession of

the primary image variance because of a smaller a value. As

shown in Figure 4-2, this concession of the primary image data

can be beneficial or detrimental. If the secondary image has

a relatively larger variance, this compromising effect is

beneficial to improve the primary image as shown by graphs (2)

and (4) in Figure 4-2. On the other hand, the effect will be








63

deleterious to the radiometric quality of a merged image as

illustrated by graphs (1) and (3) in Figure 4-2.

In summary for the confining approach (a+B=l), the

following observations are as follows. (1) The resultant

merged image will likely have a smaller radiometric variance

or lower contrast unless the primary image has a very small

variance relative to that of the secondary image and the

correlation between the two combining images is high and

positive. (2) There may exist a Bc value at which the

radiometric variance or contrast of the merged image will be

minimum, therefore, the selection of B values close or equal

to Bc should be avoided. (3) Two images with a negative

correlation should be difference rather than summed in order

to minimize the loss of radiometric information. (4) In

general, the contrast (or variance) and brightness of an image

merged by the confining method can be considered as a

compromise for each of these two quality factors between the

primary and secondary images.


Preserving Method


For most satellite imagery, the spread of image digital

data does not extend throughout the entire 0-255 dynamic

range. For a typical agricultural scene, the data spread is

about 40% of the 0-255 range in Landsat imagery (Price, 1984)

while a much smaller range is often found for SPOT images.

Therefore, the utility of the 8-bit data depth for these







64

images has not been fully utilized. In merging satellite

images, such a deficiency can be turned into an advantage by

maintaining the primary image unchanged (a=l) while the

secondary image data is merged. Hence, this method is called

the preserving approach.

By using the preserving approach to combine images, the

following merging algorithm is used


Yp = X, + B X2 [4-24]

where B is weighting coefficient, Yp is the merged image, and

X, and X2 have been defined previously. Let g12 and g2 denote

the normalized variances for the primary and secondary images,

respectively. A comparison of the relations between equations

[4-1] and [4-10a] (or [4-10b]) indicates that the normalized

variance ( 2) of an image merged by the preserving method can

be estimated by

S= 2 2+ B2(1-a_2) + 2rB a,1 J(1-Iz). [4-25a]


Since the variances of the primary (X,) and secondary (X2)

images are normalized to unity, equation [4-25a] can also be

written as

fp2 = (1-22) + 2 22 + 2rB a2 J/(1-2 ) [4-25b]


In both equations [4-25a] and [4-25b], B is the weighting

coefficient and r is the correlation coefficient for the

primary (X1) and secondary (X2) images. Note that the variance








65

of merged image Yp is normalized to o +o22. Also, the

relations of equations [4-17], [4-18], and [4-19] are needed

when using equation [4-25a] (or [4-25b]) for assessing the

radiometric variance of a merged image. As mentioned earlier,

the only distinction between summation and differencing of two

images is the sign for the last term of equation [4-25a] (or

[4-25b]). Thus, differencing two negatively correlated images

(r<0) is identical to summing up two positively correlated

ones (r>0).

Figure 4-3 shows the normalized variance g2 of merged

images by the preserving method as a function of both the

merging coefficient (B) and the correlation coefficient (r).

When the primary and secondary images are not negatively

correlated, the variance of an image merged by the preserving

method is an increasing function with merging coefficient B as

shown in graphs (1) through (3) of Figure 4-3. This implies

that the radiometric variance (contrast) of an image merged by

the preserving method will surely improve, provided that the

correlation coefficient is r20. Unlike the confining method,

which tends to make a compromise between the secondary and

secondary images, the preserving method does not subdue

(because a=l) the radiometric variance of the primary image

during the merging process. Consequently, the merged data are

always enhanced even when the images to be combined are not

correlated (r=0) as shown in graph (3) of Figure 4-3.

The results from combining two negatively correlated

images are also shown by graphs (4) and (5) of Figure 4-3.










66









0
O D4



\\ 0\ i^

S\I OB 0,-



o



,0.)
C; 00









up p Bop
S- *Ob'




OO.


S0 4
t 4a
go k






\ \ 4 .
\\ 0 001







\; o I I r.o 4





\qI 00
w-4O-r 0 0



(0 $4
00 ko v N r 00 % I 1 C a








T~C~m~r) rl

N 03 O (V rl 0 \O (O
*^
I-I ( rlr( O O O








67

Apparently, any improvement on the radiometric variance of

merged image Yp is unlikely, particularly when the correlation

coefficient rz-l. However, such negatively correlated images

can be difference. This will reverse the results to those of

summing up two positively correlated images as depicted by

graphs (1) and (2) of Figure 4-3. This differencing approach

will alleviate or even avoid the loss of image contrast in the

merged data.

The radiometric variance difference between the primary

and secondary images also has an effect on the radiometric

variance of a merged image (Figure 4-4). However, the effect

does not cause a negative impact on the radiometric variance

of merged data. The image contrast will always improve, and

the extent of improvement is inversely related to the

magnitude of the variance of the primary image. When the

radiometric variance of the primary image is relatively small,

the improvement on the merged image is more notable as

illustrated by graphs (1) and (3) of Figure 4-4. If the

radiometric variance of the primary image is relatively large,

the radiometric improvement might not be so apparent,

particularly when the correlation between the two combining

images is near zero (rz0) as shown by graph (4) of Figure 4-4.

It needs to be pointed out that large values of B can not

used for the preserving approach. Otherwise, a scaling factor

must be introduced to equation [4-24] in order to keep the

merged image data within the 0-255 range. In this case, the









68





14


0




X


*4
o~



o
44' 0






Sas U
0
N0

0 O




o 4 C






I I I I I I I
C) U 0
0 0 VU


\N \1 \-o r H o 4.







0 \.4 \0 -
S-r4








4r
~ p~reuIJO 8U~TIA p~T~UiO-
5.








69

use of an additional scaling factor will make the preserving

method less effective or even similar to the confining method.

In summary, several observations are made for the

preserving approach: (1) if the correlation coefficient (r)

between the primary and secondary images is non-negative

(rO), the image contrast in the merged data will surely be

enhanced by the preserving method; (2) as compared to that of

the confining method (a+B=l), the effect of the variance

difference between the two combining images will not create a

negative impact on the radiometric variance of a merged image

by the preserving method, provided that the correlation is

non-negative (r > 0); (3) the preserving method, which does

not subdue (a=l) the primary image in the digital merging

process, will make it less likely that the spectral signatures

of the original multispectral dataset will be altered or

corrupted in a merged dataset; (4) two images with a strong

negative correlation (rz-l) should be difference instead of

summed together in order to avoid a potential loss of

radiometric information in the merged image; and (5) the

preserving method has both a much smaller sensitivity to the

strength of correlation and a larger range of B values to use

because a minimum variance does not exist provided that r0O.


Differencing Method


From previous discussions on both the confining and the

preserving methods, it is known that, in order to enhance the







70

radiometric variance of merged image data from negatively

correlated wavebands (r<0), the differencing method must be

used. To ensure that the merged data will be positive, a

constant must be added to the merged data. Therefore, the

following relation will be used as the merging equation for

two negatively correlated images


Yd = X, B X2 + C [4-26]

where B (>0) is a weighting coefficient, C (>0) is a constant

to avoid negative merged data, Yd is the merged differencee)

image, and X1 and X2 have been defined previously.

Let g,2 and a2 denote the normalized variances for the

primary and secondary images, respectively. By comparing

equation [4-26] with the relationship between equations [4-1]

and [4-10a] (or [4-10b]), the normalized radiometric variance

(9-2) of a merged image by equation [4-26] can be estimated by

d2 = (122) + B2 22 2rB ag j(1-2) [4-27a]

Since the variances of primary and secondary images are

normalized to unity, equation [4-27a] can also be written as

a2 = 2 + B2(1-a12) 2rB a1 /(1-1 ). [4-27b]

In both equations [4-27a] and [4-27b], r is the correlation

coefficient for the primary and secondary images and B is a

weighting coefficient. Note that the variance of the merged

image is normalized to the sum of the variances (a2+a 22) of








71

the primary and secondary images. Again, the relations of

normalization equations [4-17], [4-18], and [4-19] are needed

in order to use equation [4-27a] (or [4-27b]) for estimating

the radiometric variance of a pre-differenced image.

Because the last term in equation [4-27a] (or [4-27b]) is

negative and the correlation coefficient (r) is also negative,

the relation of equation [4-27a] (or [4-27b]) is identical to

that of equation [4-25a] (or [4-25b]) of the preserving method

discussed previously. Therefore, additional information for

the effects of B values, correlation coefficient, and variance

difference on the radiometric variance of merged data can be

found in the previous section for the preserving method with

reference to both Figures 4-3 and 4-4.

In order for an image merged by the differencing approach

to have an improved radiometric variance, it is essential that

the last two terms in equation [4-27a] (or [4-27b]) be 2 0.

That is

B2 a2 2rB a2O 2 0. [4-28]


Hence, if both B*0 and 2*20, a critical Bd value for the

differencing method can be obtained as


2 r a
Bd [4-29]
-2

According to the relations of equations [4-17] through [4-19],

equation [4-29] can be rewritten as (a,40)








72

Bd, 2 r al/a2 [4-30]

where a, and 02 are the standard deviations for the primary

(X,) and secondary (X2) images, respectively. If a B value is

greater than Bd, the variance of a merged image by the

differencing method will increase. Otherwise, the merged

differencee) image will have a decreased radiometric

variance.

It must be pointed out that the relative magnitudes of

the combining image data can have a serious impact on the

tonal appearance of the merged image. Assuming that the

primary image (X,) has relatively higher values (brighter)

than the secondary image (X2), a subtraction by B X2 in

equation [4-26] will be less likely to create negative values

in the merged data. Therefore, a small constant is needed for

equation [4-26]. This will maintain the tonal gradations of

the primary image, and as a result the bright areas in the

primary image remain bright while the dark areas remain dark

in the merged data. When the secondary image has relatively

larger values, the component of B X2 in equation 4-26] will not

be small in comparison to the primary image (X1) data. This

will likely create negative values of large magnitude in the

merged data, requiring the use of a large constant in equation

[4-26] to offset these negative values. Consequently, the

areas with low values (e.g. water bodies) will have relatively

large image values in the merged data because of the use of a

large constant in equation [4-26]. This could make these dark








73

areas appear bright in the merged image (Yd), suggesting that

the tonal gradations of the original primary image have been

altered. Thus, it must be cautioned that the differencing

method may invert the merged image.


Summary: Principle of Merging Images


The principle of merging images has been discussed under

the assumption that an image is similar to a random variable

with regard to digital manipulations for statistical variation

analyses. Three fundamental approaches, which include the

confining, the preserving, and the differencing methods, have

been put forth for digitally merging image data.

Understanding these methods for digitally merging images

is essential for manipulating remote sensing data. Such an

understanding will render useful guidelines for evaluating the

existing methods as well as for developing new effective

approaches in future image processing efforts for remote

sensing applications.

When two images are digitally combined, the radiometric

improvements on the merged image will depend on three factors

which include (1) the selection of a merging method or merging

algorithm; (2) the correlation (r) between the two combining

images; and (3) the variance difference (al and az) between the

primary and secondary images. The confining approach should

be avoided because of its ineffectiveness for radiometric

enhancement. Unfortunately, this merging approach is the most








74

widely used method (Cliche et al., 1985; Carper et al., 1990).

The preserving method is recommended for merging positively

correlated images while the differencing approach is for those

with a strong negative correlation. In addition, the image

with a brighter appearance should be chosen as the primary

image (X,) for the differencing method in order to avoid a

potential of altering the tonal appearance in the merged

differencee) image.

A summary for the effectiveness of the three merging

approaches is provided in Table 4-1 for an easy comparison.

Actual satellite images will be utilized in chapter 5 to

demonstrate the results discussed throughout this chapter.










Table 4-1. Summary of the characteristics of different
merging approaches.


Radiometric improvement on merged image

When Confining Preserving Differencing

i : r>0 and

ao >> a2 No Yes No
01 a2 No Yes No
1 << a2 Yes(if r1l) Yes No

ii: r<0 and

a >> a2 No No Yes
a, z ag No No Yes
a1 << a2 No No Yes


Note: r
al
02


correlation coefficient.
standard deviation of primary image.
standard deviation of secondary image.












CHAPTER 5
DEMONSTRATION OF MERGING METHODS


The main objective in this chapter was to verify and

demonstrate the results of the three merging methods discussed

in chapter 4. To begin the process, the radiometric variance

and mean brightness of merged images by the three methods were

examined using the results from an actual satellite dataset.

The visual appearance in both image contrast and brightness

for the merged images were also evaluated.


Satellite Image Data


A satellite scene by the advanced very high resolution

radiometer (AVHRR) on a National Oceanographic and Atmospheric

Administration (NOAA) series satellite was acquired for this

demonstration. The satellite scene had five images recorded

at the 14:05h U.S. eastern standard time on December 14, 1989

by the AVHRR sensor onboard the NOAA-11 satellite. The NOAA

satellite scene consisted of two reflective (red and near-

infrared or NIR) and three thermal infrared (TIR) spectral

wavebands with wavelength characteristics shown in Table 5-1

(Kidwell, 1991). The scene had a local area coverage (LAC) of

the entire south-eastern region of the United States and all

the images of the five spectral wavebands have the same

spatial resolution of about 1,000 m (Kidwell, 1991).








77

Table 5-1. Wavelength characteristics of NOAA-11 AVHRR LAC
images.


Spatial
Waveband# Wavelength range (pm) resolution


1a 0.58 0.68 (red) 1000 m

2a 0.725 1.10 (NIRb) 1000 m

3 3.55 3.93 (TIRC) 1000 m

4 10.30 11.30 (TIRc) 1000 m

5 11.50 12.50 (TIRC) 1000 m

Source: Kidwell, 1991.


a used in this study.
b near infrared.
c -- thermal infrared.








78

The original NOAA-11 LAC scene contained image data in a

10-bit data-depth format where every three pixels were packed

to a 32-bit word (Kidwell, 1991). A program, which runs on a

PC computer environment, was developed (Appendix C) to unpack

as well as to rescale (linearly) these 10-bit data to a 8-bit

data format for compatibility with PC-based image processing

systems as well as display device. For this research, the LAC

scene was clipped to the region of the Florida peninsula

(Figure 5-1) and only the red and NIR images of the clipped

scene were used. The images of the TIR wavebands were

excluded to avoid confusions from merging thermal data. In

the discussions that follow, a NOAA-11 LAC image is simply

referred to the clipped data unless otherwise stated. The

main usage of this clipped LAC scene was for the verifications

of the three different merging methods discussed in chapter 4.

For ease of explanation, the red waveband was arbitrarily

named as LAC1 while the NIR waveband was denoted as LAC2. The

mean, standard deviation, normalized variance, maximum, and

minimum values of the LAC1 (red waveband) and LAC2 (NIR

waveband) images are presented in Table 5-2. The two selected

LAC images were positively correlated with a correlation

coefficient (r) of 0.577.

Because of the noted difference in the radiometric

variances between the two LAC images (Table 5-2), the use of

LAC1 and LAC2 for the primary and secondary images was

alternated for each of the three merging methods. In case I,



















































Figure 5-1. Location of clipped NOAA-11 AVHRR LAC images.








80

Tables 5-2. Standard deviation (a), normalized variance (g2),
mean (A), maximum and minimum values of NOAA-11
AVHRR LAC images.


Waveband A a a2 max min

LAC1 20.54 5.108 0.2286 138 14
(0.58-0.68 Am)

LAC2 26.35 9.383 0.7714 125 11
(0.725-1.10 Am)








81

LAC2 was used the primary image and LAC1 as the secondary

image, and in case II, LAC1 and LAC2 were used, respectively,

as the primary and secondary images. The purpose of this

alternative use for the LAC1 and LAC2 images was to assess the

effect of variance difference between the combining images on

the radiometric variance of merged data. In the differencing

method, the constants (C) used in equation [4-26] are provided

in Table 5-3 for both case I and case II. These constant

values, which were determined by a scanning of the original

image data, were used to avoid negative merged image data in

the difference LAC images for the corresponding B values.


Variance of Merged LAC Images


The normalized radiometric variances of merged LAC images

by the three methods are presented in Figures 5-2 (case I) and

5-3 (case II). In addition, the mean values (brightness) of

these merged LAC images are presented in Figures 5-4 and 5-5

for case I and case II, respectively. The points in these

four figures are the results computed from the actual merged

image data, while the lines represent the estimates obtained

through the equations in chapter 4. While the estimates of

radiometric variance were obtained through equations [4-15],

[4-25], and [4-27] along with the normalized variances (Table

5-2) and a correlation coefficient (r) of 0.577, the mean

digital count (Figures 5-4 and 5-5) were estimated using

equations [4-13], [4-24], and [4-26] for each corresponding










Table 5-3. Offset constant (C) used in the differencing
method for merging LAC images.


B value

Case 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


I 3 7 11 15 20 24

II 3 5 8 10 13










83






4)0
U


-H
4





o 4- 1 4


w TC Vi
o U o


Omo r. -A-
4 0









r. 4)H
4- 0 4 O











n -M I 0 1 )
>(C 4- 4 1 4






0. t u 0-
-,- 0 SH
-B $ a .
S0 *- 0 0 0 -' I
So o mo i0
\cQ ** C -0 c-r -
\ -H> IOU

tP V r ri $^4.

-. k CO) t c
0 0 o CO



00 0


0P C 0 00
*H E O tfl

Sty
I Cd M ,C1 *



0 0 0


* ** oa

-04
'-4 1-4 0 0 0 0 0 I
4 ) in
~n l U9
~C( IC
*<-
cr ( rl 3 1 ~sr CV









84




0







C;C



V--4 4V
,-I
r.*4









I I O, .
4)






4 00Q
O 0






0. to 0 0%
44 C )






o p .)4%.4 4t













0
\M 4-

O 0 01 4)
C%0 0 0*
U\ V O H
Q r. V 0 U4-'
L q O 0 *





0 n S.0
0 c
0- tp a


00 u C 0

S> I









HOv *H 00
\ \f UCM 3-W











S* I I *4




0 0-400 II*
rl r \ \ ** O O D


o n 60 0 P 0



*p N r a lo o t c

*o ~ e T~ **
^ ^ 0 0 0 0 ^
B^Bp e~l3IT J aOUT~eApaZT[BUI:ON <|
re










85











I*-

4 4 4

*0 .
o J *0

\o rro



4-,





*4 0 0
0 U H0


U) 1 I I w- I 4
\ I QC B


-C 4
O *M-l






\ C oq i to0k
00 0 -- *(



0 0I I
V -- I 00









-H
4 0 0 4)
0 7 0 A
ONQ *0 C -4 $4


ri C0 00
*) 04 O 4
0 U. 0 LO 0 C 0 0 0
al v I I 0 0 ,-
>r\ 0 41 In













quflD Tv4T TP GUx 'aI0
z



( i0 \ Id / O











fr7

















0
0

4

*- .


o U .4 -


0 0q



0- < 0 v .

Sg .4 ,
8 0

i ..I I iiI
\ U C ) e H
0(a 0




>C 1 )-,4
t0

o C .
ci >- O



r4 Ao t m *
0 *-l D* 4 a

0\ CQ II 0W

* \-o vu mm-

2-iL *T 9 !i1 In I
0 0 *4 00

Q*M \ O W r



- O \ 00 0


-o
La ,' \4 ri (*(i B O- .-


a) I
7unoo T 1T6fTP feiuxi 1 .
0 0

-9-








87

merging method. The letters P, C, and D in Figures 5-2

through 5-5 denote the preserving method, the confining

method, and the differencing method, respectively. From the

results shown in Figures 5-2 through 5-5 for all the three

methods and B values used, four observations are in order.

First, the principle of statistical variation analyses

for combining random variables can be applied in assessing the

radiometric quality (variance and brightness) of a pre-merged

image. This provides the basis for understanding the various

forms of digital manipulations of satellite image data and for

assessing the effectiveness of an image processing effort in

remote sensing applications. In practical applications when

two images are given, the values of correlation, radiometric

variance, and mean digital (brightness) for the images to be

merged are known. Therefore, the overall quality in both

radiometric variance (contrast) and brightness of a merged

image can be evaluated based on the merging method and

coefficient (B). This pre-merging evaluation will lead to

more efficient approaches because unproductive efforts can be

eliminated.

Second, an image contains many subvariables representing

the various land-use types distributed throughout the entire

scene. Note that the subvariables do not usually possess the

same correlation, radiometric variances, and mean data values

in the images of a multispectral dataset. When a merging

algorithm is used to digitally combine the entire images, the




Full Text

PAGE 1

08/7,5(62/87,21 352&(66,1* 2) 6$7(//,7( ,0$*(6 $1' *(2*5$3+,& ,1)250$7,21 6<67(06 7(&+1,48(6 )25 /$1'86( &/$66,),&$7,21 %\ <8521* 7$1 $ ',66(57$7,21 35(6(17(' 72 7+( *5$'8$7( 6&+22/ 2) 7+( 81,9(56,7< 2) )/25,'$ ,1 3$57,$/ )8/),//0(17 2) 7+( 5(48,5(0(176 )25 7+( '(*5(( 2) '2&725 2) 3+,/2623+< 81,9(56,7< 2) )/25,'$

PAGE 2

&RS\ULJKW E\
PAGE 3

$&.12:/('*(0(176 7KLV UHVHDUFK ZDV SHUIRUPHG XVLQJ WKH IDFLOLWLHV RI WKH 5HPRWH 6HQVLQJ $SSOLFDWLRQV /DERUDWRU\ 56$/f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

PAGE 4

/DVWO\ WKH DXWKRU DFNQRZOHGJHV WKDW WKLV UHVHDUFK ZRXOG QRW KDYH EHHQ FRPSOHWHG ZLWKRXW WKH FRQWLQXRXV VXSSRUW DQG HQFRXUDJHPHQW IURP KLV ORYLQJ SDUHQWV LY

PAGE 5

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

PAGE 6

6327 ,PDJH 'DWD DQG 6WXG\ $UHD $&,5 3KRWRJUDSK\ ,PDJH 3URFHVVLQJ 6\VWHPV 3KRWRJUDPPHWULF 6WHUHR 3ORWWHU 3URFHGXUHV IRU 0HUJLQJ 6327 'DWDVHW 3UHPHUJLQJ 3URFHVVLQJ *HQHUDWLQJ 0HUJHG 'DWDVHW (YDOXDWLRQ RI 0HUJHG 'DWD ,PDJH 5HVSRQVH DQG &LWUXV &DQRS\ &RYHU 3KRWRJUDPPHWULF 0HDVXUHPHQW &DQRS\ &RYHU (VWLPDWLRQ /DQGXVH &ODVVLILFDWLRQ 3UFLV DQG &RQFHSW ([WUDFWLQJ 6LJQDWXUH 3DWWHUQV *,6EDVH 'LVFUHWH &ODVVLILFDWLRQ ',6&866,216 $1' $1$/<6(6 2) 08/7,5(62/87,21 /$1'86( &/$66,),&$7,21 (YDOXDWLRQ RI 0HUJHG ,PDJH 5DGLRPHWULF 4XDOLW\ 6SDWLDO ,PSURYHPHQW DQG 6SHFWUDO ,QWHJULW\ ,PDJH 5HVSRQVH DQG &LWUXV &DQRS\ &RYHU (VWLPDWLRQ RI &LWUXV &DQRS\ &RYHU 5HODWLRQ RI ,PDJH UHVSRQVH WR &DQRS\ &RYHU 'LIIHUHQWLDWLRQ RI &DQRS\ &RYHU (IIHFW RI 0XOWLUHVROXWLRQ 0HUJLQJ /DQGXVH &ODVVLILFDWLRQ 3RWHQWLDO IRU 6LJQDWXUH ([WUDFWLRQ *,6 'LVFUHWH &ODVVLILFDWLRQ &21&/86,216 $1' 5(&200(1'$7,216 5HVHDUFK &RQFOXVLRQV 5HFRPPHQGDWLRQV $33(1',&(6 $ 5*% &2/25 ',63/$< % ,+6 75$16)250 )25 ,0$*( ',63/$< & 352*5$0 &2'(6 72 813$&. $9+55 /$& '$7$ &/$66,),&$7,21 '(&,6,21 58/(6 5()(5(1&(6 */266$5< %,2*5$3+,&$/ 6.(7&+ YL

PAGE 7

/,67 2) 7$%/(6 7DEOH )DFLD $YDLODEOH VRXUFHV RI /DQGVDW DQG 6327 UHVRXUFH VDWHOOLWH GDWD DQG V\VWHP FKDUDFWHULVWLFV 6XPPDU\ RI WKH FKDUDFWHULVWLFV RI GLIIHUHQW PHUJLQJ DSSURDFKHV :DYHOHQJWK FKDUDFWHULVWLFV RI 12$$ $9+55 /$& LPDJHV VWDQGDUG GHYLDWLRQ Df QRUPDOL]HG YDULDQFH Df PHDQ f PD[LPXP DQG PLQLPXP YDOXHV RI 12$$ $9+55 /$& LPDJHV 2IIVHW FRQVWDQW &f XVHG LQ WKH GLIIHUHQFLQJ PHWKRG IRU PHUJLQJ /$& LPDJHV 6WDQGDUG GHYLDWLRQ Df PHDQ Qf DQG PD[LPXP DQG PLQLPXP YDOXHV DQG FRUUHODWLRQ FRHIILFLHQWV Uf RI 6327 PXOWLUHVROXWLRQ GDWDVHW 0XOWLUHVROXWLRQ GDWDVHWV DQG FRUUHVSRQGLQJ PHUJLQJ HTXDWLRQV 3DUDPHWHUV XVHG LQ (5'$6 67$7&/ DQG (/$6 7075 PRGXOHV IRU VLJQDWXUH H[WUDFWLRQ 6WDQGDUG GHYLDWLRQ Df DQG PHDQ EULJKWQHVV YDOXHV Lf IRU PXOWLUHVROXWLRQ PHUJHG 6327 LPDJHV 6XPPDU\ IRU FRUUHODWLRQV EHWZHHQ D PHUJHG LPDJH DQG LWV RULJLQDO PXOWLVSHFWUDO FRXQWHUSDUW %HWZHHQZDYHEDQG FRUUHODWLRQV Uf ZLWKLQ PXOWLUHVROXWLRQ PHUJHG GDWDVHWV 6XPPDU\ IRU FRUHODWLRQV EHWZHHQ FLWUXV FDQRS\ VL]H DQG LPDJH UHVSRQVH IRU PXOWLUHVROXWLRQ PHUJHG LPDJHV 9DULDWLRQ RI LPDJH GDWD FRUUHODWLRQ Uf EHWZHHQ SDQFKURPDWLF DQG RULJLQDO PXOWLVSHFWUDO ZDYHEDQGV DPRQJ VHOHFWHG JURYHV YLL

PAGE 8

6WDQGDUG GHYLDWLRQV Df RI PHUJHG LPDJH GDWD IRU VHOHFWHG FLWUXV JURYHV 6XPPDU\ RI VSHFWUDO VLJQDWXUHV XQYHLOHG E\ (5'$6 67$7&/ PRGXOH 6XPPDU\ RI VSHFWUDO VLJQDWXUHV XQYHLOHG E\ (/$6 7075 PRGXOH &DQRS\ FRYHU IRU VSHFWUDO FODVVHV E\ *,6 EDVHG GLVFUHWH FODVVLILFDWLRQ WHFKQLTXH YLLL

PAGE 9

/,67 2) ),*85(6 )LJXUH )DJV 6FKHPDWLFV RI PHUJLQJ PXOWLUHVROXWLRQ VDWHOOLWH LPDJHV 6FKHPDWLFV RI SULQFLSDO FRPSRQHQW DQDO\VLV IRU PXOWLVSHFWUDO GDWDVHWV 5HODWLRQ RI UDGLRPHWULF YDULDQFH WR PHUJLQJ FRHIILFLHQW ILf DQG FRUUHODWLRQ FRHIILFLHQW Uf IRU WKH FRQILQLQJ PHWKRG (IIHFW RI YDULDQFH GLIIHUHQFH RQ WKH UDGLRPHWULF TXDOLW\ RI PHUJHG LPDJHV IRU WKH FRQILQLQJ PHWKRG 5HODWLRQ RI UDGLRPHWULF YDULDQFH WR PHUJLQJ FRHIILFLHQW %f DQG FRUUHODWLRQ FRHIILFLHQW Uf IRU WKH SUHVHUYLQJ PHWKRG (IIHFW RI YDULDQFH GLIIHUHQFH RQ WKH UDGLRPHWULF TXDOLW\ RI PHUJHG LPDJHV IRU WKH SUHVHUYLQJ PHWKRG /RFDWLRQ RI FOLSSHG 12$$ $9+55 /$& LPDJHV &RPSDULVRQ EHWZHHQ DFWXDO DQG HVWLPDWHG UDGLRPHWULF YDULDQFH IRU PHUJHG /$& LPDJHV FDVH ,f &RPSDULVRQ EHWZHHQ DFWXDO DQG HVWLPDWHG UDGLRPHWULF YDULDQFH IRU PHUJHG /$& LPDJHV FDVH ,,f &RPSDULVRQ EHWZHHQ DFWXDO DQG HVWLPDWHG PHDQ GLJLWDO FRXQW IRU PHUJHG /$& LPDJHV FDVH ,f &RPSDULVRQ EHWZHHQ DFWXDO DQG HVWLPDWHG PHDQ GLJLWDO FRXQW IRU PHUJHG /$& LPDJHV FDVH ,,f 2ULJLQDO FOLSSHG 12$$ /$& LPDJHV RI UHG DQG 1,5 ZDYHEDQGV 0HUJHG /$& LPDJHV E\ WKH SUHVHUYLQJ PHWKRG FDVH ,f ,;

PAGE 10

0HUJHG /$& LPDJHV E\ WKH SUHVHUYLQJ PHWKRG FDVH ,,f 0HUJHG /$& LPDJHV E\ WKH FRQILQLQJ PHWKRG FDVH ,f 0HUJHG /$& LPDJHV E\ WKH FRQILQLQJ PHWKRG FDVH ,,f 0HUJHG /$& LPDJHV E\ WKH GLIIHUHQFLQJ PHWKRG FDVH ,f 0HUJHG /$& LPDJHV E\ WKH GLIIHUHQFLQJ PHWKRG FDVH ,,f 6XPPDU\ PRVDLFf RI PHUJHG /$& LPDJHV IRU WKUHH PHWKRGV FDVH ,f 6XPPDU\ PRVDLFf RI PHUJHG /$& LPDJHV IRU WKUHH PHWKRGV FDVH ,,f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

PAGE 11

(IIHFW RI WUHH FURZQ YDULDWLRQV RQ 6327 UHG ZDYHEDQG UHVSRQVH YDULDELOLW\ IRU SDUWLDO FDQRS\ JURYHV (IIHFW RI WUHH FURZQ YDULDWLRQV RQ 6327 1,5 ZDYHEDQG UHVSRQVH YDULDELOLW\ IRU SDUWLDO FDQRS\ JURYHV 5HODWLRQ RI FLWUXV WUHH YDULDWLRQV WR FDQRS\ FRYHU GLIIHUHQFH [L

PAGE 12

$EVWUDFW RI 'LVVHUWDWLRQ 3UHVHQWHG WR WKH *UDGXDWH 6FKRRO RI WKH 8QLYHUVLW\ RI )ORULGD LQ 3DUWLDO )XOILOOPHQW RI WKH 5HTXLUHPHQWV IRU WKH 'HJUHH RI 'RFWRU RI 3KLORVRSK\ 08/7,5(62/87,21 352&(66,1* 2) 6$7(//,7( ,0$*(6 $1' *(2*5$3+,& ,1)250$7,21 6<67(06 7(&+1,48(6 )25 /$1'86( &/$66,),&$7,21 %\
PAGE 13

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

PAGE 14

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f SDUWLFXODUO\ IURP DJULFXOWXUDO DQG XUEDQ ODQGV 86(3$ 3LRQNH DQG 8UEDQ f ,Q PDQ\ FDVHV LW LV WKH FKDQJH RI ODQG XVH WKDW FUHDWHV LPPHQVH HQYLURQPHQWDO FRQFHUQV $JULFXOWXUDO ODQGXVH GDWD DUH QHHGHG WR IRUHFDVW DQG PRQLWRU SURGXFWLRQ DV ZHOO DV WR DVVHVV GDPDJH FDXVHG E\ GLVHDVHV DQG QDWXUDO FDWDVWURSKLF HYHQWV $OVR ODQGXVH GDWD DUH XVHG LQ PDQ\ RWKHU ZD\V LQFOXGLQJ IRUHVW PDQDJHPHQW &ROHPDQ HW DO f XUEDQ GHYHORSPHQW DQG SODQQLQJ &ROZHOO DQG 3RXOWRQ f K\GURORJLFDO LQYHVWLJDWLRQV DQG DSSOLFDWLRQV RI JHRJUDSKLF LQIRUPDWLRQ V\VWHPV (KOHUV 3LZRZDU HW DO 7DQ DQG 6KLK Df 7KHUHIRUH WKH DYDLODELOLW\ RI TXDOLW\ DQG WLPHO\ ODQGXVH LQIRUPDWLRQ EHFRPHV DQ LQGLVSHQVDEOH IDFWRU

PAGE 15

ZKLFK SUHVFULEHV RXU HIIRUWV LQ EHWWHU PDQDJLQJ QDWXUDO UHVRXUFHV 7UDGLWLRQDOO\ ODQGXVH GDWD DUH FROOHFWHG WKURXJK DHULDO SKRWRJUDSK\ JURXQG VXUYH\V DQG H[LVWLQJ PDSV :KLOH WKHVH PHWKRGV DUH UHOLDEOH DQG DFFXUDWH WKH\ DUH H[SHQVLYH DQG WLPHFRQVXPLQJ ,Q DGGLWLRQ WKH SURFHVV RI WUDGLWLRQDO PHWKRGV LV WHGLRXV DQG WKHUHIRUH RIWHQ SURYLGHV ODQGXVH GDWD WKDW DUH \HDUV RXW RI GDWH ZKLOH GDWD DYDLODELOLW\ EHFRPHV D OLPLWLQJ IDFWRU LQ VRPH FDVHV :KHQ D ODUJH FRYHUDJH DUHD LV QHHGHG WKH GLIILFXOWLHV LQYROYHG LQFUHDVH LQ PDJQLWXGH DV ZHOO DV LQ FRPSOH[LW\ )RUWXQDWHO\ WKH V\QRSWLF FRYHUDJH DQG SHULRGLF DYDLODELOLW\ RI VDWHOOLWH UHPRWH VHQVLQJ GDWD SURYLGH DQ H[FHOOHQW RSSRUWXQLW\ IRU WKH DFTXLVLWLRQ RI WLPHO\ ODQG XVH GDWD DQG WKH PRQLWRULQJ RI H[WHQVLYH ODQGXVH DFWLYLWLHV 7KLV VLJQLILFDQWO\ DPSOLILHV RXU DELOLW\ WR XQGHUVWDQG WKH HIIHFWV RI ODQG XVH W\SHV DQG WR PDQDJH WKH LPSDFWV DQG FRQVHTXHQFHV UHVXOWLQJ IURP WKH FKDQJH RI ODQG XVH DFWLYLWLHV :LWK LQFUHDVLQJ HQYLURQPHQWDO DZDUHQHVV PRUH FDUHIXO SODQQLQJ DQG PRQLWRULQJ RI ODQGXVH DFWLYLWLHV EHFRPHV DQ LPSRUWDQW FRQVLGHUDWLRQ LQ DOO OHYHOV RI UHVRXUFHV PDQDJHPHQW 7R GHULYH ODQGXVH LQIRUPDWLRQ IURP VDWHOOLWH GDWD D ODQGXVH FODVVLILFDWLRQ SURFHGXUH LV XVHG ZLWKLQ DQ DXWRPDWHG FRPSXWHU LPDJH SURFHVVLQJ V\VWHP 6XFK SURFHGXUHV JHQHUDWH VWDWLVWLFDOO\ VLPLODU VSHFWUDO FODVVHV ZKLFK DUH WKHQ UHODWHG WR GLIIHUHQW ODQGXVH W\SHV /LOOHVDQG DQG .LHIHU 7KRPDV HW DO f WKURXJK D JURXQGWUXWKLQJ SURFHVV 7R

PAGE 16

LPSURYH WKH DFTXLVLWLRQ RI ODQGXVH LQIRUPDWLRQ IURP VSDFH FRQWLQXRXV UHVHDUFK HIIRUWV DUH XQGHUZD\ LQ WKH GHYHORSPHQW RI ERWK QHZ VHQVLQJ V\VWHPV (QJHO 6SRWOLJKW (26$7 D Ef DQG LPDJH SURFHVVLQJ WHFKQLTXHV 6WDWHPHQW RI 5HVHDUFK 3UREOHP 2EWDLQLQJ ODQGXVH GDWD RU ODQGXVH LQIRUPDWLRQ E\ VDWHOOLWH UHPRWH VHQVLQJ UHTXLUHV D VLJQLILFDQW LPSURYHPHQW ERWK LQ DFFXUDF\ DQG LQ VSHFLILFLW\ LQ RUGHU WR EH XVHG RSHUDWLRQDOO\ LQ PDQ\ DSSOLFDWLRQV /R HW DO 'H*ORULD HW DO f )RU LQVWDQFH GD\WRGD\ RSHUDWLRQV LQ ZDWHU UHVRXUFHV PDQDJHPHQW VHOGRP XVH VDWHOOLWHEDVHG ODQGXVH GDWD PDLQO\ EHFDXVH RI WKH ODFN RI GHVLUHG VSHFLILFLW\ RU GHWDLOV 2QH IDFHW WR WKH VROXWLRQ RI WKLV SUREOHP LV WR LPSURYH WKH TXDOLW\ RI UDZ GDWD WKURXJK DGYDQFHG VHQVLQJ WHFKQRORJ\ DQG VHQVRU V\VWHP GHVLJQ 7KLV KDV EHHQ LQLWLDWHG E\ WKH GHYHORSPHQW RI QHZ VHQVLQJ V\VWHPV ZKLFK ZLOO EH RQERDUG /DQGVDW (26$7 D Ef DQG WKH )UHQFK 6\VWHPH 3UREDWRLUH GH n2EVHUYDWLRQ GH OD 7HUUH 6327f UHVRXUFHV VDWHOOLWH IRXU UHIHUUHG WR DV 6327 6SRWOLJKW f (TXDOO\ LPSRUWDQW LV WKH GHYHORSPHQW RI GDWD SURFHVVLQJ WHFKQLTXHV WR DQDO\]H DQG FODVVLI\ WKH UHPRWHO\ VHQVHG GDWD VR WKDW LPSURYHG ODQGXVH LQIRUPDWLRQ EHFRPHV IHDVLEOH LQ SUDFWLFDO DSSOLFDWLRQV &RPELQLQJ PXOWLVSHFWUDO VDWHOOLWH GDWD WKDW KDYH GLIIHUHQW VSDWLDO UHVROXWLRQV WR H[WUDFW PRUH VXEWOH ODQGXVH LQIRUPDWLRQ KDV EHFRPH DQ LPSRUWDQW FRPSRQHQW LQ LPDJH

PAGE 17

SURFHVVLQJ WHFKQLTXHV ,Q WKH SURFHVV WKH VSHFWUDO DQG VSDWLDO DGYDQWDJHV UHQGHUHG E\ GLIIHUHQW VHQVLQJ V\VWHPV 7DEOH f DUH FRPELQHG FRPSOHPHQWDULO\ LQWR D PHUJHG GDWDVHW 7KLV SURYLGHV DQ XQSDUDOOHOHG RSSRUWXQLW\ WKDW H[SDQGV RXU DELOLW\ EH\RQG XVLQJ DQ\ RI WKH RULJLQDO LQGLYLGXDO GDWDVHWV WR DFTXLUH ODQGXVH LQIRUPDWLRQ %HFDXVH RI WKH FKDOOHQJH RI IXWXUH VHQVRU V\VWHPV ZKLFK ZLOO SURYLGH PXOWLUHVROXWLRQ VHQVLQJ DV ZHOO DV RQERDUG UHJLVWUDWLRQ FDSDELOLWLHV 6SRWOLJKW (26$7 D Ef DQG WKH WUHPHQGRXV DPRXQW RI LPDJH GDWD DOUHDG\ FDSWXUHG E\ VDWHOOLWH VHQVRUV RSHUDWLQJ RYHU D ZLGH UDQJH RI VSDWLDO UHVROXWLRQV DQG VSHFWUDO ZDYHEDQGV 6KLK 0RRUH (KOHUV f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

PAGE 18

7DEOH $YDLODEH VRXUFHV RI /DQGVDW DQG 6327 UHVRXUFH VDWHOOLWH GDWD DQG V\VWHP FKDUDFWHULVWLFV 7\SH RI 6HQVRU 6SHFWUDO FKDUDFWHULVWLFV 6SDWLDO UHVROXWLRQ Pf %DQG :DYHOHQJWKQf &RORU /DLO&O6D/O FLQ4 /DQ46D/f 5%9D %OXHJUHHQ
PAGE 19

7DEOH FRQWLQXHG 7\SH RI 6HQVRU 066E +59I 6SHFWUDO FKDUDFWHULVWLFV 6SDWLDO UHVROXWLRQ Pf %DQG :DYHOHQJWKQf &RORU 1HDU LQIUDUHG ,QWHUPHGLDWH LQIUDUHG 7KHUPDO LQIUDUHG ,QWHUPHGLDWH LQIUDUHG *UHHQ 5HG 1HDU LQIUDUHG 1HDU LQIUDUHG /DQGVDW& DQG /DQGVDW 3DQFKURPDWLF %OXH *UHHQ 5HG 1HDU LQIUDUHG ,QWHUPHGLDWH LQIUDUHG 7KHUPDO LQIUDUHG ,QWHUPHGLDWH LQIUDUHG 6327HO 6327 DQG 6327 3DQFKURPDWLF *UHHQ 5HG 1HDU LQIUDUHG

PAGE 20

7DEOH f§ FRQWLQXHG 7\SH RI 6HQVRU 6SHFWUDO FKDUDFWHULVWLFV 6SDWLDO UHVROXWLRQ Pf %DQG :DYHOHQJWKQf &RORU ‘ RU8O f +59I 3DQFKURPDWLF *UHHQ 5HG 1HDU LQIUDUHG ,QWHUPHGLDWH LQIUDUHG 6RXUFH PRGLILHG IURP 6KLK 6SRWOLJKW DQG (26$7 D E D 5HWXUQ EHDP YLGLFRQ FDPHUD E 0XOWLVSHFWUDO VFDQQHU F 7R EH UHSODFHG E\ /DQGVDW EHFDXVH RI IDLOXUH WR UHDFK RUELW G 7KHPDWLF PDSSHU )UHQFKf 6\VWHPH 3UREDWRLUH GH n2EVHUYDWLRQ GH OD 7HUUH 6327f I +LJK UHVROXWLRQ YLVLEOH 1RWH 2SHUDWLRQ RI /DQGVDW /DQGVDW /DQGVDW /DQGVDW /DQGVDW /DQGVDW /DQGVDW 6327 6327 6327 6327 SUHVHQW SUHVHQW ODXQFKHG LQ EXW IDLOHG WR UHDFK RELW LGHQWLFDO WR /DQGVDW DQG WR EH ODXQFKHG LQ SUHVHQW "" SUHVHQW 7R EH ODXQFKHG LQ

PAGE 21

DQG HQKDQFHG VSDWLDO LQIRUPDWLRQ 7KHVH TXDOLW\ IDFWRUV RI LPDJH GDWD DUH YLWDO QRW RQO\ WR WKH XWLOLW\ RI WKH PHUJHG GDWDVHWV IRU SRWHQWLDO DSSOLFDWLRQV EXW DOVR WR DQ\ UHPRWH VHQVLQJ HIIRUWV WKDW DWWHPSW WR LPSURYH RXU FDSDELOLW\ LQ PRQLWRULQJ ODQGXVH UHVRXUFHV 7KHUHIRUH WKLV UHVHDUFK ZDV IRFXVHG RQ WKH WHFKQLTXHV IRU FRPELQLQJ PXOWLUHVROXWLRQ VDWHOOLWH LPDJHV DV ZHOO DV RQ WKH XWLOLW\ RI PXOWLUHVROXWLRQ SURFHVVLQJ IRU ODQGXVH FODVVLILFDWLRQ DQG LPDJH LQWHUSUHWDWLRQ &RQFHSW RI 0XOWLUHVROXWLRQ 3URFHVVLQJ 0XOWLUHVROXWLRQ SURFHVVLQJ LV DQ LPDJH SURFHVVLQJ WHFKQLTXH XVHG WR FRPELQH RU PHUJH PXOWLVSHFWUDO LPDJHV WKDW KDYH GLIIHUHQW VSDWLDO UHVROXWLRQV 2QH RI WKH LPDJHV WR EH FRPELQHG ZLOO KDYH D KLJK VSDWLDO UHVROXWLRQ RU D VPDOOHU VL]H RI SLFWXUH HOHPHQW SL[HOf DQG D SDQFKURPDWLF ZDYHEDQG ZKLOH WKH RWKHUV ZLOO EH PXOWLVSHFWUDO RU PXOWLZDYHEDQGf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

PAGE 22

0XOWLVSHFWUDO LPDJHV 0HUJHG PXOWLVSHFWUDO LPDJHV P ;066 L ;066E ;066LD [PVV )LJXUH 6FKHPDWLFV RI PHUJLQJ PXOWLUHVROXWLRQ VDWHOOLWH LPDJHV

PAGE 23

LPDJHV WR EH FRPELQHG 7KH VSDWLDO DQG VSHFWUDO YLUWXHV RI WKH RULJLQDO PXOWLUHVROXWLRQ LPDJH GDWD DUH XWLOL]HG FRPSOHPHQWDULO\ $V D UHVXOW WKH PHUJHG GDWDVHW EHFRPHV VSHFWUDOO\ DV ZHOO DV VSDWLDOO\ PRUH SRZHUIXO IRU UHPRWH VHQVLQJ DSSOLFDWLRQV 2QH H[DPSOH RI PXOWLUHVROXWLRQ SURFHVVLQJ LV WR PHUJH WKH 6327 KLJK UHVROXWLRQ YLVLEOH +59f SDQFKURPDWLF DQG PXOWLVSHFWUDO LPDJHV WKDW KDYH UHVSHFWLYH P DQG P VSDWLDO UHVROXWLRQV &OLFKH HW DO &DUSHU HW DO f 7KH SDQFKURPDWLF LPDJH ZLWK D P UHVROXWLRQ FDQ UHYHDO VXEWOH VSDWLDO GHWDLOV RI VFHQH REMHFWV EXW LWV XVDJH IRU PXOWLVSHFWUDO DQDO\VHV ODQGXVH FODVVLILFDWLRQf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n UHJLVWUDWLRQ RI WKH PXOWLUHVROXWLRQ LPDJHV 7KLV FDQ EH GRQH ZLWK WZR GLIIHUHQW DSSURDFKHV 7KH ILUVW RQH LV WR VLPSO\

PAGE 24

SURMHFW DOO LPDJHV WR D PXWXDO JHRJUDSKLF UHIHUHQFH V\VWHP ZKLFK FDQ EH HLWKHU WKH ODWLWXGHORQJLWXGH V\VWHP RU WKH XQLYHUVDO WUDQVYHUVH PHUFDWRU 870f V\VWHP RU WKH VWDWH SODQH FRRUGLQDWH 63&f V\VWHP 7KH VHFRQG DSSURDFK LV WR WUHDW RQH RI WKH LPDJHV DV D PDVWHU DQG WKH UHVW DV VODYHV $IWHU VHOHFWLQJ D QXPEHU RI WLH SRLQWV WKDW DUH PXWXDO WR DOO LPDJHV LQFOXGLQJ WKH PDVWHU RQH WKH VODYH LPDJHV DUH UHFWLILHG WR WKH PDVWHU LPDJH ,Q WKH VHFRQG DSSURDFK QR DFWXDO JHRJUDSKLFDO FRRUGLQDWH V\VWHP HJ 870f LV XWLOL]HG DQG WKH VODYH LPDJHV DUH UHIHUHQFHG UHODWLYH WR WKH PDVWHU LPDJH 8VXDOO\ WKLV UHODWLYH DSSURDFK SURGXFHV D VPDOOHU HUURU RI FRUHJLVWUDWLRQ EHFDXVH WUDQVLWLRQDO UHIHUHQFH HJ PDSVf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

PAGE 25

FRQVLGHUDEO\ WKHLU LQWURGXFWLRQ LV WKH UHVXOWV RI VSHFXODWLRQV DQG DUELWUDU\ HODERUDWLRQV EHFDXVH WKH EDVLF SULQFLSOH RI GLJLWDOO\ PHUJLQJ VDWHOOLWH LPDJHV LV QRW ZHOO XQGHUVWRRG 7KHUHIRUH LW KDV EHFRPH HVVHQWLDO WR H[SORUH DQG WR XQGHUVWDQG WKH SULQFLSOH RI LPDJH GDWD PDQLSXODWLRQV VR WKDW WKH WHFKQLTXHV RI PXOWLUHVROXWLRQ SURFHVVLQJ FDQ EH GHYHORSHG WR HIIHFWLYHO\ HQKDQFH VDWHOOLWH UHPRWH VHQVLQJ DSSOLFDWLRQV LQFOXGLQJ ODQGXVH FODVVLILFDWLRQ

PAGE 26

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

PAGE 27

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

PAGE 28

VKDGHV WR D ODUJHU UDQJH RU WR D IXOO UDQJH f IRU LQFUHDVLQJ LPDJH FRQWUDVW 7KH JUD\ VKDGHV RI DQ RULJLQDO VDWHOOLWH LPDJH RI /DQGVDW 6327 DQG RWKHU VDWHOOLWHV XVXDOO\ VSUHDG RYHU D SRUWLRQ RI WKH DYDLODEOH G\QDPLF UDQJH RU VRPHWLPHV FDOOHG GDWD GHSWKf $V D UHVXOW VXFK LPDJHV ZLWK FUDPSHG JUD\ VKDGHV GR QRW KDYH FRQVSLFXRXV WRQDO JUDGDWLRQV $IWHU D FRQWUDVWVWUHWFKLQJ SURFHVV WKH LPDJH YDOXHV RIWHQ FDOOHG LPDJH GLJLWDO FRXQWVf RI UHODWLYHO\ GDUN SL[HOV DUH VFDOHG EDFN IXUWKHU ZKLOH WKRVH RI EULJKW SL[HOV DUH VFDOHG XS $V D UHVXOW RULJLQDO GDUN SL[HOV ZLOO EHFRPH GDUNHU ZKLOH WKH EULJKW RQHV EHFRPH EULJKWHU LQ D FRQWUDVWVWUHWFKHG LPDJH *RQ]DOH] DQG :LQW] f 9HU\ RIWHQ WKLV VLPSOH SURFHGXUH FDQ SURGXFH VDWLVIDFWRU\ UHVXOWV IRU LPDJH LQWHUSUHWDWLRQ 1RWH WKDW WKH LQFUHDVH LQ LPDJH WRQDO FRQWUDVW E\ D FRQWUDVWVWUHWFKLQJ SURFHGXUH JLYHV D IDOVH VHQVH WKDW WKH SURFHGXUH FDQ LPSURYH WKH LPDJH UDGLRPHWULF TXDOLW\ 7KH FRQWUDVWVWUHWFKLQJ SURFHGXUH FDQ EH DSSOLHG WR D SRUWLRQ RI WKH H[LVWLQJ LPDJH JUD\ VKDGHV 7KRPDV HW DO f RU WR D VXELPDJH DUHD *RQ]DOH] DQG :LQW] f IRU D VHOHFWLYH HQKDQFHPHQW $OVR WKHUH DUH OLQHDU DQG QRQOLQHDU FRQWUDVW VWUHWFKLQJ PHWKRGV /LOOHVDQG DQG .LHIHU 7KRPDV HW DO f DQG WKH SURFHGXUH LV SHUIRUPHG IRU HDFK LPDJH RU ZDYHEDQG LQGHSHQGHQWO\ $ VSDWLDO ILOWHULQJ SURFHGXUH LQFOXGHV ERWK WKH KLJKSDVV DQG ORZSDVV ILOWHUV ZKLFK DUH RIWHQ XVHG WR UHPRYH RU WR

PAGE 29

HPSKDVL]H FHUWDLQ YLVXDO HIIHFWV RI D GLJLWDO LPDJH )RU LQVWDQFH D ORZSDVV ILOWHU LV XVHG IRU LPDJH VPRRWKLQJ DQG QRLVH HOLPLQDWLRQ ZKLOH D KLJKSDVV ILOWHU LV IRU HGJH HQKDQFHPHQW /LOOHVDQG DQG .LHIHU f 7KH VLPSOHVW IRUP RI D ORZSDVV ILOWHU LV WR UHSODFH WKH YDOXH RI D SL[HO E\ WKH DYHUDJH FRPSXWHG IURP LWV QHLJKERUKRRG HJ [ SL[HO DUUD\f %\ UHSODFLQJ D SL[HOnV YDOXH ZLWK LWV QHLJKERUKRRG DYHUDJH WKH ODUJH YDOXHV VXFK DV QRLVHVf ZLOO EH FRPSUHVVHG ZKLOH WKH VPDOO YDOXHV DUH LQIODWHG RU H[DJJHUDWHG /LOOHVDQG DQG .LHIHU f $V D UHVXOW D ORZSDVV ILOWHUHG LPDJH ZLOO DSSHDU VPRRWKHU DQG KDYH OHVV FRQWUDVW ,Q WKH FDVH RI D KLJKSDVV ILOWHU WKH YDOXH RI D SL[HO ZLOO EH DGGHG WR RU VXEWUDFWHG IURP E\ LWV GHYLDWLRQ IURP WKH DYHUDJH RI LWV QHLJKERUKRRG HJ [ DUUD\f GHSHQGLQJ RQ LWV UHODWLYH PDJQLWXGH ZLWK UHVSHFW WR WKH GHILQHG QHLJKERUKRRG DYHUDJH 7KHUHIRUH ERXQGDU\ SL[HOV ZKLFK XVXDOO\ KDYH WKH ODUJHVW GHYLDWLRQV ZLOO EHFRPH HLWKHU PXFK GDUNHU RU EULJKWHU 2IWHQ WKH GHYLDWLRQV DUH GRXEOHG RU HYHQ WULSOHG LQ RUGHU WR PDNH HGJHV RU OLQHDU IHDWXUHV PRUH FRQVSLFXRXV /LOOHVDQG DQG .LHIHU f 7KH RSHUDWLRQ RI D VSDWLDO ILOWHULQJ SURFHGXUH KLJKSDVV RU D ORZSDVVf LV SHUIRUPHG LQGHSHQGHQWO\ IRU HDFK LPDJH RU ZDYHEDQG $Q LPSRUWDQW SRLQW LQ VSDWLDO ILOWHULQJ LV WKDW WKH UHVXOWDQW LPDJH GDWD DUH UDGLRPHWULFDOO\ DOWHUHG E\ VXFK ILOWHULQJ SURFHGXUHV $V FRPSDUHG WR WKH PHWKRGV RI ERWK FRQWUDVW VWUHWFKLQJ DQG VSDWLDO ILOWHULQJ SULQFLSDO FRPSRQHQW DQDO\VLV 3&$f LV

PAGE 30

D SURFHGXUH ZKLFK LQYROYHV D PXOWLGLPHQVLRQDO WUDQVIRUPDWLRQ IRU D VHW RI PXOWLVSHFWUDO LPDJHV ,Q WKH SURFHVV WKH PXOWLn ZDYHEDQG GDWD DUH WUDQVIRUPHG IURP WKH RULJLQDO FRRUGLQDWH V\VWHP IRUPHG E\ WKH VSHFWUDO ZDYHEDQGV LQWR RQH GHILQHG E\ QHZ V\QWKHVL]HG ZDYHEDQGV 7KHUH DUH VHYHUDO XVDJHV IRU D 3&$ SURFHGXUH )LUVW LW FDQ EH XVHG WR UHGXFH WKH GLPHQVLRQDOLW\ RI PXOWLZDYHEDQG GDWDVHWV 7KRPDV HW DO f )RU LQVWDQFH ZKHQ D 3&$ WUDQVIRUP LV DSSOLHG WKH LPDJH GDWD RI D WZRZDYHEDQG GDWDVHW FDQ EH HIIHFWLYHO\ UHSUHVHQWHG E\ WKH ILUVW SULQFLSDO FRPSRQHQW 3&,f DV VKRZQ LQ )LJXUH WKXV UHGXFLQJ WKH GDWDVHW WR HVVHQWLDOO\ RQH GLPHQVLRQ RU RQH V\QWKHVL]HG ZDYHEDQGf 7KH VHFRQG XVDJH LV WR LQFUHDVH WKH LPDJH FRQWUDVW DV ZHOO DV WKH VHSDUDELOLW\ IRU ODQGXVH HOHPHQWV /LOOHVDQG DQG .LHIHU f )RU LQVWDQFH WKH LPDJH GDWD YDULDQFH HQFRPSDVVHG E\ WKH 3&, FRPSRQHQW )LJXUH f LV JUHDWHU WKDQ HLWKHU RI WKRVH IRU WKH WZR RULJLQDO ZDYHEDQGV 7KHUHIRUH WKH LPDJH RI WKH 3&, FRPSRQHQW ZLOO KDYH PRUH FRQWUDVW DV ZHOO DV JUHDWHU VHSDUDWLRQ DPRQJ WKH GLIIHUHQW ODQGXVH HOHPHQWV LQ WKH LPDJH 7KH WKLUG XVDJH RI D 3&$ SURFHGXUH LV IRU WKH GHFRUUHODWLRQ RI PXOWLVSHFWUDO LPDJHV *LOOHVSLH HW DO f ,Q VXFK D FDVH D 3&$ WUDQVIRUP LV IROORZHG E\ D FRQWUDVWVWUHWFKLQJ SURFHGXUH DSSOLHG WR WKH 3& FRPSRQHQWV SDUWLFXODUO\ WKH 3& FRPSRQHQW DV VKRZQ LQ )LJXUH 7KHQ WKH ILUVW 3&,f DQG VHFRQG 3&f FRPSRQHQWV DUH WRJHWKHU UHWUDQVIRUPHG EDFN WR WKHLU RULJLQDO PXOWLVSHFWUDO VSDFH ,Q D GHFRUUHODWHG GDWDVHW WKH

PAGE 31

L R S 7 & 2 ;, 4f UW2 S S R f D Z 6SHFWUDO ZDYHEDQG RQH )LJXUH 6FKHPDWLFV RI SULQFLSDO FRPSRQHQW DQDO\VLV IRU PXOWLVSHFWUDO GDWDVHWV

PAGE 32

LGHQWLWLHV IRU WKH YDULRXV W\SHV RI VSHFWUDO HOHPHQWV PD\ EH VLJQLILFDQWO\ GLIIHUHQW IURP WKRVH RI WKH RULJLQDO LPDJHV *LOOHVSLH HW DO f ,I WKH 3&$ SURFHGXUH LV DSSOLHG WR D PXOWLVSHFWUDO LPDJH GDWDVHW ZLWK Q ZDYHEDQGV WKH LPDJH GDWD WUDQVIRUPDWLRQ ZLOO WDNH SODFH ZLWKLQ D QGLPHQVLRQDO VSDFH 7KH UHVXOWV DUH WKDW WKH DPRXQW RI UDGLRPHWULF LQIRUPDWLRQ UHSUHVHQWHG E\ WKH ILUVW WKH VHFRQG DQG WKH QWK FRPSRQHQW ZLOO EH LQ D GHFUHDVLQJ RUGHU $OVR WKH WUDQVIRUPHG FRPSRQHQWV FDQ HDFK EH FRQWUDVWVWUHWFKHG /LOOHVDQG DQG .LHIHU f WR IXUWKHU HQKDQFH WKH WRQDO JUDGDWLRQV RI WUDQVIRUPHG LPDJHV 7KH 3&$ WUDQVIRUP LV XVXDOO\ FDUULHG RXW EHIRUH LQLWLDWLQJ ODQGXVH FODVVLILFDWLRQ SURFHGXUHV WR UHGXFH GDWD GLPHQVLRQDOLW\ DV ZHOO DV WR HQKDQFH WKH UDGLRPHWULF VHSDUDELOLW\ RI VSHFWUDO FODVVHV 7KRPDV HW DO f SUHVHQWV LQGHSWK GLVFXVVLRQV DERXW 3&$ WUDQVIRUPV ZKLFK DUH H[HPSOLILHG E\ XVLQJ D /DQGVDW PXOWLVSHFWUDO VFDQQHU 066f GDWDVHW )LQDOO\ LW LV ZRUWKZKLOH WR SRLQW RXW WKDW WKH SURFHGXUHV RI FRQWUDVW VWUHWFKLQJ VSDWLDO ILOWHULQJ DQG SULQFLSDO FRPSRQHQW DQDO\VLV ZLOO QRW HQKDQFH RU LPSURYH WKH VSDWLDO UHVROXWLRQ RI WKH RULJLQDO LPDJHV ,Q DGGLWLRQ D FRQWUDVWVWUHWFKLQJ SURFHGXUH ZLOO QRW LQFUHDVH WKH DFWXDO QXPEHU RI JUD\ VKDGHV LQ DQ LPDJH HYHQ WKRXJK WKH UDGLRPHWULF YDULDQFH RI VWUHWFKHG LPDJH GDWD LV LQFUHDVHG

PAGE 33

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f FRORU GLVSOD\ V\VWHP $SSHQGL[ $f DQG WKH LQWHQVLW\KXHVDWXUDWLRQ ,+6f FRORU WUDQVIRUP $SSHQGL[ %f )RU PXOWLUHVROXWLRQ GDWDVHWV WKH 5*% V\VWHP LV VLPSOH DQG HDV\ WR XVH EXW WKH UHVXOWDQW FRORU FRPSRVLWHV RIWHQ KDYH D EORFN\ DSSHDUDQFH SDUWLFXODUO\ ZKHQ WKH VSDWLDO UHVROXWLRQ GLIIHUHQFH LV ODUJH 5HFHQWO\ WKH ,+6 WUDQVIRUP KDV JDLQHG SRSXODULW\ PDLQO\ EHFDXVH RI LWV HIIHFWLYHQHVV WR SURGXFH PRUH EDODQFHG FRORU SURGXFWV IRU D ZLGH UDQJH RI GDWDVHWV 7R

PAGE 34

JHQHUDWH D FRORU FRPSRVLWH IURP D PXOWLUHVROXWLRQ GDWDVHW WKH ,+6 PHWKRG ILUVW WDNHV D IRUZDUG WUDQVIRUPDWLRQ IURP WKH ORZ VSDWLDO UHVROXWLRQ LPDJHV RI WKUHH ZDYHEDQGV LQWR WKH LQWHQVLW\ ,f KXH +f DQG VDWXUDWLRQ 6f FRPSRQHQWV $SSHQGL[ %f 7KHQ D UHYHUVH WUDQVIRUPDWLRQ LV FDUULHG RXW WR FRQYHUW WKH + DQG 6 FRPSRQHQWV WR WKH 5*% YDOXHV LQ RUGHU WR JHQHUDWH FRORU FRPSRVLWHV WKURXJK D 5*% FRORU GLVSOD\ GHYLFH 7KH KLJK VSDWLDO UHVROXWLRQ LPDJH LV PHUJHG LQ WKH SURFHVV E\ UHSODFLQJ WKH FRPSRQHQW GXULQJ WKH UHYHUVH WUDQVIRUPDWLRQ +D\GQ HW DO &DUSHU HW DO f 1RWH WKDW D FRORU FRPSRVLWH E\ HLWKHU WKH 5*% V\VWHP RU WKH ,+6 WUDQVIRUP XVHV D PD[LPXP RI RQO\ WKUHH VSHFWUDO FKDQQHOV DQG VXFFHVVIXO UHVXOWV RIWHQ GHSHQG RQ D WHGLRXV WULDODQG HUURU SURFHVV 'DLO\ HW DO f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

PAGE 35

JHRORJLF XQLWV WKURXJK D YLVXDO LPDJH LQWHUSUHWDWLRQ 8VLQJ D VLPLODU DSSURDFK :RQJ DQG 2UWK f DOVR JHQHUDWHG XVHIXO FRORU FRPSRVLWHV IURP 6HDVDW V\QWKHWLF DSHUWXUH UDGDU 6$5f DQG /DQGVDW 066 LPDJHV ZKLFK KDYH P DQG P VSDWLDO UHVROXWLRQV UHVSHFWLYHO\ 7KHVH WZR HDUO\ VWXGLHV XQGHUOLQHG WKH EHQHILWV LQ WKH XQLILHG XVH RI VDWHOOLWH GDWD DFTXLUHG E\ FRPSOHWHO\ GLIIHUHQW VHQVLQJ V\VWHPV PXOWLVSHFWUDO YV UDGDUf IRU LPSURYLQJ WKH LQWHUSUHWDELOLW\ RI UHPRWH VHQVLQJ LPDJHV :KHQ WKH 5*% FRORU GLVSOD\ V\VWHP LV XVHG VDWHOOLWH LPDJHV GR QRW UHDGLO\ GHILQH RU ILW LQWR WKH UHG JUHHQ DQG EOXH SULPDU\ FRORUV +DUULV HW DO f ,Q RWKHU ZRUGV WKH LPDJHV FDQ QRW VLPSO\ VXEVWLWXWH WKH UHG JUHHQ DQG EOXH SULPDULHV LQ WKH 5*% GLVSOD\ V\VWHP EHFDXVH RI WKH VSHFWUDO LQFRPSDWLELOLW\ ZKLFK FRXOG OHDG WR VHULRXV FRORU GLVWRUWLRQV DQG SRRUTXDOLW\ FRPSRVLWHV +D\GQ HW DO +DUULV HW DO DQG &DUSHU HW DO f $V D UHVXOW WKH ,+6 FRORU SHUFHSWLRQ V\VWHP KDV EHFRPH WKH ZLGHO\ DGRSWHG DSSURDFK WR UHVROYH WKH FRORU GLVWRUWLRQ SUREOHPV HQFRXQWHUHG LQ WKH 5*% GLVSOD\ RI PXOWLVSHFWUDO LPDJHV 7KH HQWLUH SURFHVV RI DQ ,+6 WUDQVIRUP IRU PXOWLUHVROXWLRQ SURFHVVLQJ WDNHV IRXU VWHSV ZKLFK LQFOXGH Lf FRUHJLVWUDWLRQ RI PXOWLUHVROXWLRQ LPDJHV LLf D IRUZDUG WUDQVIRUPDWLRQ IURP WKUHH PXOWLVSHFWUDO LPDJHV WR WKH WKUHH ,+6 FRPSRQHQWV LLLf D UHYHUVH WUDQVIRUPDWLRQ IURP WKH ,+6 FRPSRQHQWV WR 5*% YDOXHV XVXDOO\ ZLWK WKH UHSODFHPHQW RI WKH LQWHQVLW\ FRPSRQHQW E\ WKH KLJK VSDWLDO UHVROXWLRQ LPDJH DQG LYf GLVSOD\ WKH UHVXOWV WKURXJK D 5*%

PAGE 36

FRORU GLVSOD\ V\VWHP )RU WKH ,+6 V\VWHP WKH LQWHQVLW\ RU EULJKWQHVV RI D VFHQH LV D IXQFWLRQ RI LOOXPLQDWLRQ %R\QWRQ f 7KHUHIRUH WKH LQWHQVLW\ FRPSRQHQW VKRXOG HQFRPSDVV D EURDGHU UDQJH RI ZDYHOHQJWK +D\GQ HW DO f DQG LV H[WHQVLYHO\ DVVRFLDWHG ZLWK WKH VSDWLDO UHODWLRQV RI VFHQH REMHFWV -XGG DQG :\V]HFKL f )RU WKLV UHDVRQ WKH LQWHQVLW\ FRPSRQHQW LV DOZD\V DVVXPHG WR EH UHSODFHG E\ WKH KLJK VSDWLDO UHVROXWLRQ SDQFKURPDWLF LPDJH LQ WKH UHYHUVH ,+6 WUDQVIRUPDWLRQ =REULVW HW DO f ZHUH DPRQJ WKH ILUVW WR DSSO\ WKH ,+6 WUDQVIRUP WR VDWHOOLWH GDWD IRU LPDJH HQKDQFHPHQW ,Q WKH VWXG\ /DQGVDW 066 P DQG PHWHRURORJLFDO 6HDVDW P UDGDU LPDJHV ZHUH XVHG 7KH LQWHQVLW\ FRPSRQHQW WUDQVIRUPHG IURP WKH /DQGVDW 066 GDWD ZDV VLPSO\ UHSODFHG E\ WKH P UDGDU LPDJH 7KHQ DQ ,+6 UHYHUVH WUDQVIRUPDWLRQ ZDV WDNHQ WR FUHDWH FRORU FRPSRVLWHV +D\GQ HW DO f IXUWKHU GHPRQVWUDWHG WKH XWLOLW\ RI WKH ,+6 WUDQVIRUP IRU LPDJH HQKDQFHPHQW /DQGVDW 066 /DQGVDW UHWXUQ EHDP YLGLFRQ 5%9f DQG WKH +HDW &DSDFLW\ 0DSSLQJ 0LVVLRQ +&00f WKHUPDO LQIUDUHG 7,5f LPDJHV ZLWK UHVSHFWLYH VSDWLDO UHVROXWLRQV RI P P DQG P ZHUH PHUJHG EHWZHHQ WKH 5%9 DQG 066 DQG EHWZHHQ WKH 066 DQG +&00 LPDJHV $ GLUHFW UHSODFHPHQW RI WKH WUDQVIRUPHG LQWHQVLW\ FRPSRQHQW E\ WKH FRUUHVSRQGLQJ KLJK VSDWLDO UHVROXWLRQ LPDJH ZDV HPSOR\HG LQ WKH UHYHUVH WUDQVIRUPDWLRQ IRU HDFK FDVH $OVR UDWLRHG GDWD EHWZHHQ VSHFWUDO ZDYHEDQGV ZDV GHPRQVWUDWHG IRU WKH XVH

PAGE 37

RI WKH ,+6 WUDQVIRUP )RU H[DPSOH ZKLOH WKH LQWHQVLW\ FRPSRQHQW ZDV WUDQVIRUPHG IURP /DQGVDW 066 ZDYHEDQGV IRXU ILYH DQG VHYHQ GHQRWHG UHVSHFWLYHO\ DV 066 066 DQG 066f WKH + DQG 6 FRPSRQHQWV ZHUH VXEVWLWXWHG UHVSHFWLYHO\ E\ WKH 066066 DQG 066066 UDWLRHG GDWD 6XEVWDQWLDO HQKDQFHPHQW LQ FRORU FRPSRVLWHV ZDV REVHUYHG 7KH ,+6 FRORU WUDQVIRUP ZDV DGRSWHG LQ WKH HQWLUH VWXG\ EHFDXVH WKH GLUHFW 5*% FRORU PRGHO SURGXFHG FRQIXVLQJ DQG ORZ TXDOLW\ LPDJH SUHVHQWDWLRQV 8VLQJ D VLPLODU PHWKRGRORJ\ :HOFK DQG (KOHUV f ZHUH DEOH WR SURGXFH HQKDQFHG FRORU FRPSRVLWHV IURP /DQGVDW Pf WKHPDWLF PDSSHU 70f DQG 6327 +59 P SDQFKURPDWLF LPDJHV 9HU\ GLIIHUHQW DSSURDFKHV IRU XVLQJ WKH ,+6 WUDQVIRUP KDYH DOVR EHHQ UHSRUWHG $ FRORU FRPSRVLWH ZDV FUHDWHG IURP D 6HDVDW PRQREDQG UDGDU LPDJH 'DLO\ f %RWK WKH VWURQJ DQG ZHDN UDGDU UHVSRQVHV UHODWHG WR VORSLQJ WDUJHWV DQG YHJHWDWLRQ IHDWXUHV ZHUH H[WUDFWHG UHVSHFWLYHO\ E\ KLJKSDVV DQG ORZSDVV ILOWHUV DQG WKHQ XVHG DV WKH KXH DQG VDWXUDWLRQ FRPSRQHQWV ZKLOH WKH RULJLQDO UDGDU LPDJH ZDV XVHG GLUHFWO\ DV WKH LQWHQVLW\ FRPSRQHQW IRU WKH ,+6 WUDQVIRUP 7KH FRORU FRPSRVLWH ZDV DEOH WR UHYHDO PDMRU VWUXFWXUDO IHDWXUHV LQYLVLEOH LQ WKH RULJLQDO EODFNDQGZKLWH UDGDU LPDJH +DUULV HW DO f WRRN D VWHS IXUWKHU ZKHQ FRPELQLQJ /DQGVDW P 70 DQG P DLUERUQH UDGDU LPDJHV ,Q WZR LQVWDQFHV WKH KLJK VSDWLDO UHVROXWLRQ LPDJH ZDV XVHG GLUHFWO\ DV WKH LQWHQVLW\ FRPSRQHQW ZKLOH WKH KXH FRPSRQHQWV ZHUH FUHDWHG IURP D

PAGE 38

FRPELQDWLRQ RI /DQGVDW 70 ZDYHEDQGV WZR IRXU DQG VHYHQ GHQRWHG DV 70 70 DQG 70f RU RI /DQGVDW 70 ZDYHEDQGV WZR ILYH DQG VHYHQ GHQRWHG DV 70 70 DQG 70f +RZHYHU WKH VDWXUDWLRQ FRPSRQHQW ZDV KHOG DW D FRQVWDQW YDOXH f ,Q DQRWKHU LQVWDQFH RI WKH VDPH VWXG\ E\ +DUULV HW DO f WKH UDGDU LPDJH ZDV XVHG DV WKH LQWHQVLW\ FRPSRQHQW DQG WKH JHRORJLFDO XQLWV QXPHULFDO FRGHVf LQ D GLJLWL]HG PDS DV WKH KXH FRPSRQHQW ZKLOH WKH VDWXUDWLRQ FRPSRQHQW ZDV KHOG DW D FRQVWDQW f %DVHG RQ D YLVXDO DVVHVVPHQW WKH VWXG\ FRQFOXGHG WKDW WKH FRORU FRPSRVLWHV ZHUH DEOH WR GHILQH OLWKRORJLFDO DQG VWUXFWXUDO IHDWXUHV WKDW ZHUH DEVHQW IURP H[LVWLQJ JHRORJLFDO PDSV 7KHVH WZR VWXGLHV E\ 'DLO\ f DQG +DUULV HW DO f QRW RQO\ RSHQHG D QHZ GLPHQVLRQ LQ WKH XVH RI WKH ,+6 WUDQVIRUP IRU UHPRWH VHQVLQJ DSSOLFDWLRQV EXW DOVR GHPRQVWUDWHG WKH HIIHFWLYHQHVV DQG FRPSDWLELOLW\ RI WKH ,+6 WUDQVIRUP IRU D EURDG UDQJH RI GDWD FKDUDFWHULVWLFV LQFOXGLQJ VDWHOOLWH LPDJHV DQG GLJLWDO PDSV 7KH XVH RI WKH ,+6 WUDQVIRUP FDQ EH H[WHQGHG WR LQFOXGH WKH LPDJHU\ GLJLWL]HG IURP DQ DHULDO FRORU LQIUDUHG $&,5f SKRWRJUDSK\ *UDVVR f ,Q WKH VWXG\ D GLJLWL]HG $&,5 KLJK VSDWLDO UHVROXWLRQ Pf LPDJH ZDV PHUJHG ZLWK /DQGVDW 066 DQG /DQGVDW 70 GDWD WR HQKDQFH JHRORJLFDO LQWHUSUHWDWLRQ 7KH LQWHQVLW\ FRPSRQHQWV WUDQVIRUPHG IURP HLWKHU /DQGVDW 066 RU /DQGVDW 70 LPDJHV ZHUH GLUHFWO\ UHSODFHG E\ WKH $&,5 LPDJH GXULQJ WKH ,+6 UHYHUVH WUDQVIRUPDWLRQ 7KH FRORU FRPSRVLWHV ZKLFK KDG D [ OLQHDU VSDWLDO UHVROXWLRQ IDFWRU ZHUH VWLOO

PAGE 39

XVHIXO IRU JHRORJLFDO PDSSLQJ $OVR LQ WKH VWXG\ D GLIIHUHQW DSSURDFK LQ XWLOL]LQJ WKH ,+6 WUDQVIRUP ZDV GHPRQVWUDWHG LQ ZKLFK WKH GLJLWL]HG $&,5 LPDJH ZDV XVHG DV WKH LQWHQVLW\ FRPSRQHQW WKH /DQGVDW 70 UDWLR GDWD 7070f DV WKH VDWXUDWLRQ FRPSRQHQW ZKLOH WKH KXH FRPSRQHQW ZDV KHOG DW D FRQVWDQW YDOXH f 7KH UHVXOWV ZHUH YHU\ XVHIXO IRU GHOLQHDWLQJ WKH KLJK DQG ORZ FOD\ FRQWHQW DUHDV 1RWH WKDW WKH KLJK DQG ORZ 7070 UDWLRV ZHUH HVVHQWLDOO\ XVHG WR UHJXODWH WKH OHYHO RI FRORU VDWXUDWLRQ 6 FRPSRQHQWf VR WKDW KLJK FOD\ FRQWHQW DUHDV ZRXOG VKRZ PRUH YLYLG FRORUV WKDQ LWV FRXQWHUSDUWV +RZHYHU UHVXOWV DOVR VKRZHG WKDW WKH FRORUV RI WKHVH FRPSRVLWHV FRXOG FKDQJH YHU\ UDSLGO\ E\ MXVW YDU\LQJ WKH KXH FRPSRQHQW ZLWK D PRGHUDWH PDJQLWXGH 7KRXJK WKH FRQFHSW RI WKH ODWWHU H[DPSOH LV VRPHZKDW GLIIHUHQW IURP WKH SUHYLRXV RQH E\ +DUULV HW DO f ZKR HPSKDVL]HG WKH FRORU GLYHUVLW\ + FRPSRQHQWf UDWKHU WKDQ WKH FRORU SXULW\ 6 FRPSRQHQWf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

PAGE 40

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n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f VLPXODWHG 6327 +59 SDQFKURPDWLF

PAGE 41

DQG PXOWLVSHFWUDO LPDJHV IURP DQ DLUERUQH GDWDVHW ZKLFK KDG VSHFWUDO ZDYHEDQGV ZHUH GLJLWDOO\ PHUJHG SL[HO E\ SL[HO XVLQJ WKH IROORZLQJ PHWKRGV 0,M $ r 3$1 r +59Mfr %M >@ ,, 0, $ r 3$1 r +59Mf % >@ ,,, 0, $ r 3$1 r +59fnK % >D@ 0, $ r 3$1 r +59fnD % > E@ 0, $ r 3$1 +59f % >F@ ZKHUH 0, LV WKH PHUJHG PXOWLVSHFWUDO LPDJHV L LQ PHWKRGV DQG ,, DQG VXEVFULSWV LQ PHWKRG ,,,f LV ZDYHEDQG LQGH[ 3$1 DQG +59 DUH UHVSHFWLYHO\ WKH VLPXODWHG 6327 SDQFKURPDWLF DQG PXOWLVSHFWUDO LPDJHV DQG $ DQG % DUH FRHIILFLHQWV RU VFDOLQJ IDFWRUV WR PDLQWDLQ WKH PHUJHG GDWD ZLWKLQ WKH G\QDPLF UDQJH )URP WKH FRORU FRPSRVLWHV JHQHUDWHG WKURXJK WKH XVH RI WKH 5*% FRORU GLVSOD\ V\VWHP WKH VWXG\ FRQFOXGHG WKDW ZKLOH WKH LPSURYHPHQW RQ VSDWLDO UHVROXWLRQ ZDV DSSDUHQW IRU DOO WKUHH PHWKRGV PHWKRG ,,,f SURGXFHG WKH EHVW FRORU FRPSRVLWH 7KH LPSURYHPHQW E\ PHWKRG ,,,f ZDV DWWULEXWHG WR WKH XVH RI GLIIHUHQW PHUJLQJ DOJRULWKPV ZKLFK KHOSHG SUHVHUYH WKH 6327 +59M QHDU LQIUDUHG LQIRUPDWLRQ )RU PHWKRG ,,f WKH SL[HO YDOXHV ZHUH ORZ DQG FRQFHQWUDWHG UHVXOWLQJ LQ GDUN DQG QRn FRQWUDVW PHUJHG LPDJHV %HFDXVH RI WKH KLJK FRUUHODWLRQV LQ WKH PHUJHG LPDJHV EHWZHHQ WKH QHDU LQIUDUHG DQG YLVLEOH

PAGE 42

ZDYHEDQGV PHWKRG ,f SURGXFHG ZDVKRXW LPDJHV (YHQ WKRXJK DOO WKHVH PHUJLQJ PHWKRGV ZHUH EDVHG RQ DUELWUDU\ VSHFXODWLRQV DQG WKH UHVXOWV ZHUH GLVSOD\HG XVLQJ WKH 5*% V\VWHP WKH SRWHQWLDO EHQHILWV RI GLJLWDOO\ PHUJLQJ LPDJH GDWDVHWV ZHUH LQGLFDWHG ZLWK LPSURYHG VSDWLDO LQIRUPDWLRQ ,Q GLJLWDOO\ PHUJLQJ PXOWLUHVROXWLRQ LPDJHV VSHFXODWLRQV IRU D FRPELQLQJ DSSURDFK GR QRW EULQJ DERXW FRQVLVWHQW UHVXOWV ,Q DQ HIIRUW WR ILQG D JHQHUDO DSSURDFK WKDW GRHV QRW GHSHQG RQ DUELWUDU\ HODERUDWLRQV 3ULFH f FRQWHQGHG WKDW WKH KLJK FRUUHODWLRQV EHWZHHQ WKH SDQFKURPDWLF DQG ERWK WKH PXOWLVSHFWUDO JUHHQ DQG UHG ZDYHEDQGV ZLWKLQ D 6327 PXOWLUHVROXWLRQ GDWDVHW FRXOG EH XWLOL]HG WR HVWLPDWH WKH FRUUHVSRQGLQJ KLJK VSDWLDO UHVROXWLRQ PXOWLVSHFWUDO PHUJHG LPDJHV ,Q WKH VWXG\ WKH RULJLQDO 6327 P SDQFKURPDWLF DQG P PXOWLVSHFWUDO LPDJHV ZHUH DUWLILFLDOO\ GHJUDGHG E\ DYHUDJLQJ WR P SDQFKURPDWLF 3f DQG P PXOWLVSHFWUDO 0f LPDJHV UHVSHFWLYHO\ 7KHQ WKH ZKROH DSSURDFK WRRN WZR VWHSV 7KH P PXOWLVSHFWUDO PHUJHG LPDJHV 0,f ZHUH ILUVW HVWLPDWHG IURP WKH GHJUDGHG SDQFKURPDWLF 3 GDWD E\ D UHJUHVVLRQ HJXDWLRQ 0,L $L r 3 %L >@ ZKHUH 0,L LV WKH HVWLPDWHG PXOWLVSHFWUDO LPDJH L EDVHG RQ WKH GHJUDGHG Pf SDQFKURPDWLF LPDJH $ DQG % DUH UHJUHVVLRQ FRHIILFLHQWV GHWHUPLQHG IURP WKH GHJUDGHG SDQFKURPDWLF 3 DQG WKH RULJLQDO P VSDWLDO UHVROXWLRQ PXOWLVSHFWUDO LPDJH DQG

PAGE 43

' LV D FRUUHFWLRQ IDFWRU WR EDODQFH WKH QXPHULFDO VXP RI HVWLPDWHG VXESL[HOV ZLWK WKH UHFRUGHG YDOXH RI D ORZ UHVROXWLRQ SL[HO 0f ,I WKH VXP RI WKH HVWLPDWHG GLJLWDO FRXQWV RI VXESL[HOV GLG QRW HTXDO WKH UHFRUGHG YDOXH RI WKH ORZ UHVROXWLRQ SL[HO LQ TXHVWLRQ D FRUUHFWLRQ ZDV DSSOLHG 7KH HVWLPDWHG P LPDJHV IURP WKH GHJUDGHG Pf SDQFKURPDWLF ZDYHEDQG ZHUH DEOH WR UHWDLQ b RI WKH YDULDQFHV RI WKH RULJLQDO P LPDJHV RI WKH JUHHQ DQG UHG ZDYHEDQGV +RZHYHU D SRWHQWLDOO\ VHULRXV SUREOHP FRXOG KDYH H[LVWHG ZLWK D KLJK FRUUHODWLRQ EHWZHHQ WKH WZR HVWLPDWHG LPDJHV EHFDXVH WKH\ ERWK GHSHQGHG RQ WKH VDPH LGHQWLFDO SDQFKURPDWLF GDWD ,Q IDFW WKH PXOWLVSHFWUDO LPDJHV ZHUH XVHG RQO\ DV FRPSOHPHQWDU\ LQIRUPDWLRQ WKURXJK D FRUUHFWLRQ SURFHGXUH $ GLIIHUHQW DSSURDFK ZDV XQGHUWDNHQ WR HVWLPDWH WKH 6327 QHDULQIUDUHG 1,5f LPDJH ZKLFK LQ JHQHUDO GRHV QRW FRUUHODWH ZHOO ZLWK WKH SDQFKURPDWLF ZDYHEDQG 7KH HVWLPDWHGf PHUJHG P 1,5 LPDJH 0,f ZDV ILUVW REWDLQHG IURP D ORRNXS WDEOH FUHDWHG E\ ERWK WKH GHJUDGHG P SDQFKURPDWLF 3f DQG WKH RULJLQDO P 1,5 LPDJHV 7KHQ FRUUHFWLRQ ZDV DSSOLHG VLPLODU WR WKRVH XVHG IRU WKH JUHHQ DQG UHG ZDYHEDQGV 5HVXOWV LQGLFDWHG WKDW RQO\ b RI WKH UDGLRPHWULF YDULDQFH RI WKH RULJLQDO 1,5 LPDJH ZDV UHWDLQHG GXULQJ WKH PHUJLQJ SURFHVV 7KRXJK WKH EURDG VSHFWUDO EDQGZLGWK RI WKH SDQFKURPDWLF LPDJH HQFRPSDVVHV SDUW RU HYHQ WKH HQWLUH UDQJH RI WKH PXOWLVSHFWUDO

PAGE 44

JUHHQ DQG UHG ZDYHEDQGV LW LV LPSRVVLEOH WKDW WKH SRUWLRQ RI LPDJH GLJLWDO FRXQW IRU D PHUJHG KLJK VSDWLDO UHVROXWLRQ LPDJH FDQ EH VHSDUDWHG IURP D SDQFKURPDWLF SL[HO 7KH GLIILFXOW\ LV DQDORJRXV WR LVRODWLQJ IURP D MDU RI RLO WKH SDUW WKDW FDPH IURP D SDUWLFXODU SHDQXW ,Q DGGLWLRQ WKH SURFHVV RI VSDWLDO GHJUDGDWLRQ E\ DYHUDJLQJ SL[HOVf FRXOG VPRRWK RXW RU FRPSUHVV WKH UDGLRPHWULF LQIRUPDWLRQ LQ WKH RULJLQDO LPDJH GDWD 7R H[SORUH WKH XWLOLW\ RI GLJLWDO PDQLSXODWLRQV IRU GDWDVHWV DFTXLUHG E\ PXOWLSOH VHQVRUV /DQGVDW 066 DQG 6KXWWOH LPDJLQJ UDGDU $EDQG 6,5$f LPDJHV ZHUH GLJLWDOO\ PHUJHG LQ D OLWKRORJLFDO PDSSLQJ VWXG\ &KDYH] HW DO f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f KDYH WZR LPSRUWDQW LPSOLFDWLRQV )LUVW GLJLWDO PDQLSXODWLRQV RI LPDJH GDWD FDQ EH H[WHQGHG WR LQFOXGH WKRVH LPDJHV DFTXLUHG E\ GLIIHUHQW VHQVLQJ V\VWHPV 6HFRQG WKH DULWKPHWLFDO

PAGE 45

PDQLSXODWLRQV RI LPDJH GDWD FDQ EH DSSOLHG WR LPDJHV ZLWK GLIIHUHQW VSDWLDO UHVROXWLRQV DV ZHOO DV WKRVH ZKLFK KDYH WKH VDPH VSDWLDO UHVROXWLRQ 'LJLWDO PHUJLQJ PXOWLUHVROXWLRQ LPDJHV KDV EHHQ XVHG LQ HIIRUWV WR IXUWKHU HQKDQFH WKH UHVXOWV RI DQ ,+6 WUDQVIRUP ,Q RUGHU WR PRUH HIIHFWLYHO\ XVH WKH ,+6 WUDQVIRUP WKH VHOHFWLRQ RI D SURSHU LQWHQVLW\ RU EULJKWQHVV FRPSRQHQW LV YHU\ FULWLFDO WR WKH JXDOLW\ RI FRORU GLVSOD\ %R\QWRQ f $ ORZ LQWHQVLW\ FRPSRQHQW FRXOG UHVXOW LQ VHYHUH LPDJH GHJUDGDWLRQV -XGG DQG :\V]HFKL +D\GQ HW DO f ,Q WKH FDVH RI D ORZ LQWHQVLW\ YDOXH FRUUHFWLRQV DUH QHHGHG IRU WKH KXH DQG VDWXUDWLRQ FRPSRQHQWV -XGG DQG :\V]HFKL f RU IRU WKH LQWHQVLW\ FRPSRQHQW %R\QWRQ +D\GQ HW DO *LOOHVSLH HW DO f +RZHYHU E\ DSSO\LQJ VXFK FRUUHFWLRQ SURFHGXUHV WKH ILQDO LPDJH LV YHU\ GLIILFXOW WR LQWHUSUHW EHFDXVH WKH RULJLQDO FRORUV FDQ EH DOWHUHG VLJQLILFDQWO\ =REULVW HW DO f 7KH LPSRUWDQFH RI ILQGLQJ WKH PRVW HIIHFWLYH PHWKRG WR JHQHUDWH WKH LQWHQVLW\ FRPSRQHQW IRU WKH ,+6 WUDQVIRUP IRU PHUJLQJ PXOWLUHVROXWLRQ GDWDVHWV KDV EHHQ UHFRJQL]HG E\ VRPH UHVHDUFKHUV LQFOXGLQJ &DUSHU HW DO f ,QVWHDG RI DGRSWLQJ WKH GLUHFW UHSODFHPHQW RI WKH SDQFKURPDWLF LPDJH IRU WKH LQWHQVLW\ FRPSRQHQW &DUSHU HW DO f FRQGXFWHG VRPH H[SHULPHQWV RQ GLIIHUHQW PHUJLQJ PHWKRGV LQ RUGHU WR ILQG WKH EHVW LQWHQVLW\ FRPSRQHQW ,Q DGGLWLRQ WR PDQ\ SUHYLRXV VWXGLHV WKDW UHOLHG RQ LPDJHU\ GDWD DFTXLUHG RQ GLIIHUHQW

PAGE 46

GDWHV RU HYHQ LQ GLIIHUHQW \HDUV VLPXOWDQHRXVO\DFTXLUHG 6327 P SDQFKURPDWLF DQG P PXOWLVSHFWUDO LPDJHV ZHUH XVHG 7KLV ZDV GRQH WR HOLPLQDWH WKH FRQWULEXWLRQ RI WHPSRUDO LQIRUPDWLRQ ZKLFK FRXOG LQWURGXFH VRPH GLIILFXOW\ WR WKH DVVHVVPHQW RI WKH EHQHILWV RI DQ ,+6 WUDQVIRUP &DUSHU HW DO f SURSRVHG WKH IROORZLQJ VHW RI PHUJLQJ DOJRULWKPV WR FDOFXODWH WKH LQWHQVLW\ FRPSRQHQWV ,D 3$1 5+9f >@ ,E 3$1 r 3$1 r +59f >@ ,F r 3$1 +59f >@ ,G 3$1 r +59f >@ +59 +59 +59f >@ ZKHUH ZLWK DOSKDEHWLFDO VXEVFULSWV IRU PHWKRG LQGH[ LV WKH FDOFXODWHG LQWHQVLW\ FRPSRQHQW WR UHSODFH WKH RULJLQDO LQWHQVLW\ FRPSRQHQW ,4 WUDQVIRUPHG IURP WKH P PXOWLVSHFWUDO LPDJHV 3$1 LV WKH 6327 SDQFKURPDWLF LPDJH DQG +59 LV WKH PXOWLVSHFWUDO GDWD ZLWK QXPHULFDO VXEVFULSWV IRU ZDYHEDQG LQGH[ 7KH VWXG\ FRQFOXGHG WKDW WKH ZHLJKWHG DYHUDJH PHWKRG ,Ff FRQVLVWHQWO\ SURGXFHG UHVXOWV DV JRRG DV RU EHWWHU WKDQ WKH RWKHUV 7KH HIIHFWLYHQHVV RI WKLV ZHLJKWHG DYHUDJH PHWKRG ,Ff ZDV DWWULEXWHG WR WKH JUHDWHU KLVWRJUDP VLPLODULW\ EHWZHHQ WKH FDOFXODWHG ,Ff DQG WKH RULJLQDO ,Rf LQWHQVLW\ FRPSRQHQWV +RZHYHU VRPH SRLQWV LQ WKH UHVXOWV ZHUH OHIW

PAGE 47

XQGLVFXVVHG )RU LQVWDQFH ZKLOH WKH KLVWRJUDP RI ,F FRUUHODWHG H[WUHPHO\ ZHOO WR WKDW RI WKH SDQFKURPDWLF LPDJH H[FHSW ZLWK D PRGHUDWH VKLIW WR KLJKHU YDOXHV LW GLG QRW KDYH DQ\ UHVHPEODQFH WR WKDW RI WKH RULJLQDO +59 LPDJH 7KLV LQGLFDWHG WKDW WKH FRHIILFLHQW f IRU WKH 3$1 LPDJH LQ HTXDWLRQ >@ VLJQLILFDQWO\ H[DJJHUDWHG WKH HIIHFW RI WKH SDQFKURPDWLF LPDJH LQ WKH ,F FRPSRQHQW LPSO\LQJ QRW RQO\ D GXSOLFDWLRQ RI WKH SDQFKURPDWLF LQIRUPDWLRQ EXW DOVR D VLJQLILFDQW ORVV RI UDGLRPHWULF LQIRUPDWLRQ IRU WKH +59 LPDJH LQ WKH PHUJLQJ SURFHVV ,Q DGGLWLRQ WKH JUHDW VLPLODULW\ EHWZHHQ WKH KLVWRJUDPV RI LQWHQVLW\ ,F DQG WKH SDQFKURPDWLF LPDJH VXJJHVWHG WKDW D GLUHFW UHSODFHPHQW RI WKH LQWHQVLW\ FRPSRQHQW ,4f E\ WKH SDQFKURPDWLF LPDJH DV XVHG LQ PDQ\ RWKHU VWXGLHV LV ZRUNDEOH LQ DQ ,+6 WUDQVIRUP ,Q UHVSRQVH WR D EURDG DUUD\ RI GLYHUVH DSSURDFKHV ZKLFK KDYH EHHQ XVHG WR PHUJH PXOWLUHVROXWLRQ GDWDVHWV VHYHUDO PHWKRGV WR FRPELQH PXOWLUHVROXWLRQ LPDJHV ZHUH HYDOXDWHG E\ &KDYH] HW DO f XVLQJ VWDWLVWLFDO YLVXDO DQG JUDSKLFDO FRPSDULVRQV 0RUH VSHFLILFDOO\ WKRVH GLIIHUHQW FRPELQLQJ PHWKRGV LQFOXGHG WKH ,+6 WUDQVIRUP WKH 3&$ PHWKRG DQG WKH KLJKSDVV VSDWLDOf ILOWHULQJ +3)f )RU WKH /DQGVDW 70 DQG 6327 SDQFKURPDWLF GDWDVHWV XVHG LQ WKH VWXG\ D FRQWUDVWn VWUHWFKLQJ SURFHGXUH ZDV DSSOLHG WR WKH 6327 SDQFKURPDWLF LPDJH LQ DQ DWWHPSW WR LQFUHDVH DUELWUDULO\ VFDOH XSf WKH UDGLRPHWULF YDULDQFH 7KHQ LQ WKH ,+6 PHWKRG WKH LQWHQVLW\ FRPSRQHQW WUDQVIRUPHG IURP /DQGVDW 70 LPDJHV ZDV VLPSO\

PAGE 48

UHSODFHG E\ WKH FRQWUDVWVWUHWFKHG SDQFKURPDWLF LPDJH GXULQJ WKH ,+6 UHYHUVH WUDQVIRUPDWLRQ ,Q WKH 3&$ PHWKRG WKH VWUHWFKHG SDQFKURPDWLF LPDJH ZDV DVVXPHG WR EH VLPLODU WR WKH ILUVW SULQFLSDO FRPSRQHQW WUDQVIRUPHG IURP WKH /DQGVDW 70 LPDJHV RI DOO VL[ ZDYHEDQGV H[FOXGLQJ WKH 7,5 ZDYHEDQGf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f FRQFOXGHG WKDW WKRXJK WKH ,+6 PHWKRG SURGXFHG WKH EHVW FRORU FRPSRVLWH DPRQJ WKH WKUHH PHWKRGV LW GLVWRUWHG WKH VSHFWUDO FKDUDFWHULVWLFV RI WKH PHUJHG LPDJHV WKH PRVW )RU WKH +3) PHWKRG WKH PHUJHG LPDJHV SRVVHVVHG WKH VSHFWUDO FKDUDFWHULVWLFV FRPSDUDEOH WR WKRVH RI WKH RULJLQDO /DQGVDW 70 GDWD 7KH GLVWRUWLRQ RI VSHFWUDO LQIRUPDWLRQ E\ WKH ,+6 PHWKRG ZDV DWWULEXWHG WR WKH IDFW WKDW WKH FXVWRPDU\ DVVXPSWLRQ RI VLPLODULW\ EHWZHHQ WKH ,+6 LQWHQVLW\ FRPSRQHQW

PAGE 49

DQG WKH SDQFKURPDWLF LPDJH LV QRW DOZD\V YDOLG :KHQ RQH H[DPLQHV WKH LPSOLFLW VSHFWUDO UHTXLUHPHQWV LQ D GHFUHDVLQJ RUGHU RI VSHFWUDO EDQGZLGWK IRU WKH + DQG 6 FRPSRQHQWVf E\ WKH ,+6 WUDQVIRUP DV GLVFXVVHG E\ +D\GQ HW DO f LW LV QRW VXUSULVLQJ WR UHFRJQL]H WKDW WKH GLVWRUWLRQV RI VSHFWUDO LQWHJULW\ ZRXOG EH LQHYLWDEOH LQ WKH WUDQVIRUPHG + DQG 6 FRPSRQHQWV 1RWH WKDW WKH UHTXLUHPHQW IRU GHFUHDVLQJ VSHFWUDO EDQGZLGWKV IRU WKH + DQG 6 FRPSRQHQWV ZRXOG JHQHUDOO\ UHVXOW LQ WKH QXPHULFDO YDOXHV RI WKRVH FRPSRQHQWV EHLQJ LQ WKH VDPH RUGHU ,Q XVLQJ WKH ,+6 WUDQVIRUPHG GDWD IRU SRVWn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f +H FRQWHQGHG WKDW WKH GDWD YROXPH IRU VWRUDJH DQG WUDQVPLVVLRQ FDQ EH VLJQLILFDQWO\ UHGXFHG LI D KLJK VSDWLDO UHVROXWLRQ PXOWLVSHFWUDO GDWDVHW FDQ EH FRQVWUXFWHG E\ FRPELQLQJ D KLJK VSDWLDO UHVROXWLRQ LPDJH ZLWK

PAGE 50

D UHODWLYHO\ ORZ VSDWLDO UHVROXWLRQ PXOWLVSHFWUDO GDWDVHW :LWK WKDW DUJXPHQW LQ PLQG WKH VSDWLDO UHVROXWLRQ RI WKH /DQGVDW 066 LPDJHV RI ZDYHEDQGV IRXU JUHHQf VL[ 1,5f DQG VHYHQ 1,5f ZLWK WKH RULJLQDO P VSDWLDO UHVROXWLRQ ZDV DUWLILFLDOO\ GHJUDGHG E\ D OLQHDU IDFWRU RI WKUHH WR D P VSDWLDO UHVROXWLRQ GDWDVHW 7KH RULJLQDO P UHVROXWLRQ LPDJH RI ZDYHEDQG ILYH UHGf UHPDLQHG XQFKDQJHG DQG ZDV XVHG DV WKH KLJK VSDWLDO UHVROXWLRQ LPDJH $VVXPLQJ WKDW DQ LPDJH FRQVLVWV RI ERWK VSHFWUDO DQG VSDWLDO FRPSRQHQWV WKH IROORZLQJ PHUJLQJ HJXDWLRQV ZHUH SURSRVHG 0, 066M N r + >@ DQG N D D >@ ZKHUH 0,L LV WKH UHFRQVWUXFWHG LPDJH L DQG VXEVFULSW f LV ZDYHEDQG LQGH[ + LV WKH KLJK IUHJXHQF\ VSDWLDO LQIRUPDWLRQ DQG D LV WKH LPDJHZLGH VWDQGDUG GHYLDWLRQ 7KH KLJK IUHJXHQF\ VSDWLDO FRPSRQHQW +f ZDV REWDLQHG E\ D VXEWUDFWLRQ EHWZHHQ WKH ORZSDVV DQG WKH KLJKSDVV ILOWHUHG LPDJHV RI ZDYHEDQG ILYH 1HZ LPDJHV ZLWK D P VSDWLDO UHVROXWLRQ ZHUH UHFRQVWUXFWHG WKURXJK SL[HOE\SL[HO PDQLSXODWLRQV XVLQJ HTXDWLRQV >@ DQG >@ 9LVXDO HYDOXDWLRQ RI WKH UHFRQVWUXFWHG LPDJHV LQGLFDWHG WKDW D JUHDW GHDO RI KLJK IUHTXHQF\ LQIRUPDWLRQ HGJHVf FRXOG EH UHVWRUHG H[FHSW IRU YHJHWDWLRQGRPLQDWHG DUHDV ZKHUH D UHYHUVH WRQDO DSSHDUDQFH

PAGE 51

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f XVLQJ /DQGVDW 066 ZDYHEDQGV IRXU JUHHQf ILYH UHGf DQG VHYHQ 1,5f 7KH KXH DQG VDWXUDWLRQ FRPSRQHQWV WUDQVIRUPHG IURP WKH WKUHH /DQGVDW 066 LPDJHV ZHUH HDFK DUELWUDULO\ GHJUDGHG 7KH VSDWLDO UHVROXWLRQ ZDV UHGXFHG E\ OLQHDU IDFWRUV RI WZR IRXU DQG VL[ ZKLFK FRUUHVSRQGHG WR GDWD FRPSUHVVLRQ IDFWRUV RI IRXU VL[WHHQ DQG WKLUW\VL[ UHVSHFWLYHO\ &RORU FRPSRVLWHV ZHUH UHJHQHUDWHG IRU HDFK GDWD FRPSUHVVLRQ IDFWRU XVLQJ WKH GHJUDGHG + DQG 6 FRPSRQHQWV DORQJ ZLWK WKH RULJLQDO FRPSRQHQW 9LVXDO FRPSDULVRQV RI WKH UHJHQHUDWHG FRORU FRPSRVLWHV WR WKDW RI WKH WKUHH RULJLQDO ZDYHEDQGV GLG QRW LQGLFDWH VXEVWDQWLDO TXDOLW\ GHWHULRUDWLRQ H[FHSW IRU WKH FDVH ZKLFK KDG D GDWD FRPSUHVVLRQ IDFWRU RI WKLUW\VL[ RU D [ OLQHDU UHVROXWLRQ IDFWRU $ KDOISL[HO VKLIWLQJ PHWKRG WR LPSURYH WKH HIIHFWLYH VSDWLDO UHVROXWLRQ RI UHPRWH VHQVLQJ GDWD ZDV VWXGLHG E\ '\H DQG :RRG f 7KH\ DUJXHG WKDW IRU D JLYHQ SL[HO LQ D

PAGE 52

VFHQH LPDJHG WZLFH RYHU D WLPH SHULRG ERWK LWV QXPHULFDO YDOXH DQG JHRJUDSKLF ORFDWLRQ ZRXOG QRW EH LGHQWLFDO EHFDXVH RI WKH SRWHQWLDO RIIVHW HUURUf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f SRLQWHG RXW WKH IROORZLQJ UHTXLUHPHQWV QHFHVVDU\ IRU WKLV KDOISL[HO VKLIWLQJ PHWKRG WR EH VXFFHVVIXO f WKH VFHQH PXVW EH LPDJHG VHYHUDO WLPHVf§ SUHIHUDEO\ PRUH WKDQ IRXU f WKHUH ZLOO EH QR VLJQLILFDQW FKDQJHV LQ WKH VFHQH HQYLURQPHQWV VSHFWUDOO\ VWDWLF REMHFWVf DQG f LPDJH JHRUHIHUHQFLQJ RU FRUHJLVWUDWLRQ PXVW EH YHU\ DFFXUDWH LQ RUGHU WR KDYH WKH SUHFLVH KDOISL[HO RIIVHW :LWK WKH DGYHQW RI JHRJUDSKLF LQIRUPDWLRQ V\VWHPV *,6f WHFKQLTXHV YDULRXV W\SHV RI JHRJUDSKLFDO GDWD LQFOXGLQJ H[LVWLQJ PDS GDWD DQG PXOWLGDWH LPDJHU\ GDWD KDYH EHHQ LQWHJUDWHG GXULQJ DQ LPDJH SURFHVVLQJ VFKHPH +RZHYHU WKH PDLQ SXUSRVH RI VXFK LPDJH SURFHVVLQJ HIIRUWV LV WR GHWHFW FKDQJHV UDWKHU WKDQ WR LPSURYH WKH VSDWLDO DQG UDGLRPHWULF

PAGE 53

TXDOLWLHV RI WKH ILQDO UHVXOWV 7R LPSURYH DJULFXOWXUDO ODQG XVH FODVVLILFDWLRQ /R HW DO f FRPELQHG WZR /DQGVDW 066 VFHQHV DFTXLUHG LQ GLIIHUHQW JURZLQJ VHDVRQV 7KH WZR VFHQHV ZHUH FRUHJLVWHUHG DQG VRPH ZDYHEDQG UDWLRLQJ ZDV XQGHUWDNHQ EHIRUH LQYRNLQJ ODQGXVH FODVVLILFDWLRQ SURFHGXUHV 8VLQJ WKLV PXOWLWHPSRUDO DSSURDFK WKH ODQGXVH FODVVLILFDWLRQ E\ DQ XQVXSHUYLVHG FODVVLILFDWLRQ VFKHPH ZDV LPSURYHG IURP b WR b +RZHYHU LW LV DUJXDEOH WKDW WKH LQIRUPDWLRQ DFFXPXODWHG IURP WKH WZR VFHQHV DQG WKH XVH RI PRUH VSHFWUDO ZDYHEDQGV ZRXOG GHILQLWHO\ EH D IDFWRU FRQWULEXWLQJ WR WKH LPSURYHPHQW RI FODVVLILFDWLRQ UHVXOWV $ VLPLODU VWXG\ IRU FRUQVR\EHDQ ILHOG FODVVLILFDWLRQV ZDV FRQGXFWHG E\ %DGKZDU HW DO f XVLQJ /DQGVDW 066 GDWD 7KHUH DUH PDQ\ RWKHU H[DPSOHV WKDW LQYROYHG WKH XVH RI VDWHOOLWH LPDJHU\ GDWD DQG WKHPDWLF RYHUOD\ WHFKQLTXHV )RU LQVWDQFH WKH VWXG\ E\ :DOVK HW DO f FRPELQHG /DQGVDW 70 LPDJHV ZLWK GLJLWDO HOHYDWLRQ PRGHO '(0f GDWD WR VWXG\ WKH K\GURORJLFDO SURFHVVHV LQ UXJJHG WHUUDLQ HQYLURQPHQWV DQG WKDW E\ 6KLK f ZKR FRPELQHG /DQGVDW 066 GDWD ZLWK WKH GLJLWL]HG YHUVLRQ RI WKH 8QLWHG 6WDWHV *HRORJLFDO 6XUYH\ 86*6f ODQG XVHODQG FRYHU PDSV ZLWKLQ D *,6 HQYLURQPHQW IRU ODQGXVH FODVVLILFDWLRQ FRPSDULVRQV 6XPPDU\ $VVHVVPHQW RI 3UREOHPV 0DQ\ VWXGLHV KDYH EHHQ PDGH WR GHYHORS LPDJH SURFHVVLQJ WHFKQLTXHV WR FRPELQH PXOWLUHVROXWLRQ LPDJHV IRU UHPRWH

PAGE 54

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

PAGE 55

FDWHJRUL]HG DV f OLQHDU FRPELQDWLRQ RI LPDJHV f SULQFLSDO FRPSRQHQW DQDO\VLV f UHJUHVVLRQ WHFKQLJXH ZKLFK LV VLPLODU WR OLQHDU FRPELQDWLRQ DQG f PXOWLSOLFDWLRQ RU SURGXFW LQFOXGLQJ VTXDUHURRW RI SURGXFWf 7KRXJK DUELWUDU\ DQG ODUJHO\ GHSHQGHQW RQ VSHFXODWLRQ WKHVH PHWKRGV SURYLGH NQRZOHGJH DERXW PHUJLQJ PXOWLUHVROXWLRQ LPDJHV 7KH VWXGLHV E\ 6FKRZHQJHUGW f &OLFKH HW DO f 3ULFH f &DUSHU HW DO f DQG &KDYH] HW DO f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

PAGE 56

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f DQG WKH PHWKRGV RI HQWHULQJ RU GLJLWL]LQJf UHIHUHQFH FRRUGLQDWHV PXVW DOVR EH DGGUHVVHG $6356 %ROVWDG HW DO DQG 7DQ DQG 6KLK Ef )RU WKH FXUUHQW PDS

PAGE 57

VWDQGDUG ZKLFK LV PP LQFKf WLPHV WKH UHFLSURFDO RI PDS VFDOH $3656 %ROVWDG HW DO f WKH JHRJUDSKLFDO HUURU IRU WKH 86*6 PLQXWH VHULHV PDSV f LV DERXW P DQG WKH GLJLWL]LQJ SURFHVV FRXOG LQWURGXFH DGGLWLRQDO HUURUV RI VLJQLILFDQW PDJQLWXGH 7DQ DQG 6KLK Ef 7KHUHIRUH LW ZLOO EH QHFHVVDU\ WR XWLOL]H KLJKSUHFLVLRQ WHFKQLTXHV VXFK DV WKH JOREDO SRVLWLRQLQJ V\VWHP *36f WR E\SDVV WKH LQWHUPHGLDWH UHIHUHQFH PDSf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

PAGE 58

FODVVLILFDWLRQV %DGKZDU HW DO /R HW DO f LW GRHV FUHDWH GLIILFXOWLHV LQ HYDOXDWLQJ WKH WHFKQLTXH )RUWXQDWHO\ IXWXUH VDWHOOLWH VHQVRU V\VWHPV FDQ SURYLGH VLPXOWDQHRXV PXOWLUHVROXWLRQ VHQVLQJ FDSDELOLWLHV DV ZHOO DV RQERDUG LPDJH FRUHJLVWUDWLRQ WHFKQLTXHV 6SRWOLJKW (26$7 D Ef 7KHUHIRUH WKH SUREOHPV ZLWK PXOWLGDWH PHUJLQJ DQG LPDJH FRUHJLVWUDWLRQ ZLOO QR ORQJHU EH D FRQFHUQ WR WKH XVHU FRPPXQLW\ RI IXWXUH VDWHOOLWH UHPRWH VHQVLQJ GDWD

PAGE 59

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

PAGE 60

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f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f 3ULFH f DQG &DUSHU HW DO f WKH PHWKRG RI OLQHDU

PAGE 61

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f DQG 0HQGHQKDOO HW DO f FRPELQLQJ ERWK VXPPLQJ XS DQG GLIIHUHQFLQJf WZR UDQGRP YDULDEOHV ; DQG ; ZLWK PHDQV DQG L DQG YDULDQFHV D DQG D UHVSHFWLYHO\ ZLOO FUHDWH

PAGE 62

D PHUJHG YDULDEOH @ 7KLV QHZ YDULDEOH < ZLOO KDYH D PHDQ YDOXH Q\f +\ D s 0 >@ DQG D YDULDQFH ^Df D D D 5 D s D 5 FRY;W ;f >@ ZKHUH D !f DQG !f DUH QXPHULFDO FRQVWDQWV DQG FRY; ;f LV WKH FRYDULDQFH EHWZHHQ ; DQG ; ,Q GLJLWDOO\ FRPELQLQJ LPDJHV < LV WKH PHUJHG LPDJH ; DQG ; UHSUHVHQW LPDJHV RQH DQG WZR WR EH FRPELQHG DQG WKH FRUUHVSRQGLQJ FRQVWDQWV D DQG 5 DUH RIWHQ FDOOHG ZHLJKWLQJ IDFWRUV RU PHUJLQJ FRHIILFLHQWV 7KH FRYDULDQFH FRY ; ;f WHUP LQ HTXDWLRQ >@ FDQ EH ZULWWHQ DV 0HQGHQKDOO HW DO f FRY; ;f U D D >@ ZKHUH D DQG D DUH WKH VWDQGDUG GHYLDWLRQV DQG U LV WKH FRUUHODWLRQ FRHIILFLHQW IRU ; DQG ; 7KH YDOXH RI U FDQ EH QHJDWLYH RU SRVLWLYH GHSHQGLQJ RQ WKH DFWXDO UHODWLRQVKLS EHWZHHQ YDULDEOHV ; DQG ; 6XEVWLWXWLQJ WKH FRYDULDQFH RI HTXDWLRQ >@ LQWR HTXDWLRQ >@ ZLOO \LHOG D D D 5 D s D 5 U D D >@ ZKLFK LV WKH HTXDWLRQ IRU FDOFXODWLQJHVWLPDWLQJ WKH YDULDQFH RI D PHUJHG YDULDEOH EDVHG RQ WKH PHUJLQJ FRHIILFLHQWV WKH

PAGE 63

YDULDQFHV RU VWDQGDUG GHYLDWLRQVf DQG WKH FRUUHODWLRQ FRHIILFLHQW IRU ; DQG ; )RU D PHUJHG LPDJH WKH TXDOLW\ IDFWRU RI JUHDWHVW FRQFHUQ LV WKH FRQWUDVW RU JUD\ VKDGHVf DQG WKH FRQWUDVW RI DQ LPDJH LV GLUHFWO\ UHODWHG WR WKH YDULDQFH RI LPDJH UDGLRPHWULF GDWD )RU LQVWDQFH DQ LPDJH ZLOO KDYH QR FRQWUDVW LI LWV UDGLRPHWULF YDULDQFH LV ]HUR 7KHUHIRUH DWWHQWLRQ LQ WKH FRQWLQXLQJ GLVFXVVLRQ ZLOO EH JLYHQ WR WKH YDULDQFH D\f RI PHUJHG YDULDEOH < )URP HTXDWLRQ >@ WKH IDFWRUV WKDW FROOHFWLYHO\ DIIHFW WKH UDGLRPHWULF YDULDQFH RU FRQWUDVW RI D PHUJHG LPDJH DUH WKH ZHLJKWLQJ FRHIILFLHQWV D DQG WKH FRUUHODWLRQ FRHIILFLHQW Uf DQG WKH YDULDQFHV DA DQG Df RI WKH WZR LPDJHV WR EH FRPELQHG 7R DVVLVW WKH HIIRUWV LQ H[DPLQLQJ WKH HIIHFWV RI WKHVH YDULRXV IDFWRUV RQ WKH YDULDQFH X\f RI PHUJHG YDULDEOH < LW ZRXOG EH DGYDQWDJHRXV WR UHGXFH WKH QXPEHU RI WKH LQYROYHG HOHPHQWV LQ HTXDWLRQ >@ 2QH PHWKRG WR DFKLHYH WKDW LV WR QRUPDOL]H WKH YDULDQFHV RI ; DQG ; WR XQLW\ f XVLQJ WKH IROORZLQJ HTXDWLRQ R" D >@ ZKHUH D DQG D DUH WKH QRUPDOL]HG YDULDQFHV IRU ; DQG ; UHVSHFWLYHO\ ,I WKH FRQGLWLRQ RrR] LV VDWLVILHG Rr DQG D DUH GHILQHG UHVSHFWLYHO\ DV D >@

PAGE 64

DQG >@ )RU HDV\ FRPSDULVRQV OHW D DOVR EH QRUPDOL]HG WR RRf E\ WKH IROORZLQJ HTXDWLRQ &7 < D >@ ZKHUH D LV WKH QRUPDOL]HG YDULDQFH RI < 1RWH WKDW WKH f§\ QRUPDOL]HG YDOXHV DUH D UHODWLYH PHDVXUH IRU WKH YDULDQFHV RI ; ; DQG < 'LYLGLQJ HTXDWLRQ >@ E\ RRf DQG PDNLQJ UHDUUDQJHPHQWV WKURXJK WKH XVH RI HTXDWLRQV >@ >@ > @ DQG >@ ZLOO \LHOG D D 5 Rf s D 5 U D OJBf >D@ %HFDXVH WKH YDULDQFHV RI ; DQG ; DUH QRUPDOL]HG WR XQLW\ HTXDWLRQ >D@ FDQ DOVR EH ZULWWHQ DV D D ODf 5 D s D U D ORBf >E@ ZKHUH Af >OOD@ -^4Bf >OOE@

PAGE 65

7KUHH EHQHILWV UHVXOW IURP QRUPDOL]LQJ WKH YDULDQFHV RI ; DQG ; 7KHVH EHQHILWV DUH f UHGXFWLRQ RI WKH QXPEHU RI WKH LQYROYHG IDFWRUV LQ HTXDWLRQ >@ f UHOLHI IURP JHWWLQJ LQYROYHG ZLWK DFWXDO LPDJH GDWD IRU FRQFHSWXDO GLVFXVVLRQV DQG f HDV\ FRPSDULVRQ RI WKH YDULDQFH RI WKH PHUJHG YDULDEOH ZLWK WKRVH RI WKH RULJLQDO YDULDEOHV ,W EHFRPHV FOHDU WKDW HTXDWLRQ >D@ RU >E@f LV WKH EDVLF UHODWLRQ WKDW UHIOHFWV WKH HIIHFWV RI WKH YDULRXV IDFWRUV D % U DQG Df RQ WKH UDGLRPHWULF YDULDQFH RU FRQWUDVW D\f RI D PHUJHG LPDJH $ FRPSDULVRQ RI WKH UHODWLRQV EHWZHHQ HTXDWLRQV >@ DQG ERWK >D@ DQG >E@ UHYHDOV WKDW WKH RQO\ GLVWLQFWLRQ EHWZHHQ VXPPDWLRQ DQG GLIIHUHQFLQJ RI WZR YDULDEOHV LV WKH s VLJQ IRU WKH ODVW WHUPV LQ HTXDWLRQV >D@ DQG >E@ 7KHUHIRUH LQ WKH FRQWH[W RI HYDOXDWLQJ WKH YDULDQFH RI WKH PHUJHG YDULDEOH GLIIHUHQFLQJ WZR QHJDWLYHO\ FRUUHODWHG YDULDEOHV Uf LV WHFKQLFDOO\ LGHQWLFDO WR VXPPLQJ XS WZR SRVLWLYHO\ FRUUHODWHG RQHV U!f %HFDXVH PHUJHG LPDJH GDWD PXVW EH SRVLWLYH GLIIHUHQFLQJ WZR LPDJHV PD\ UHTXLUH WKH DGGLWLRQ RI D SRVLWLYH FRQVWDQW &f WR WKH HQG RI HTXDWLRQ > @ VXFK WKDW < D;; & >@ LQ RUGHU WR DYRLG QHJDWLYH LPDJH GDWD +RZHYHU IURP WKH UHODWLRQV RI HTXDWLRQ >@ WKH FRQVWDQW & LQ HTXDWLRQ > @ ZKLFK LV XVXDOO\ GHWHUPLQHG E\ D SUHPHUJLQJ VFDQQLQJ RI

PAGE 66

WKH JLYHQ LPDJH GDWD ZLOO QRW DIIHFW WKH UDGLRPHWULF YDULDQFH RI WKH GLIIHUHQFHG LPDJH ,Q SUDFWLFDO DSSOLFDWLRQV ZKHUH WZR LPDJHV DUH JLYHQ WKH UDGLRPHWULF YDULDQFHV D DQG Df DQG WKH FRUUHODWLRQ FRHIILFLHQW Uf DUH NQRZQ 7KH RQO\ IDFWRUV WKDW QHHG WR EH GHWHUPLQHG IRU HTXDWLRQ >@ DUH WKH PHUJLQJ FRHIILFLHQWV D DQG )URP WKH UHODWLRQV RI HJXDWLRQ >@ DQG EDVHG RQ WKH JLYHQ IDFWRUV D D DQG U WKH VHOHFWLRQ RI DSSURSULDWH PHUJLQJ FRHIILFLHQWV D DQG IRU HJXDWLRQ >@ LV WKH NH\ IDFWRU WKDW DIIHFWV WKH UDGLRPHWULF YDULDQFH RI PHUJHG LPDJH GDWD 7R DVVHVV WKH LPSDFWV RI WKHVH PHUJLQJ FRHIILFLHQWV D DQG 5f RQ WKH UDGLRPHWULF YDULDQFH RI PHUJHG LPDJHV WKUHH DSSURDFKHV IRU GLJLWDOO\ FRPELQLQJ LPDJHV ZLOO EH GLVFXVVHG ,Q DGGLWLRQ RI WKH WZR LPDJHV ; DQG ;f WR EH FRPELQHG ; ZLOO EH GHQRWHG DV WKH SULPDU\ LPDJH DQG ; DV WKH VHFRQGDU\ LPDJH LQ RUGHU WR GLVWLQJXLVK WKHLU UHODWLYH LPSRUWDQFH LQ WKH PHUJLQJ SURFHVV :KHQ DFWXDO LPDJH GDWD DUH XVHG WKH SULPDU\ LPDJH ;f ZLOO EH DVVXPHG WR FRQWDLQ SULPDU\ LQIRUPDWLRQ ZKLOH WKH VHFRQGDU\ LPDJH ;f LV XVHG DV WKH VXSSOHPHQWDU\ GDWD IRU LPSURYLQJ WKH SULPDU\ LPDJH &RQILQLQJ 0HWKRG 7KH ILUVW PHWKRG WR EH GLVFXVVHG LV WKH FRQILQLQJ PHWKRG ZKLFK LV GHILQHG PDWKHPDWLFDOO\ DV @

PAGE 67

ZKHUH @ VXFK WKDW D 5 >D@ ZKLFK FDQ EH ZULWWHQ DOWHUQDWLYHO\ LQ WKH IROORZLQJ IRUPV RI D 5 >E@ DQG 5 D >F@ %HFDXVH WKH PHUJHG LPDJH GDWD LV DXWRPDWLFDOO\ FRQILQHG WR WKH G\QDPLF UDQJH WKLV PHUJLQJ PHWKRG LV FDOOHG WKH FRQILQLQJ DSSURDFK /HW R DQG R GHQRWH WKH QRUPDOL]HG UDGLRPHWULF YDULDQFHV IRU WKH SULPDU\ ;A DQG VHFRQGDU\ ;f LPDJHV UHVSHFWLYHO\ %HFDXVH WKH JHQHUDO SXUSRVH WR FRPELQH LPDJHV LV WR XVH WKH FRPSOHPHQWDU\ VHFRQGDU\ LPDJH GDWD IRU LPSURYLQJ WKH SULPDU\ LPDJH WKH ZHLJKWLQJ FRHIILFLHQW 5 IRU WKH VHFRQGDU\ LPDJH ZLOO EH RI JUHDWHU LQWHUHVW )RU WKLV UHDVRQ WKH UHODWLRQ RI HTXDWLRQ >E@ LV SUHIHUUHG DQG E\ VXEVWLWXWLQJ LW LQWR HTXDWLRQ >@ WKH IROORZLQJ UHODWLRQ

PAGE 68

LV REWDLQHG DV @ ,Q FRPSDULQJ HTXDWLRQ >@ ZLWK WKH UHODWLRQV EHWZHHQ HTXDWLRQV >@ DQG >D@ RU >E@f WKH QRUPDOL]HG YDULDQFH RAf RI PHUJHG LPDJH D@ 6LQFH WKH YDULDQFHV RI ; DQG ; DUH QRUPDOL]HG WR XQLW\ HTXDWLRQ >D@ FDQ DOVR EH ZULWWHQ DV RM f Df D U f D ODf >E@ 7KH IROORZLQJ UHODWLRQV IRU WKH QRUPDOL]DWLRQ RI YDULDQFHV DUH DOVR QHHGHG LQ RUGHU WR XVH HTXDWLRQ >D@ RU >E@ e‘ r] >@ \Df >@ e ef f >@ )URP HTXDWLRQV >D@ DQG >E@ WKH UDGLRPHWULF YDULDQFH DFf RI DQ LPDJH PHUJHG E\ WKH FRQILQLQJ PHWKRG LV LQIOXHQFHG RQO\ E\ WKH VHFRQGDU\ LPDJH FRHIILFLHQW 7KH YDOXH ZLOO

PAGE 69

KDYH D GLUHFW LPSDFW RQ F f§ D PHDVXUH RI WKH UDGLRPHWULF TXDOLW\ RI D PHUJHG LPDJH E\ WKH FRQILQLQJ PHWKRG ,Q FRPELQLQJ PXOWLUHVROXWLRQ LPDJHV VHOHFWLQJ DQ DSSURSULDWH 5 YDOXH LV SDUWLFXODUO\ LPSRUWDQW EHFDXVH LW QRW RQO\ DIIHFWV WKH UDGLRPHWULF YDULDQFH EXW DOVR LQGLUHFWO\ LPSDFWV WKH VSHFWUDO LQIRUPDWLRQ RI WKH HQWLUH PHUJHG GDWDVHW )RU LQVWDQFH LI D ODUJH 5 LV XVHG WR PHUJH D SDQFKURPDWLF LPDJH WR HDFK LPDJH LQ D PXOWLZDYHEDQG GDWDVHW DOO WKH LPDJHV LQ WKH UHVXOWDQW PHUJHG GDWDVHW ZLOO EH YHU\ VLPLODU WR HDFK RWKHU $VVXPLQJ WKDW WKH YDULDQFHV RI WKH SULPDU\ ;f DQG VHFRQGDU\ ;f LPDJHV DUH HTXDO RU FORVH WR HDFK RWKHU WKH UHODWLRQ RI DF DV D IXQFWLRQ RI ZHLJKWLQJ IDFWRU 5 LV GHSLFWHG LQ )LJXUH IRU WKH FRQILQLQJ PHWKRG $OWKRXJK WKH JUDSKV LQ )LJXUH FDQ WLOW VRPHZKDW IURP RQH VLGH WR WKH RWKHU LQ UHVSRQVH WR WKH YDULDQFH GLIIHUHQFH EHWZHHQ WKH SULPDU\ DQG VHFRQGDU\ LPDJHV IRXU LPSRUWDQW REVHUYDWLRQV FDQ EH PDGH IRU WKH FRQILQLQJ PHWKRG )LUVW WKH UDGLRPHWULF YDULDQFH RI D PHUJHG LPDJH E\ WKH FRQILQLQJ PHWKRG LV OLNHO\ WR EH VPDOOHU WKDQ WKDW RI HLWKHU WKH SULPDU\ DQG VHFRQGDU\ LPDJH GDWD $ VPDOOHU UDGLRPHWULF YDULDQFH LPSOLHV WKDW WKH PHUJHG LPDJH E\ WKH FRQILQLQJ PHWKRG ZLOO KDYH ORZ FRQWUDVW DQG LQIHULRU UDGLRPHWULF GDWD 6HFRQG WKH VWDWH SRVLWLYH RU QHJDWLYHf DV ZHOO DV WKH VWUHQJWK RI FRUUHODWLRQ EHWZHHQ WKH SULPDU\ DQG VHFRQGDU\ LPDJH LPDJHV DOVR KDV D VWURQJ HIIHFW RQ WKH UDGLRPHWULF

PAGE 70

1RUPDOL]HG YDULDQFH RI PHUJHG GDWD 1RWH D t )LJXUH 5HODWLRQ RI UDGLRPHWULF YDULDQFH WR PHUJLQJ FRHIILFLHQW f DQG FRUUHODWLRQ FRHIILFLHQW Uf IRU WKH FRQILQLQJ PHWKRG XL YM

PAGE 71

YDULDQFH RI D PHUJHG LPDJH ,I WKH SULPDU\ LPDJH LV QHJDWLYHO\ FRUUHODWHG WR WKH VHFRQGDU\ LPDJH WKH ORVV RI UDGLRPHWULF LQIRUPDWLRQ LQ WKH PHUJHG LPDJH D@ RU >E@f ZLWK UHVSHFW WR 5 reFf f ILODf GIL U D -OR\f %f >@

PAGE 72

DQG WKHQ VHWWLQJ WKH ILUVW GHULYDWLYH WR HTXDO WR ]HUR VXFK DV OFfRr %FODf UD OFf >@ 7KURXJK WKH XVH RI HTXDWLRQV >@ >@ >@ DQG >@ WKH %F YDOXH FDQ EH HVWLPDWHG E\ WKH IROORZLQJ HTXDWLRQ D UD D %F f§ >@ RI r U D D ZKHUH D DQG D DUH WKH YDULDQFHV D DQG R DUH WKH VWDQGDUG GHYLDWLRQVf RI WKH SULPDU\ DQG VHFRQGDU\ LPDJHV UHVSHFWLYHO\ 1RWH WKDW WKH UDQJH RI YDOLG YDOXHV IRU LV WR ,I F LV RXWVLGH WKH UDQJH WKH PLQLPXP UDGLRPHWULF YDULDQFH RI D PHUJHG LPDJH ZLOO QRW H[LVW ZLWKLQ WKDW UDQJH 2EWDLQLQJ WKH %F YDOXH EHIRUH PHUJLQJ WKH LPDJHV ZLOO JLYH D ILUVW DVVHVVPHQW RQ WKH YDULDQFH RI D PHUJHG LPDJH )RU LQVWDQFH LI %F WKH UDGLRPHWULF YDULDQFH RI PHUJHG GDWD LV DQ LQFUHDVLQJ IXQFWLRQ ZLWK LPSO\LQJ WKDW DQ LPSURYHPHQW IRU LPDJH FRQWUDVW LV SRVVLEOH ,I %F m WKH YDULDQFH RI PHUJHG GDWD ZLOO GHFUHDVHV DV % LQFUHDVHV $V D UHVXOW WKH FRQWUDVW RI WKH PHUJHG LPDJH ZLOO GHWHULRUDWH %\ VXEVWLWXWLQJ %F LQWR HTXDWLRQ >D@ RU >E@f DQG E\ XVLQJ WKH UHODWLRQV RI HTXDWLRQV >@ >@ >@ DQG > @ WKH PLQLPXP YDULDQFH DPf IRU DQ LPDJH PHUJHG E\ WKH FRQILQLQJ PHWKRG FDQ EH HVWLPDWHG DV

PAGE 73

D D Uf U D >@ &DXWLRQ VKRXOG EH H[HUFLVHG LQ XVLQJ HTXDWLRQ >@ WR HVWLPDWH WKH PLQLPXP UDGLRPHWULF YDULDQFH RI D PHUJHG LPDJH ,I tF LV QRW ZLWKLQ WKH UDQJH WKH HVWLPDWHG PLQLPXP UDGLRPHWULF YDULDQFH LV D IDOVH YDOXH WKDW FDQQRW H[LVW IRU D PHUJHG LPDJH )RXUWK DV t FRQWLQXHV WR LQFUHDVH EH\RQG WKH 5F YDOXH WKH YDULDQFH RI PHUJHG LPDJH
PAGE 74

1RUPDOL]HG YDULDQFH RI PHUJHG GDWD 1RWH U FRUUHODWLRQ FRHIILFLHQW )LJXUH (IIHFW RI YDULDQFH GLIIHUHQFH RQ WKH UDGLRPHWULF TXDOLW\ RI PHUJHG LPDJHV IRU WKH FRQILQLQJ PHWKRG

PAGE 75

E\ JUDSKV f DQG f RI )LJXUH ,I WKH SULPDU\ LPDJH KDV D VPDOOHU YDULDQFH WKH UDGLRPHWULF LQIRUPDWLRQ LQ WKH PHUJHG LPDJH ZLOO HLWKHU LQFUHDVH RU GHFUHDVH GHSHQGLQJ RQ WKH PDJQLWXGH RI WKH YDULDQFH GLIIHUHQFH DV ZHOO DV WKH VWDWH RI FRUUHODWLRQ EHWZHHQ WKH WZR LPDJHV DV VKRZQ E\ JUDSKV f DQG f LQ )LJXUH 1RWH WKDW RQO\ ZKHQ WKH SULPDU\ LPDJH KDV D YHU\ VPDOO YDULDQFH UHODWLYH WR WKDW RI WKH VHFRQGDU\ LPDJH DQG WKH FRUUHODWLRQ EHWZHHQ WKH WZR LPDJHV WR EH FRPELQHG LV KLJK DQG SRVLWLYH ZLOO DQ LPDJH PHUJHG E\ WKH FRQILQLQJ PHWKRG KDYH DQ HQKDQFHG FRQWUDVW 7KLV LQGLFDWHV WKDW f WKH FRQILQLQJ PHWKRG LV QRW DQ HIIHFWLYH PHUJLQJ DSSURDFK IRU GLJLWDOO\ FRPELQLQJ LPDJHV DQG f WKH GHWHUPLQDWLRQ RI D % YDOXH IRU WKH FRQILQLQJ PHWKRG FDQ QRW EH DUELWUDU\ QRU LQGHSHQGHQW RI WKH IDFWRUV VXFK DV WKH YDULDQFH GLIIHUHQFH DQG WKH FRUUHODWLRQ EHWZHHQ WKH WZR FRPELQLQJ LPDJHV 7KH ZD\ E\ ZKLFK WKH PHUJLQJ FRHIILFLHQWV DUH GHWHUPLQHG DIL Of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f DQG f LQ )LJXUH 2Q WKH RWKHU KDQG WKH HIIHFW ZLOO EH

PAGE 76

GHOHWHULRXV WR WKH UDGLRPHWULF TXDOLW\ RI D PHUJHG LPDJH DV LOOXVWUDWHG E\ JUDSKV f DQG f LQ )LJXUH ,Q VXPPDU\ IRU WKH FRQILQLQJ DSSURDFK D% Of WKH IROORZLQJ REVHUYDWLRQV DUH DV IROORZV f 7KH UHVXOWDQW PHUJHG LPDJH ZLOO OLNHO\ KDYH D VPDOOHU UDGLRPHWULF YDULDQFH RU ORZHU FRQWUDVW XQOHVV WKH SULPDU\ LPDJH KDV D YHU\ VPDOO YDULDQFH UHODWLYH WR WKDW RI WKH VHFRQGDU\ LPDJH DQG WKH FRUUHODWLRQ EHWZHHQ WKH WZR FRPELQLQJ LPDJHV LV KLJK DQG SRVLWLYH f 7KHUH PD\ H[LVW D 5F YDOXH DW ZKLFK WKH UDGLRPHWULF YDULDQFH RU FRQWUDVW RI WKH PHUJHG LPDJH ZLOO EH PLQLPXP WKHUHIRUH WKH VHOHFWLRQ RI YDOXHV FORVH RU HTXDO WR -F VKRXOG EH DYRLGHG f 7ZR LPDJHV ZLWK D QHJDWLYH FRUUHODWLRQ VKRXOG EH GLIIHUHQFHG UDWKHU WKDQ VXPPHG LQ RUGHU WR PLQLPL]H WKH ORVV RI UDGLRPHWULF LQIRUPDWLRQ f ,Q JHQHUDO WKH FRQWUDVW RU YDULDQFHf DQG EULJKWQHVV RI DQ LPDJH PHUJHG E\ WKH FRQILQLQJ PHWKRG FDQ EH FRQVLGHUHG DV D FRPSURPLVH IRU HDFK RI WKHVH WZR TXDOLW\ IDFWRUV EHWZHHQ WKH SULPDU\ DQG VHFRQGDU\ LPDJHV 3UHVHUYLQJ 0HWKRG )RU PRVW VDWHOOLWH LPDJHU\ WKH VSUHDG RI LPDJH GLJLWDO GDWD GRHV QRW H[WHQG WKURXJKRXW WKH HQWLUH G\QDPLF UDQJH )RU D W\SLFDO DJULFXOWXUDO VFHQH WKH GDWD VSUHDG LV DERXW b RI WKH UDQJH LQ /DQGVDW LPDJHU\ 3ULFH f ZKLOH D PXFK VPDOOHU UDQJH LV RIWHQ IRXQG IRU 6327 LPDJHV 7KHUHIRUH WKH XWLOLW\ RI WKH ELW GDWD GHSWK IRU WKHVH

PAGE 77

LPDJHV KDV QRW EHHQ IXOO\ XWLOL]HG ,Q PHUJLQJ VDWHOOLWH LPDJHV VXFK D GHILFLHQF\ FDQ EH WXUQHG LQWR DQ DGYDQWDJH E\ PDLQWDLQLQJ WKH SULPDU\ LPDJH XQFKDQJHG D Of ZKLOH WKH VHFRQGDU\ LPDJH GDWD LV PHUJHG +HQFH WKLV PHWKRG LV FDOOHG WKH SUHVHUYLQJ DSSURDFK %\ XVLQJ WKH SUHVHUYLQJ DSSURDFK WR FRPELQH LPDJHV WKH IROORZLQJ PHUJLQJ DOJRULWKP LV XVHG @ ZKHUH 5 LV ZHLJKWLQJ FRHIILFLHQW @ DQG >D@ RU >E@f LQGLFDWHV WKDW WKH QRUPDOL]HG YDULDQFH eSf RI DQ LPDJH PHUJHG E\ WKH SUHVHUYLQJ PHWKRG FDQ EH HVWLPDWHG E\ 2S R 5ORf U D -Df >D@ 6LQFH WKH YDULDQFHV RI WKH SULPDU\ ;f DQG VHFRQGDU\ ;f LPDJHV DUH QRUPDOL]HG WR XQLW\ HTXDWLRQ >D@ FDQ DOVR EH ZULWWHQ DV 2S ODf 5 R U% D Rf >E@ ,Q ERWK HTXDWLRQV >D@ DQG >E@ 5 LV WKH ZHLJKWLQJ FRHIILFLHQW DQG U LV WKH FRUUHODWLRQ FRHIILFLHQW IRU WKH SULPDU\ ;f DQG VHFRQGDU\ ;f LPDJHV 1RWH WKDW WKH YDULDQFH

PAGE 78

RI PHUJHG LPDJH @ >@ DQG >@ DUH QHHGHG ZKHQ XVLQJ HTXDWLRQ >D@ RU >E@f IRU DVVHVVLQJ WKH UDGLRPHWULF YDULDQFH RI D PHUJHG LPDJH $V PHQWLRQHG HDUOLHU WKH RQO\ GLVWLQFWLRQ EHWZHHQ VXPPDWLRQ DQG GLIIHUHQFLQJ RI WZR LPDJHV LV WKH s VLJQ IRU WKH ODVW WHUP RI HTXDWLRQ >D@ RU >E@f 7KXV GLIIHUHQFLQJ WZR QHJDWLYHO\ FRUUHODWHG LPDJHV Uf LV LGHQWLFDO WR VXPPLQJ XS WZR SRVLWLYHO\ FRUUHODWHG RQHV U!f )LJXUH VKRZV WKH QRUPDOL]HG YDULDQFH DU RI PHUJHG LPDJHV E\ WKH SUHVHUYLQJ PHWKRG DV D IXQFWLRQ RI ERWK WKH PHUJLQJ FRHIILFLHQW f DQG WKH FRUUHODWLRQ FRHIILFLHQW Uf :KHQ WKH SULPDU\ DQG VHFRQGDU\ LPDJHV DUH QRW QHJDWLYHO\ FRUUHODWHG WKH YDULDQFH RI DQ LPDJH PHUJHG E\ WKH SUHVHUYLQJ PHWKRG LV DQ LQFUHDVLQJ IXQFWLRQ ZLWK PHUJLQJ FRHIILFLHQW 5 DV VKRZQ LQ JUDSKV f WKURXJK f RI )LJXUH 7KLV LPSOLHV WKDW WKH UDGLRPHWULF YDULDQFH FRQWUDVWf RI DQ LPDJH PHUJHG E\ WKH SUHVHUYLQJ PHWKRG ZLOO VXUHO\ LPSURYH SURYLGHG WKDW WKH FRUUHODWLRQ FRHIILFLHQW LV U! 8QOLNH WKH FRQILQLQJ PHWKRG ZKLFK WHQGV WR PDNH D FRPSURPLVH EHWZHHQ WKH VHFRQGDU\ DQG VHFRQGDU\ LPDJHV WKH SUHVHUYLQJ PHWKRG GRHV QRW VXEGXH EHFDXVH D Of WKH UDGLRPHWULF YDULDQFH RI WKH SULPDU\ LPDJH GXULQJ WKH PHUJLQJ SURFHVV &RQVHTXHQWO\ WKH PHUJHG GDWD DUH DOZD\V HQKDQFHG HYHQ ZKHQ WKH LPDJHV WR EH FRPELQHG DUH QRW FRUUHODWHG U f DV VKRZQ LQ JUDSK f RI )LJXUH 7KH UHVXOWV IURP FRPELQLQJ WZR QHJDWLYHO\ FRUUHODWHG LPDJHV DUH DOVR VKRZQ E\ JUDSKV f DQG f RI )LJXUH

PAGE 79

1RUPDOL]HG YDULDQFH RI PHUJHG GDWD 1RWH D O DQG IL! )LJXUH 5HODWLRQ RI UDGLRPHWULF YDULDQFH WR PHUJLQJ FRHIILFLHQW f DQG FRUUHODWLRQ FRHIILFLHQW Uf IRU WKH SUHVHUYLQJ PHWKRG &7L 7L

PAGE 80

$SSDUHQWO\ DQ\ LPSURYHPHQW RQ WKH UDGLRPHWULF YDULDQFH RI PHUJHG LPDJH @ LQ RUGHU WR NHHS WKH PHUJHG LPDJH GDWD ZLWKLQ WKH UDQJH ,Q WKLV FDVH WKH

PAGE 81

1RUPDOL]HG YDULDQFH RI PHUJHG GDWD 1RWH U FRUUHODWLRQ FRHIILFLHQW )LJXUH (IIHFW RI YDULDQFH GLIIHUHQFH RQ WKH UDGLRPHWULF TXDOLW\ RI PHUJHG LPDJHV IRU WKH SUHVHUYLQJ PHWKRG

PAGE 82

XVH RI DQ DGGLWLRQDO VFDOLQJ IDFWRU ZLOO PDNH WKH SUHVHUYLQJ PHWKRG OHVV HIIHFWLYH RU HYHQ VLPLODU WR WKH FRQILQLQJ PHWKRG ,Q VXPPDU\ VHYHUDO REVHUYDWLRQV DUH PDGH IRU WKH SUHVHUYLQJ DSSURDFK f LI WKH FRUUHODWLRQ FRHIILFLHQW Uf EHWZHHQ WKH SULPDU\ DQG VHFRQGDU\ LPDJHV LV QRQQHJDWLYH U!f WKH LPDJH FRQWUDVW LQ WKH PHUJHG GDWD ZLOO VXUHO\ EH HQKDQFHG E\ WKH SUHVHUYLQJ PHWKRG f DV FRPSDUHG WR WKDW RI WKH FRQILQLQJ PHWKRG D% Of WKH HIIHFW RI WKH YDULDQFH GLIIHUHQFH EHWZHHQ WKH WZR FRPELQLQJ LPDJHV ZLOO QRW FUHDWH D QHJDWLYH LPSDFW RQ WKH UDGLRPHWULF YDULDQFH RI D PHUJHG LPDJH E\ WKH SUHVHUYLQJ PHWKRG SURYLGHG WKDW WKH FRUUHODWLRQ LV QRQQHJDWLYH U f f WKH SUHVHUYLQJ PHWKRG ZKLFK GRHV QRW VXEGXH D Of WKH SULPDU\ LPDJH LQ WKH GLJLWDO PHUJLQJ SURFHVV ZLOO PDNH LW OHVV OLNHO\ WKDW WKH VSHFWUDO VLJQDWXUHV RI WKH RULJLQDO PXOWLVSHFWUDO GDWDVHW ZLOO EH DOWHUHG RU FRUUXSWHG LQ D PHUJHG GDWDVHW f WZR LPDJHV ZLWK D VWURQJ QHJDWLYH FRUUHODWLRQ U}Of VKRXOG EH GLIIHUHQFHG LQVWHDG RI VXPPHG WRJHWKHU LQ RUGHU WR DYRLG D SRWHQWLDO ORVV RI UDGLRPHWULF LQIRUPDWLRQ LQ WKH PHUJHG LPDJH DQG f WKH SUHVHUYLQJ PHWKRG KDV ERWK D PXFK VPDOOHU VHQVLWLYLW\ WR WKH VWUHQJWK RI FRUUHODWLRQ DQG D ODUJHU UDQJH RI 5 YDOXHV WR XVH EHFDXVH D PLQLPXP YDULDQFH GRHV QRW H[LVW SURYLGHG WKDW U! 'LIIHUHQFLQJ 0HWKRG )URP SUHYLRXV GLVFXVVLRQV RQ ERWK WKH FRQILQLQJ DQG WKH SUHVHUYLQJ PHWKRGV LW LV NQRZQ WKDW LQ RUGHU WR HQKDQFH WKH

PAGE 83

UDGLRPHWULF YDULDQFH RI PHUJHG LPDJH GDWD IURP QHJDWLYHO\ FRUUHODWHG ZDYHEDQGV Uf WKH GLIIHUHQFLQJ PHWKRG PXVW EH XVHG 7R HQVXUH WKDW WKH PHUJHG GDWD ZLOO EH SRVLWLYH D FRQVWDQW PXVW EH DGGHG WR WKH PHUJHG GDWD 7KHUHIRUH WKH IROORZLQJ UHODWLRQ ZLOO EH XVHG DV WKH PHUJLQJ HTXDWLRQ IRU WZR QHJDWLYHO\ FRUUHODWHG LPDJHV @ ZKHUH 5 !f LV D ZHLJKWLQJ FRHIILFLHQW & !f LV D FRQVWDQW WR DYRLG QHJDWLYH PHUJHG GDWD @ ZLWK WKH UHODWLRQVKLS EHWZHHQ HTXDWLRQV >@ DQG >D@ RU >E@f WKH QRUPDOL]HG UDGLRPHWULF YDULDQFH 2Ff RI D PHUJHG LPDJH E\ HTXDWLRQ >@ FDQ EH HVWLPDWHG E\ JM ODf %D UIO J -^OJf >D@ 6LQFH WKH YDULDQFHV RI SULPDU\ DQG VHFRQGDU\ LPDJHV DUH QRUPDOL]HG WR XQLW\ HTXDWLRQ >D@ FDQ DOVR EH ZULWWHQ DV JM J] 5OJ]f U% D -OJIf >E@ ,Q ERWK HTXDWLRQV >D@ DQG >E@ U LV WKH FRUUHODWLRQ FRHIILFLHQW IRU WKH SULPDU\ DQG VHFRQGDU\ LPDJHV DQG 5 LV D ZHLJKWLQJ FRHIILFLHQW 1RWH WKDW WKH YDULDQFH RI WKH PHUJHG LPDJH LV QRUPDOL]HG WR WKH VXP RI WKH YDULDQFHV R]R]f RI

PAGE 84

WKH SULPDU\ DQG VHFRQGDU\ LPDJHV $JDLQ WKH UHODWLRQV RI QRUPDOL]DWLRQ HTXDWLRQV >@ >@ DQG >@ DUH QHHGHG LQ RUGHU WR XVH HTXDWLRQ >D@ RU >E@f IRU HVWLPDWLQJ WKH UDGLRPHWULF YDULDQFH RI D SUHGLIIHUHQFHG LPDJH %HFDXVH WKH ODVW WHUP LQ HTXDWLRQ >D@ RU >E@f LV QHJDWLYH DQG WKH FRUUHODWLRQ FRHIILFLHQW Uf LV DOVR QHJDWLYH WKH UHODWLRQ RI HTXDWLRQ >D@ RU >E@f LV LGHQWLFDO WR WKDW RI HTXDWLRQ >D@ RU >E@f RI WKH SUHVHUYLQJ PHWKRG GLVFXVVHG SUHYLRXVO\ 7KHUHIRUH DGGLWLRQDO LQIRUPDWLRQ IRU WKH HIIHFWV RI % YDOXHV FRUUHODWLRQ FRHIILFLHQW DQG YDULDQFH GLIIHUHQFH RQ WKH UDGLRPHWULF YDULDQFH RI PHUJHG GDWD FDQ EH IRXQG LQ WKH SUHYLRXV VHFWLRQ IRU WKH SUHVHUYLQJ PHWKRG ZLWK UHIHUHQFH WR ERWK )LJXUHV DQG ,Q RUGHU IRU DQ LPDJH PHUJHG E\ WKH GLIIHUHQFLQJ DSSURDFK WR KDYH DQ LPSURYHG UDGLRPHWULF YDULDQFH LW LV HVVHQWLDO WKDW WKH ODVW WZR WHUPV LQ HTXDWLRQ >D@ RU >E@f EH 7KDW LV % R] U% R FW >@ +HQFH LI ERWK r DQG Dr D FULWLFDO G YDOXH IRU WKH GLIIHUHQFLQJ PHWKRG FDQ EH REWDLQHG DV G r U D f§ >@ $FFRUGLQJ WR WKH UHODWLRQV RI HTXDWLRQV >@ WKURXJK >@ HTXDWLRQ >@ FDQ EH UHZULWWHQ DV Drf

PAGE 85

ILG U D\D >@ ZKHUH D DQG R DUH WKH VWDQGDUG GHYLDWLRQV IRU WKH SULPDU\ ;f DQG VHFRQGDU\ ;f LPDJHV UHVSHFWLYHO\ ,I D YDOXH LV JUHDWHU WKDQ G WKH YDULDQFH RI D PHUJHG LPDJH E\ WKH GLIIHUHQFLQJ PHWKRG ZLOO LQFUHDVH 2WKHUZLVH WKH PHUJHG GLIIHUHQFHGf LPDJH ZLOO KDYH D GHFUHDVHG UDGLRPHWULF YDULDQFH ,W PXVW EH SRLQWHG RXW WKDW WKH UHODWLYH PDJQLWXGHV RI WKH FRPELQLQJ LPDJH GDWD FDQ KDYH D VHULRXV LPSDFW RQ WKH WRQDO DSSHDUDQFH RI WKH PHUJHG LPDJH $VVXPLQJ WKDW WKH SULPDU\ LPDJH ;A KDV UHODWLYHO\ KLJKHU YDOXHV EULJKWHUf WKDQ WKH VHFRQGDU\ LPDJH ;f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f ZLOO KDYH UHODWLYHO\ ODUJH LPDJH YDOXHV LQ WKH PHUJHG GDWD EHFDXVH RI WKH XVH RI D ODUJH FRQVWDQW LQ HTXDWLRQ >@ 7KLV FRXOG PDNH WKHVH GDUN

PAGE 86

DUHDV DSSHDU EULJKW LQ WKH PHUJHG LPDJH
PAGE 87

ZLGHO\ XVHG PHWKRG &OLFKH HW DO &DUSHU HW DO f 7KH SUHVHUYLQJ PHWKRG LV UHFRPPHQGHG IRU PHUJLQJ SRVLWLYHO\ FRUUHODWHG LPDJHV ZKLOH WKH GLIIHUHQFLQJ DSSURDFK LV IRU WKRVH ZLWK D VWURQJ QHJDWLYH FRUUHODWLRQ ,Q DGGLWLRQ WKH LPDJH ZLWK D EULJKWHU DSSHDUDQFH VKRXOG EH FKRVHQ DV WKH SULPDU\ LPDJH ;f IRU WKH GLIIHUHQFLQJ PHWKRG LQ RUGHU WR DYRLG D SRWHQWLDO RI DOWHULQJ WKH WRQDO DSSHDUDQFH LQ WKH PHUJHG GLIIHUHQFHGf LPDJH $ VXPPDU\ IRU WKH HIIHFWLYHQHVV RI WKH WKUHH PHUJLQJ DSSURDFKHV LV SURYLGHG LQ 7DEOH IRU DQ HDV\ FRPSDULVRQ $FWXDO VDWHOOLWH LPDJHV ZLOO EH XWLOL]HG LQ FKDSWHU WR GHPRQVWUDWH WKH UHVXOWV GLVFXVVHG WKURXJKRXW WKLV FKDSWHU

PAGE 88

7DEOH 6XPPDU\ RI WKH FKDUDFWHULVWLFV RI GLIIHUHQW PHUJLQJ DSSURDFKHV 5DGLRPHWULF LPSURYHPHQW RQ PHUJHG LPDJH :KHQ &RQILQLQJ 3UHVHUYLQJ 'LIIHUHQFLQJ L U! DQG FW } D 1R
PAGE 89

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f RQ D 1DWLRQDO 2FHDQRJUDSKLF DQG $WPRVSKHULF $GPLQLVWUDWLRQ 12$$f VHULHV VDWHOOLWH ZDV DFTXLUHG IRU WKLV GHPRQVWUDWLRQ 7KH VDWHOOLWH VFHQH KDG ILYH LPDJHV UHFRUGHG DW WKH K 86 HDVWHUQ VWDQGDUG WLPH RQ 'HFHPEHU E\ WKH $9+55 VHQVRU RQERDUG WKH 12$$ VDWHOOLWH 7KH 12$$ VDWHOOLWH VFHQH FRQVLVWHG RI WZR UHIOHFWLYH UHG DQG QHDU LQIUDUHG RU 1,5f DQG WKUHH WKHUPDO LQIUDUHG 7,5f VSHFWUDO ZDYHEDQGV ZLWK ZDYHOHQJWK FKDUDFWHULVWLFV VKRZQ LQ 7DEOH .LGZHOO f 7KH VFHQH KDG D ORFDO DUHD FRYHUDJH /$&f RI WKH HQWLUH VRXWKHDVWHUQ UHJLRQ RI WKH 8QLWHG 6WDWHV DQG DOO WKH LPDJHV RI WKH ILYH VSHFWUDO ZDYHEDQGV KDYH WKH VDPH VSDWLDO UHVROXWLRQ RI DERXW P .LGZHOO f

PAGE 90

7DEOH :DYHOHQJWK FKDUDFWHULVWLFV RI 12$$ $9+55 /$& LPDJHV :DYHEDQG :DYHOHQJWK UDQJH MXPf 6SDWLDO UHVROXWLRQ ,D UHGf P D 1,5Ef P 7,5&f P 7,5&f P 7,5&f P 6RXUFH .LGZHOO D f§ XVHG LQ WKLV VWXG\ E f§ QHDU LQIUDUHG F f§ WKHUPDO LQIUDUHG

PAGE 91

7KH RULJLQDO 12$$ /$& VFHQH FRQWDLQHG LPDJH GDWD LQ D ELW GDWDGHSWK IRUPDW ZKHUH HYHU\ WKUHH SL[HOV ZHUH SDFNHG WR D ELW ZRUG .LGZHOO f $ SURJUDP ZKLFK UXQV RQ D 3& FRPSXWHU HQYLURQPHQW ZDV GHYHORSHG $SSHQGL[ &f WR XQSDFN DV ZHOO DV WR UHVFDOH OLQHDUO\f WKHVH ELW GDWD WR D ELW GDWD IRUPDW IRU FRPSDWLELOLW\ ZLWK 3&EDVHG LPDJH SURFHVVLQJ V\VWHPV DV ZHOO DV GLVSOD\ GHYLFH )RU WKLV UHVHDUFK WKH /$& VFHQH ZDV FOLSSHG WR WKH UHJLRQ RI WKH )ORULGD SHQLQVXOD )LJXUH f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f DQG /$& 1,5 ZDYHEDQGf LPDJHV DUH SUHVHQWHG LQ 7DEOH 7KH WZR VHOHFWHG /$& LPDJHV ZHUH SRVLWLYHO\ FRUUHODWHG ZLWK D FRUUHODWLRQ FRHIILFLHQW Uf RI %HFDXVH RI WKH QRWHG GLIIHUHQFH LQ WKH UDGLRPHWULF YDULDQFHV EHWZHHQ WKH WZR /$& LPDJHV 7DEOH f WKH XVH RI /$& DQG /$& IRU WKH SULPDU\ DQG VHFRQGDU\ LPDJHV ZDV DOWHUQDWHG IRU HDFK RI WKH WKUHH PHUJLQJ PHWKRGV ,Q FDVH ,

PAGE 92

)LJXUH /RFDWLRQ RI FOLSSHG 12$$ $9+55 /$& LPDJHV

PAGE 93

7DEOHV 6WDQGDUG GHYLDWLRQ Df QRUPDOL]HG YDULDQFH Df PHDQ [f PD[LPXP DQG PLQLPXP YDOXHV RI 12$$ $9+55 /$& LPDJHV :DYHEDQG D J` PD[ PLQ /$& WXUQf /$& SPf

PAGE 94

/$& ZDV XVHG WKH SULPDU\ LPDJH DQG /$& DV WKH VHFRQGDU\ LPDJH DQG LQ FDVH ,, /$& DQG /$& ZHUH XVHG UHVSHFWLYHO\ DV WKH SULPDU\ DQG VHFRQGDU\ LPDJHV 7KH SXUSRVH RI WKLV DOWHUQDWLYH XVH IRU WKH /$& DQG /$& LPDJHV ZDV WR DVVHVV WKH HIIHFW RI YDULDQFH GLIIHUHQFH EHWZHHQ WKH FRPELQLQJ LPDJHV RQ WKH UDGLRPHWULF YDULDQFH RI PHUJHG GDWD ,Q WKH GLIIHUHQFLQJ PHWKRG WKH FRQVWDQWV &f XVHG LQ HTXDWLRQ >@ DUH SURYLGHG LQ 7DEOH IRU ERWK FDVH DQG FDVH ,, 7KHVH FRQVWDQW YDOXHV ZKLFK ZHUH GHWHUPLQHG E\ D VFDQQLQJ RI WKH RULJLQDO LPDJH GDWD ZHUH XVHG WR DYRLG QHJDWLYH PHUJHG LPDJH GDWD LQ WKH GLIIHUHQFHG /$& LPDJHV IRU WKH FRUUHVSRQGLQJ 5 YDOXHV 9DULDQFH RI 0HUJHG /$& ,PDJHV 7KH QRUPDOL]HG UDGLRPHWULF YDULDQFHV RI PHUJHG /$& LPDJHV E\ WKH WKUHH PHWKRGV DUH SUHVHQWHG LQ )LJXUHV FDVH ,f DQG FDVH ,,f ,Q DGGLWLRQ WKH PHDQ YDOXHV EULJKWQHVVf RI WKHVH PHUJHG /$& LPDJHV DUH SUHVHQWHG LQ )LJXUHV DQG IRU FDVH DQG FDVH ,, UHVSHFWLYHO\ 7KH SRLQWV LQ WKHVH IRXU ILJXUHV DUH WKH UHVXOWV FRPSXWHG IURP WKH DFWXDO PHUJHG LPDJH GDWD ZKLOH WKH OLQHV UHSUHVHQW WKH HVWLPDWHV REWDLQHG WKURXJK WKH HTXDWLRQV LQ FKDSWHU :KLOH WKH HVWLPDWHV RI UDGLRPHWULF YDULDQFH ZHUH REWDLQHG WKURXJK HTXDWLRQV >@ >@ DQG >@ DORQJ ZLWK WKH QRUPDOL]HG YDULDQFHV 7DEOH f DQG D FRUUHODWLRQ FRHIILFLHQW Uf RI WKH PHDQ GLJLWDO FRXQW )LJXUHV DQG f ZHUH HVWLPDWHG XVLQJ HTXDWLRQV >@ >@ DQG >@ IRU HDFK FRUUHVSRQGLQJ

PAGE 95

7DEOH 2IIVHW FRQVWDQW &f XVHG LQ WKH GLIIHUHQFLQJ PHWKRG IRU PHUJLQJ /$& LPDJHV t YDOXH &DVH ,,

PAGE 96

1RUPDOL]HG YDULDQFH RI LPDJH GDWD 0HUJLQJ FRHIILFLHQW %f IRU VHFRQGDU\ LPDJH 1RWH L 3ULPDU\ LPDJH LV /$& VHFRQGDU\ LPDJH LV /$& LL 0HWKRGV &ff§FRQILQLQJ 'ff§GLIIHUHQFLQJ DQG 3ff§SUHVHUYLQJ )LJXUH &RPSDULVRQ EHWZHHQ DFWXDO DQG HVWLPDWHG UDGLRPHWULF YDULDQFH IRU PHUJHG /$& LPDJHV FDVH ,f &' 2-

PAGE 97

1RUPDOL]HG YDULDQFH RI LPDJH GDWD 0HUJLQJ FRHIILFLHQW %f IRU VHFRQGDU\ LPDJH 1RWH L 3ULPDU\ LPDJH LV /$& VHFRQGDU\ LPDJH LV /$& LL 0HWKRGV &ff§FRQILQLQJ 'ff§GLIIHUHQFLQJ DQG 3ff§SUHVHUYLQJ )LJXUH &RPSDULVRQ EHWZHHQ DFWXDO DQG HVWLPDWHG UDGLRPHWULF YDULDQFH IRU PHUJHG /$& LPDJHV FDVH ,,f

PAGE 98

0HUJLQJ FRHIILFLHQW %f IRU VHFRQGDU\ LPDJH 1RWH L 3ULPDU\ LPDJH LV /$& VHFRQGDU\ LPDJH LV /$& LL 0HWKRGV &ff§FRQILQLQJ 'ff§GLIIHUHQFLQJ DQG 3ff§SUHVHUYLQJ )LJXUH &RPSDULVRQ EHWZHHQ DFWXDO DQG HVWLPDWHG PHDQ GLJLWDO FRXQW IRU PHUJHG /$& LPDJHV FDVH ,f 8

PAGE 99

0HUJLQJ FRHIILFLHQW ILf IRU VHFRQGDU\ LPDJH 1RWH L 3ULPDU\ LPDJH LV /$& VHFRQGDU\ LPDJH LV /$& LL 0HWKRGV &ff§FRQILQLQJ 'ff§GLIIHUHQFLQJ DQG 3ff§SUHVHUYLQJ )LJXUH &RPSDULVRQ EHWZHHQ DFWXDO DQG HVWLPDWHG PHDQ GLJLWDO FRXQW IRU PHUJHG /$& LPDJHV FDVH ,,f 2L

PAGE 100

PHUJLQJ PHWKRG 7KH OHWWHUV 3 & DQG LQ )LJXUHV WKURXJK GHQRWH WKH SUHVHUYLQJ PHWKRG WKH FRQILQLQJ PHWKRG DQG WKH GLIIHUHQFLQJ PHWKRG UHVSHFWLYHO\ )URP WKH UHVXOWV VKRZQ LQ )LJXUHV WKURXJK IRU DOO WKH WKUHH PHWKRGV DQG % YDOXHV XVHG IRXU REVHUYDWLRQV DUH LQ RUGHU )LUVW WKH SULQFLSOH RI VWDWLVWLFDO YDULDWLRQ DQDO\VHV IRU FRPELQLQJ UDQGRP YDULDEOHV FDQ EH DSSOLHG LQ DVVHVVLQJ WKH UDGLRPHWULF TXDOLW\ YDULDQFH DQG EULJKWQHVVf RI D SUHPHUJHG LPDJH 7KLV SURYLGHV WKH EDVLV IRU XQGHUVWDQGLQJ WKH YDULRXV IRUPV RI GLJLWDO PDQLSXODWLRQV RI VDWHOOLWH LPDJH GDWD DQG IRU DVVHVVLQJ WKH HIIHFWLYHQHVV RI DQ LPDJH SURFHVVLQJ HIIRUW LQ UHPRWH VHQVLQJ DSSOLFDWLRQV ,Q SUDFWLFDO DSSOLFDWLRQV ZKHQ WZR LPDJHV DUH JLYHQ WKH YDOXHV RI FRUUHODWLRQ UDGLRPHWULF YDULDQFH DQG PHDQ GLJLWDO EULJKWQHVVf IRU WKH LPDJHV WR EH PHUJHG DUH NQRZQ 7KHUHIRUH WKH RYHUDOO TXDOLW\ LQ ERWK UDGLRPHWULF YDULDQFH FRQWUDVWf DQG EULJKWQHVV RI D PHUJHG LPDJH FDQ EH HYDOXDWHG EDVHG RQ WKH PHUJLQJ PHWKRG DQG FRHIILFLHQW %f 7KLV SUHPHUJLQJ HYDOXDWLRQ ZLOO OHDG WR PRUH HIILFLHQW DSSURDFKHV EHFDXVH XQSURGXFWLYH HIIRUWV FDQ EH HOLPLQDWHG 6HFRQG DQ LPDJH FRQWDLQV PDQ\ VXEYDULDEOHV UHSUHVHQWLQJ WKH YDULRXV ODQGXVH W\SHV GLVWULEXWHG WKURXJKRXW WKH HQWLUH VFHQH 1RWH WKDW WKH VXEYDULDEOHV GR QRW XVXDOO\ SRVVHVV WKH VDPH FRUUHODWLRQ UDGLRPHWULF YDULDQFHV DQG PHDQ GDWD YDOXHV LQ WKH LPDJHV RI D PXOWLVSHFWUDO GDWDVHW :KHQ D PHUJLQJ DOJRULWKP LV XVHG WR GLJLWDOO\ FRPELQH WKH HQWLUH LPDJHV WKH

PAGE 101

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f RSHUDWLRQV RI LPDJH GDWD WKH IXQGDPHQWDO SULQFLSOH FDQ EH H[WHQGHG WR DVVHVVLQJ WKH HIIHFWLYHQHVV RI PRUH HODERUDWH PHUJLQJ DOJRULWKPV VXFK DV ZDYHEDQG UDWLRLQJ PHWKRG $ SUHPHUJLQJ

PAGE 102

DVVHVVPHQW ZLOO DOORZ WKH IHDVLELOLW\ RI D SDUWLFXODU LPDJH SURFHVVLQJ HIIRUW WR EH HIIHFWLYHO\ HYDOXDWHG EHIRUH YLJRURXV DWWHPSWV DUH PDGH WR DFWXDOO\ FRPELQH WKH LPDJH GDWD %HFDXVH WKH SULPDU\ REMHFWLYH RI WKLV VWXG\ LV IRU PXOWLUHVROXWLRQ PHUJLQJ RQO\ D EULHI GLVFXVVLRQ RI WKH UDWLRLQJ PHWKRG ZLOO EH SUHVHQWHG ODWHU LQ WKLV FKDSWHU WR H[DPLQH WKH WHFKQLFDOLW\ RI LPDJH GDWD UDWLRLQJ $V LOOXVWUDWHG LQ JUDSKV 3f RI )LJXUHV DQG WKH SUHVHUYLQJ PHWKRG ZDV DEOH WR LPSURYH WKH UDGLRPHWULF YDULDQFH RI DOO PHUJHG LPDJHV LQ ERWK FDVH DQG FDVH ,, ,Q DGGLWLRQ WKH PHUJHG LPDJHV IRU HDFK % YDOXH DOVR KDG KLJKHU YDOXHV WKDQ WKH FRUUHVSRQGLQJ SULPDU\ LPDJH DV VKRZQ LQ JUDSKV 3f RI )LJXUHV DQG 7KH LPSURYHPHQW LQ UDGLRPHWULF YDULDQFH DQG PHDQ EULJKWQHVV LQGLFDWHV WKDW WKRVH PHUJHG LPDJHV ZRXOG EH EULJKWHU DQG KDYH PRUH FRQWUDVW WKDQ WKHLU SULPDU\ GDWD 7KH UDGLRPHWULF HQKDQFHPHQW ZLOO UHQGHU D JUHDWHU GLIIHUHQWLDWLRQ RI D VDWHOOLWH VFHQH IRU ODQGXVH FODVVLILFDWLRQ DSSOLFDWLRQV XVLQJ WKH PHUJHG GDWD :KHQ WKH YDULDQFH RI WKH VHFRQGDU\ LPDJH ZDV ODUJHU WKDQ WKDW RI WKH SULPDU\ LPDJH FDVH ,,f WKH UHODWLYH LPSURYHPHQW WR D PHUJHG LPDJH ZDV PRUH VXEVWDQWLDO 7KLV VLJQLILHV DQ LPSRUWDQFH RI LPSURYLQJ WKH UDGLRPHWULF JXDOLW\ RI WKH KLJK VSDWLDO UHVROXWLRQ SDQFKURPDWLFf LPDJH LQ D PXOWLUHVROXWLRQ GDWDVHW 7KH SULPDU\ FDXVH IRU LQFUHDVLQJ WKH UDGLRPHWULF YDULDQFH DQG EULJKWQHVV LQ WKH PHUJHG GDWD LV WKH DSSHQGLYH HIIHFW FUHDWHG E\ WKH SUHVHUYLQJ DSSURDFK

PAGE 103

)RU WKH FRQILQLQJ DSSURDFK WKH UDGLRPHWULF TXDOLW\ RI D PHUJHG LPDJH ZRXOG GHSHQG RQ WKH UHODWLYH UDGLRPHWULF YDULDQFH DQG EULJKWQHVV RI WKH SULPDU\ LPDJH GXH WR WKH FRPSURPLVLQJ HIIHFW )RU H[DPSOH LQ FDVH ZKHQ WKH SULPDU\ LPDJH /$&f KDG KLJKHU YDOXHV DQG D ODUJHU YDULDQFH WKDQ WKH VHFRQGDU\ LPDJH /$&f WKH UHVXOWDQW PHUJHG LPDJHV HDFK KDG D VPDOOHU UDGLRPHWULF YDULDQFH DQG ORZHU YDOXHV DV VKRZQ LQ JUDSKV &f RI )LJXUHV DQG +RZHYHU ZKHQ WKH UDGLRPHWULF YDULDQFH DQG WKH GDWD YDOXH RI WKH SULPDU\ LPDJH ZHUH VPDOOHU WKDQ WKRVH RI WKH VHFRQGDU\ LPDJH GDWD FDVH ,,f WKH PHUJHG LPDJHV ZHUH LPSURYHG ZLWK VOLJKWO\ ODUJHU UDGLRPHWULF YDULDQFHV DQG KLJKHU LPDJH YDOXHV DV LQGLFDWHG E\ JUDSKV &f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f ,I 5F WKH UDGLRPHWULF YDULDQFH RI D PHUJHG LPDJH LV RQ WKH DVFHQGLQJ VLGH RI D SDUDEROLF IXQFWLRQ IRU WKH ZKROH f UDQJH RI 5 YDOXHV :KHQ %FmVLR LW ZLOO EH FHUWDLQ WKDW WKH PHUJHG LPDJH ZLOO KDYH D VPDOOHU UDGLRPHWULF YDULDQFH OHVV FRQWUDVWf

PAGE 104

8VLQJ HTXDWLRQ >@ ZLWK WKH YDOXHV LQ 7DEOH DQG D FRUUHODWLRQ FRHIILFLHQW RI U WKH F YDOXHV IRU FDVH DQG FDVH ,, ZHUH HVWLPDWHG DW DQG UHVSHFWLYHO\ +HQFH WKH FRQILQLQJ DSSURDFK ZRXOG GHJUDGH D PHUJHG LPDJH LQ FDVH & f \HW LPSURYH LW LQ FDVH ,, %F f 7KH UDGLRPHWULF YDULDQFHV DQG PHDQ YDOXHV RI PHUJHG /$& LPDJH GDWD E\ WKH GLIIHUHQFLQJ DSSURDFK DUH VKRZQ LQ JUDSKV 'f RI )LJXUHV WKURXJK 6LPLODUO\ WR WKH FRQILQLQJ DSSURDFK DQ HQKDQFHPHQW RU D GHWUDFWLRQ RQ WKH UDGLRPHWULF YDULDQFH RI D PHUJHG LPDJH E\ WKH GLIIHUHQFLQJ PHWKRG FDQ EH DVVHVVHG E\ D FRPSDULVRQ EHWZHHQ WKH XVHG DQG WKH FULWLFDO G YDOXHV IURP HTXDWLRQ >@ 8VLQJ WKH YDOXHV LQ 7DEOH DQG D FRUUHODWLRQ FRHIILFLHQW U WKH G YDOXH ZDV DQG IRU FDVH DQG FDVH ,, UHVSHFWLYHO\ $V VKRZQ LQ JUDSK 'f RI )LJXUH FDVH ,f D PHUJHG LPDJH DOZD\V KDG D VPDOOHU UDGLRPHWULF YDULDQFH WKDQ WKH SULPDU\ LPDJH XQOHVV WKH PHUJLQJ FRHIILFLHQW f ZRXOG WDNH D YDOXH JUHDWHU WKDQ ZKLFK ZRXOG EH YHU\ XQOLNHO\ IRU WKH GLIIHUHQFLQJ PHWKRG ,Q FDVH ,, KRZHYHU WKH UDGLRPHWULF YDULDQFH RI PHUJHG LPDJHV EHFDPH VOLJKWO\ ODUJHU WKDQ WKDW RI WKH SULPDU\ LPDJH /$&f ZKHQ % WRRN YDOXHV JUHDWHU WKDQ DV VKRZQ LQ JUDSK 'f RI )LJXUH WKRXJK LW ZDV GHFUHDVLQJ LQLWLDOO\ GXH WR WKH SRVLWLYH FRUUHODWLRQ EHWZHHQ WKH WZR /$& LPDJHV &RPSDULVRQ RI 0HUJHG /$& ,PDJHV )URP WKH DERYH GLVFXVVLRQV RQ WKH UDGLRPHWULF TXDOLW\ YDULDQFH DQG PHDQVf RI PHUJHG LPDJHV WKLV VHFWLRQ DWWHPSWV

PAGE 105

WR IXUWKHU GHPRQVWUDWH WKRVH UHVXOWV XVLQJ LPDJH GLVSOD\V 7KH LPDJH FRQWUDVW EULJKWQHVV DQG WRQDO JUDGDWLRQV RI WKH PHUJHG /$& LPDJHV ZHUH HYDOXDWHG WKURXJK YLVXDO FRPSDULVRQV EHWZHHQ WKH SULPDU\ LPDJH DQG WKH PHUJHG GDWD 7R UHGXFH WKH VXEMHFWLYLW\ RI HYDOXDWLRQ DQG WR DYRLG FRORU SUHIHUHQFH EODFNDQGZKLWH GLVSOD\V ZHUH XVHG ,Q DGGLWLRQ DOO WKH LPDJHV WR EH HYDOXDWHG KDYH QRW EHHQ VXEMHFWHG WR DQ\ GLJLWDO HQKDQFHPHQW SURFHGXUHV HJ VSDWLDO ILOWHULQJ DQG FRQWUDVW VWUHWFKLQJf ZKLFK ZRXOG DOWHU WKH EULJKWQHVV DQG FRQWUDVW 7KH GLVSOD\V DUH VWULFWO\ WKH UHVXOWV RI XQDOWHUHG PHUJHG LPDJH GDWD JUD\ VKDGH GDWDf 1RWH WKDW WKH HYDOXDWLRQV ZHUH EDVHG RQ WKH RYHUDOO JXDOLW\ RI LPDJH DSSHDUDQFH DQG RQO\ WKUHH PHUJHG LPDJHV DW YDOXHV RI DQG ZHUH VHOHFWHG IRU HDFK FDVH 7KH RULJLQDO /$& DQG /$& LPDJHV DUH SUHVHQWHG LQ )LJXUH 2EYLRXVO\ WKHVH WZR /$& LPDJHV KDYH YHU\ GLIIHUHQW TXDOLWLHV LQ WHUPV RI FRQWUDVW DQG EULJKWQHVV %HFDXVH RI LWV ODUJHU UDGLRPHWULF YDULDQFH DQG JUHDWHU PHDQ GDWD YDOXH 7DEOH f WKH /$& 1,5f LPDJH KDV PRUH FRQWUDVW DV ZHOO DV D EULJKWHU DSSHDUDQFH WKDQ WKH /$& UHGf )RU FDVH RI WKH SUHVHUYLQJ PHWKRG WKH WKUHH VHOHFWHG PHUJHG LPDJHV DW % DQG DUH SUHVHQWHG LQ )LJXUH 2QH XQDPELJXRXV LQGLFDWLRQ LQ )LJXUH LV WKDW WKH LQFUHDVH LQ UDGLRPHWULF TXDOLW\ LQ D PHUJHG LPDJH FRUUHVSRQGV WR WKH LQFUHDVH LQ YLVXDO TXDOLW\ FRQWUDVW DQG EULJKWQHVVf 7KH LQFUHDVLQJ UDGLRPHWULF YDULDQFHV IRU DQG

PAGE 106

/$& 1,5f /$& UHGf )LJXUH 2ULJLQDO FOLSSHG 12$$ /$& LPDJHV RI UHG DQG 1,5 ZDYHEDQGV 92 :

PAGE 107

f f f 1RWH 3ULPDU\ LPDJH /$& 1,5f 6HFRQGDU\ LPDJH /$& UHGf )LJXUH 0HUJHG /$& LPDJHV E\ WKH SUHVHUYLQJ PHWKRG FDVH ,f

PAGE 108

UHVXOWHG LQ PRUH DQG PRUH FRQWUDVW LQ WKH PHUJHG LPDJH GDWD 7KH PHUJHG LPDJHV DOVR EHFDPH LQFUHDVLQJO\ EULJKWHU DV 5 LQFUHDVHV )RU FDVH ,, WKH FRUUHVSRQGLQJ PHUJHG LPDJHV DUH SUHVHQWHG LQ )LJXUH ZKHUH VLPLODU LPSURYHPHQWV RQ LPDJH FRQWUDVW DQG EULJKWQHVV ZHUH REVHUYHG HYHQ ZKHQ WKH SULPDU\ LPDJH KDG D PXFK VPDOOHU UDGLRPHWULF YDULDQFH 7DEOH f ,Q FRPSDULVRQ ZLWK FDVH WKH LPSURYHPHQWV LQ FDVH ,, ZHUH PRUH VXEVWDQWLDO EHFDXVH LWV VHFRQGDU\ LPDJH /$&f KDG D ODUJHU YDULDQFH 7KRXJK WKH HQKDQFHPHQW ZDV OHVV DSSDUHQW DW VPDOO 5 YDOXHV f DOO PHUJHG LPDJHV E\ WKH SUHVHUYLQJ PHWKRG KDYH HYLGHQFHG LPSURYHPHQWV LQ LPDJH FRQWUDVW DQG EULJKWQHVV ZKHQ FRPSDUHG WR WKH FRUUHVSRQGLQJ SULPDU\ LPDJH 7KH UHDVRQ IRU VXFK D FRQVLVWHQW HQKDQFHPHQW LV WKDW JLYHQ WKH SRVLWLYH FRUUHODWLRQ U f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

PAGE 109

f f f 1RWH 3ULPDU\ LPDJH /$& UHGf 6HFRQGDU\ LPDJH /$& 1,5f )LJXUH 0HUJHG /$& LPDJHV E\ WKH SUHVHUYLQJ PHWKRG FDVH ,,f YR FU!

PAGE 110

f f f 1RWH 3ULPDU\ LPDJH /$& 1,5f 6HFRQGDU\ LPDJH /$& UHGf )LJXUH 0HUJHG /$& LPDJHV E\ WKH FRQILQLQJ PHWKRG FDVH ,f

PAGE 111

f f f 1RWH 3ULPDU\ LPDJH /$& UHGf 6HFRQGDU\ LPDJH /$& 1,5f )LJXUH 0HUJHG /$& LPDJHV E\ WKH FLQILQLQJ PHWKRG FDVH ,,f e!

PAGE 112

/$&f KDG D ODUJHU YDULDQFH DQG JUHDWHU EULJKWQHVV DV FRPSDUHG WR WKH VHFRQGDU\ LPDJH GDWD /$&f WKH PHUJHG LPDJHV EHFDPH LQFUHDVLQJO\ GDUNHU DQG KDG OHVV FRQWUDVW )LJXUH f DV WKH PHUJLQJ FRHIILFLHQW LQFUHDVHG IURP WR +RZHYHU D VOLJKWO\ LPSURYHPHQW LQ ERWK LPDJH FRQWUDVW DQG EULJKWQHVV LV REVHUYHG IRU WKH PHUJHG LPDJHV LQ FDVH ,, ZKHQ WKH SULPDU\ LPDJH ZDV UHODWLYHO\ GDUNHU DQG KDG D VPDOOHU YDULDQFH )LJXUH f 2QH PHWKRG WR HYDOXDWH WKH HIIHFWLYHQHVV RI WKH FRQILQLQJ PHWKRG LV WR H[DPLQH WKH FULWLFDO F YDOXH ZKLFK ZDV FDOFXODWHG DV DQG IRU FDVH DQG FDVH ,, UHVSHFWLYHO\ $SSDUHQWO\ WKH FRQILQLQJ DSSURDFK GHFUHDVHG WKH FRQWUDVW RI D PHUJHG /$& LPDJH LQ FDVH )LJXUH f EXW VOLJKWO\ LPSURYHG LW LQ FDVH ,, DV VKRZQ LQ )LJXUH )RU WKH GLIIHUHQFLQJ PHWKRG WKH PHUJHG /$& LPDJHV ZLWK % YDOXHV RI DQG IRU ERWK FDVH DQG FDVH ,, DUH SUHVHQWHG LQ )LJXUHV DQG 1RWH WKDW WZR FRPSOHWHO\ GLIIHUHQW VHWV RI PHUJHG LPDJHV ZHUH JHQHUDWHG ZKHQ WKH GLIIHUHQFLQJ DSSURDFK ZDV XWLOL]HG 5HFDOO IURP 7DEOH DQG )LJXUH WKDW WKH /$& LPDJH QRW RQO\ KDG D PXFK VPDOOHU YDULDQFH EXW DOVR ZDV PXFK GDUNHU D VPDOOHU PHDQ YDOXHf LQ FRPSDULVRQ WR WKH /$& LPDJH ,Q DGGLWLRQ WKH WZR /$& LPDJHV ZHUH DOVR SRVLWLYHO\ FRUUHODWHG U f %HFDXVH RI WKH SRVLWLYH FRUUHODWLRQ EHWZHHQ WKH WZR /$& LPDJHV WKH GLIIHUHQFLQJ PHWKRG VKRXOG QRW EH XWLOL]HG WR PHUJH WKH /$& LPDJHV LQ SUDFWLFDO DSSOLFDWLRQV +RZHYHU WKH

PAGE 113

f f f 1RWH 3ULPDU\ LPDJH /$& 1,5f 6HFRQGDU\ LPDJH /$& UHGf )LJXUH 0HUJHG /$& LPDJHV E\ WKH GLIIHUHQFLQJ PHWKRG FDVH ,f R R

PAGE 114

f f f 1RWH 3ULPDU\ LPDJH /$& UHGf 6HFRQGDU\ LPDJH /$& 1,5f )LJXUH 0HUJHG /$& LPDJHV E\ WKH GLIIHUHQFLQJ PHWKRG FDVH ,,f

PAGE 115

SXUSRVH IRU WKH GLVFXVVLRQV KHUH LV WR XQGHUVWDQG WKH PHUJLQJ SURFHVV DV LW DIIHFWV WKH UDGLRPHWULF TXDOLW\ RI PHUJHG LPDJHV ,Q FDVH ZKHQ WKH /$& LPDJH ZDV GLIIHUHQFHG E\ WKH /$& GDWD WKH UHVXOWV )LJXUH f VKRZHG WKDW WKH PHUJHG LPDJH ZDV QRW VHULRXVO\ LPSDFWHG EHFDXVH WKH RULJLQDO /$& LPDJH KDG ERWK D EULJKWHU DSSHDUDQFH DQG D UHODWLYH ODUJHU YDULDQFH $W D UHVXOW DOO WKH PHUJHG GLIIHUHQFHGf LPDJHV )LJXUH f PDLQWDLQHG D JUHDW GHDO RI WRQDO VLPLODULW\ WR WKH SULPDU\ LPDJH /$&f +RZHYHU WKH UHVXOWV ZHUH FRPSOHWHO\ GLIIHUHQW ZKHQ WKH SULPDU\ LPDJH /$&f KDG ERWK D VPDOOHU PHDQ DQG YDULDQFH FDVH ,,f $W IL WKH PHUJHG LPDJH DSSHDUDQFH EHJDQ WR IDGH RXW DQG VLJQLILFDQW LPDJH FRQWUDVW ZDV ORVW DV D UHVXOW RI D VPDOOHU UDGLRPHWULF YDULDQFH LQ WKH PHUJHG GDWD )LJXUH f :KHQ D VOLJKWO\ ODUJHU 5 YDOXH f ZDV XVHG D UHYHUVH WRQDO EHJDQ WR VXUIDFH LQ WKH PHUJHG LPDJH )RU LQVWDQFH WKH GDUN DSSHDUDQFH RI ZDWHU ERGLHV HJ /DNH 2NHHFKREHH DQG VHD ZDWHUf EHFDPH VOLJKWO\ EULJKW RU VLPLODU WR WKRVH RI ODQG DUHDV $W 5 YDOXH RI WKH WRQDO JUDGDWLRQV RI WKH HQWLUH LPDJH ZHUH FRPSOHWHO\ UHYHUVHG PDNLQJ GDUN ZDWHU ERGLHV VKRZ XS DV EULJKW DQG EULJKW DUHDV ODQGVf DSSHDU DV GDUN LQ WKH PHUJHG LPDJH :KLOH WKH SRVLWLYH FRUUHODWLRQ ZDV UHVSRQVLEOH IRU WKH GHFUHDVH LQ PHUJHG LPDJH FRQWUDVW WKH UHYHUVHG WRQDO DSSHDUDQFH ZDV FDXVHG E\ WKH JUHDWHU EULJKWQHVV RI WKH VHFRQGDU\ LPDJH GDWD /$&f ZKLFK UHTXLUHG WKH XVH RI D ODUJHU SRVLWLYH FRQVWDQW 7DEOH f LQ WKH GLIIHUHQFLQJ HTXDWLRQ

PAGE 116

$ PRVDLF RI DOO WKH QLQH VHOHFWHG PHUJHG LPDJHV IRU WKH SUHVHUYLQJ FRQILQLQJ DQG GLIIHUHQFLQJ PHWKRGV LV SUHVHQWHG LQ )LJXUH DV D VXPPDU\ IRU WKH WKUHH VHOHFWHG 5 YDOXHV RI DQG 7KHVH LPDJHV DUH VKRZQ LQ D ZD\ WKDW WKH FKDQJHV RI UDGLRPHWULF JXDOLW\ LQ WKH KRUL]RQWDO GLUHFWLRQ LQGLFDWH WKH HIIHFWV RI LQFUHDVLQJ 5 YDOXHV IRU D JLYHQ PHWKRG ZKLOH WKRVH LQ WKH YHUWLFDO GLUHFWLRQ DUH UHODWHG WR WKH HIIHFWV RI WKH GLIIHUHQW PHUJLQJ PHWKRGV 6LPLODUO\ WKH QLQH PHUJHG LPDJHV IRU FDVH ,, RI WKH SUHVHUYLQJ FRQILQLQJ DQG GLIIHUHQFLQJ PHWKRGV DW 5 YDOXHV RI DQG DUH VKRZQ LQ )LJXUH ZLWK WKH VDPH LPDJH DUUDQJHPHQWV DV LQ )LJXUH )URP DOO WKH PHUJHG LPDJHV LQ WKH WZR PRVDLFV RI )LJXUHV DQG WKUHH FRQFOXVLRQV DUH DV IROORZV )LUVW WKH SUHVHUYLQJ DSSURDFK LV D YHU\ HIIHFWLYH PHWKRG WR JHQHUDWH PHUJHG LPDJHV ZLWK WKH JUHDWHVW LPSURYHPHQW LQ UDGLRPHWULF TXDOLW\ 7KH UDGLRPHWULFDOO\ HQKDQFHG LPDJHV ZLOO EH PRUH XVHIXO IRU JUHDWHU GLIIHUHQWLDWLRQV RI ODQGXVH HOHPHQWV LQ PXOWLVSHFWUDO DQDO\VHV XVLQJ WKH PHUJHG LPDJH GDWD 6HFRQG WKH FRQILQLQJ DSSURDFK LV VXERUGLQDWH WR WKH SUHVHUYLQJ PHWKRG LQ HYHU\ DVSHFW 7KH LPDJHV PHUJHG E\ WKH FRQILQLQJ DSSURDFK FDQ KDYH HLWKHU DQ HQKDQFHPHQW RU D GHWUDFWLRQ LQ UDGLRPHWULF TXDOLW\ GHSHQGLQJ RQ WKH GDWD FKDUDFWHULVWLFV RI ERWK WKH SULPDU\ DQG WKH VHFRQGDU\ LPDJHV (YHQ ZKHQ D UDGLRPHWULF HQKDQFHPHQW LV UHYHDOHG WKH H[WHQW RI LPSURYHPHQW ZLOO QRW EH FRPSDUDEOH WR WKDW E\ WKH SUHVHUYLQJ DSSURDFK 7KLUG WKH

PAGE 117

f f f )LJXUH 6XPPDU\ PRVDLFf RI PHUJHG /$& LPDJHV IRU WKUHH PHWKRGV LQ FDVH ,

PAGE 118

'LIIHUHQFLQJ &RQILQLQJ 3UHVHUYLQJ f f f )LJXUH 6XPPDU\ PRVDLFf RI PHUJHG /$& LPDJHV IRU WKUHH PHWKRGV LQ FDVH ,,

PAGE 119

GLIIHUHQFLQJ DSSURDFK PXVW EH XVHG ZLWK JUHDW FDXWLRQ EHFDXVH RI WKH SRVVLELOLW\ RI LQYHUWLQJ WKH PHUJHG LPDJH SDUWLFXODUO\ ZKHQ WKH SULPDU\ LPDJH KDV UHODWLYHO\ YDOXHV 7KH HIILFDF\ RI WKH GLIIHUHQFLQJ PHWKRG LV OLPLWHG WR WKH FLUFXPVWDQFHV ZKHQ WKH LPDJHV WR EH FRPELQHG KDYH D VWURQJ QHJDWLYH FRUUHODWLRQ 5DWLRLQT RI 6DWHOOLWH ,PDJHV 7KH UDWLRLQJ RI VDWHOOLWH LPDJHV RIWHQ FDOOHG ZDYHEDQG UDWLRLQJf LV D ZLGHO\ DGRSWHG DSSURDFK IRU LPDJH HQKDQFHPHQW /LOOHVDQG DQG .LHIHU /R HW DO +XHWH DQG -DFNVRQ .LGZHOO f %HFDXVH VXFFHVVIXO DSSOLFDWLRQV RI WKH UDWLRLQJ WHFKQLTXH RIWHQ GHSHQG RQ D WUDLODQGHUURU SURFHVV ZLWK PDQ\ IDLOHG HIIRUWV WKLV VHFWLRQ DWWHPSWV WR H[DPLQH DQG XQGHUVWDQG WKH PHFKDQLFV RI ZDYHEDQG UDWLRLQJ E\ XVLQJ WKH SULQFLSOH RI UDQGRP YDULDEOH PDQLSXODWLRQV $FFRUGLQJ WR 0RRG HW DO f WKH UDWLR @ [ IRU ZKLFK WKH PHDQ YDOXH QUf RI UDWLRHG YDULDEOH @ 0 0 [ ZKLOH WKH YDULDQFH DUf FDQ EH DSSUR[LPDWHG DV

PAGE 120

0L 2 \ &29;I;f r f > @ >@ 0 0L 0 0W 0 ZKHUH L rf DQG [ f DUH WKH PHDQV DQG 2\ DQG D DUH WKH YDULDQFHV IRU YDULDEOHV ; DQG ; ,Q UDWLRLQJ LPDJHV ; DQG ; DUH WKH QXPHUDWRU DQG GHQRPLQDWRU LPDJHV UHVSHFWLYHO\ 7KH FRYDULDQFH FTY;;f WHUP LQ ERWK HTXDWLRQV >@ DQG > @ FDQ EH UHZULWWHQ LQ WKH IROORZLQJ IRUP 0RRG HW DO f FTY;;f U D D >@ ZKHUH FW DQG D DUH WKH VWDQGDUG GHYLDWLRQV DQG U LV WKH FRUUHODWLRQ FRHIILFLHQW IRU ; DQG ; 6XEVWLWXWLQJ HTXDWLRQ >@ LQWR HTXDWLRQV >@ DQG >@ \LHOGV 0L U R\ FW +\ 0U f§ >@ 0 P P IRU WKH PHDQ [Uf DQG f U 2\ R 0W P >@ IRU WKH YDULDQFH DSf RI UDWLRHG YDULDEOH @ DQG >@ DUH LQ IDFW WKH FRHIILFLHQW RI YDULDWLRQ &9 DX ZKHUH Prf 7KXV XVLQJ WKH &9 YDOXHV ERWK HTXDWLRQV >@ DQG >@ FDQ EH UHZULWWHQ DV &9 U &9 &9f 0 >@

PAGE 121

DQG R f &9 &9 a U &9 &9f >@ U IRU WKH PHDQ YDOXH DQG WKH YDULDQFH RI @ 9 DV WKH YDULDELOLW\ IDFWRU DQG 5E DV WKH EULJKWQHVV UDWLR 5E 0P >@ ZKHUH Qr 1RWH WKDW LV D PHDVXUH RI WKH UHODWLYH PDJQLWXGHV RI EULJKWQHVV EHWZHHQ WKH QXPHUDWRU ;f DQG WKH GHQRPLQDWRU ;f LPDJHV ZKLOH )Y SURYLGHV D FROOHFWLYH DVVHVVPHQW RI WKH GDWD YDULDELOLW\ DQG UHODWLRQ LQ ; DQG ; $V LQGLFDWHG E\ HTXDWLRQV >@ DQG >@ )\ LV D FRQVWDQW ZKHQ WZR LPDJHV DUH JLYHQ D D DQG U DUH NQRZQf ,WV YDOXH GRHV QRW FKDQJH ZKHQ WKH QXPHUDWRU DQG GHQRPLQDWRU LPDJHV DUH DOWHUQDWHG +RZHYHU 5E FDQ EH VLJQLILFDQWO\ GLIIHUHQW LI WKH QXPHUDWRU LPDJH LV UHSODFHG E\ WKH GHQRPLQDWRU GDWD 6XEVWLWXWLQJ ERWK DQG )\ LQWR HTXDWLRQV >@ DQG >@ \LHOGV WKH IROORZLQJV 0U 5E &9 U &9 &9f >@ >@

PAGE 122

IRU WKH PHDQ DQG YDULDQFH RI UDWLRHG LPDJH @ DQG >@ LV WKDW ERWK WKH YDULDQFH DQG PHDQ EULJKWQHVV RI UDWLRHG LPDJH @f WR D UDQJH W\SLFDOO\ f RI LQWHJHUV 7KLV PDNHV LW DUELWUDU\ WR FRPSDUH ERWK WKH UDGLRPHWULF YDULDQFH DUf DQG PHDQ EULJKWQHVV QUf WR WKRVH RI WKH WZR RULJLQDO LPDJHV ; DQG ;f 6LQFH WKH VFDOLQJ IDFWRU LV DSSOLHG WR WKH HQWLUH VFHQH WKH FRQFHSWV RI DQG )\ FDQ EH H[WHQGHG WR WKH YDULRXV ODQG XVH HOHPHQWV ZKHQ DVVHVVLQJ WKH IHDVLELOLW\ RI ZDYHEDQG UDWLRLQJ ,Q UHPRWH VHQVLQJ DSSOLFDWLRQV ZKHQ WZR LPDJHV DUH WR EH UDWLRHG WKH YDOXH RI )\ IRU HDFK DQG HYHU\ ODQGXVH HOHPHQW LV GHWHUPLQHG UHJDUGOHVV RI WKH VHOHFWLRQ RI WKH QXPHUDWRU RU GHQRPLQDWRUf LPDJH +RZHYHU WKH YDOXHV DPRQJ WKH ODQGXVH HOHPHQWV LQ D VDWHOOLWH VFHQH FDQ EH VLJQLILFDQWO\ GLIIHUHQW GHSHQGLQJ RQ ZKLFK RI WKH WZR UDWLRLQJ LPDJHV LV XVHG DV WKH QXPHUDWRU ;f IRU HTXDWLRQ >@ 1RWH WKDW D UHODWLYH ODUJH 5MM YDOXH SURYLGHV DQ DGYDQWDJH LQ DWWDLQLQJ D SRWHQWLDO UDGLRPHWULF HQKDQFHPHQW ZKLOH D VPDOO YDOXH LV WKH LQGLFDWLRQ RI GLIILFXOW\ LQ DFKLHYLQJ DQ\ HQKDQFHPHQW )RU LQVWDQFH LQ

PAGE 123

RUGHU WR HQKDQFH YHJHWDWLRQ ODQGV WKH UDWLRLQJ LPDJH ZLWK JUHDWHU YDOXHV IRU YHJHWDWLRQ DUHDV VKRXOG EH FKRVHQ DV WKH QXPHUDWRU LPDJH WR DFKLHYH D UHODWLYH ODUJH YDOXH IRU LQFUHDVHG UDGLRPHWULF YDULDQFH DQG EULJKWQHVV ,I WKH UDWLRLQJ LPDJH WKDW SRVVHVVHV WKH ODUJHU PHDQ YDOXH EULJKWHUf IRU YHJHWDWLYH DUHDV LV XVHG DV WKH GHQRPLQDWRU LPDJH WKH YDOXH ZLOO EH VPDOO PDNLQJ LW GLIILFXOW RU HYHQ LPSRVVLEOH IRU YHJHWDWLRQ ODQG XVH WR VWDQG RXW LQ WKH UHVXOWDQW UDWLRHG LPDJH 7KLV SRLQWV RXW WKDW RQH LPSRUWDQW FRQVLGHUDWLRQ LQ D UDWLRLQJ DSSURDFK LV WR VHOHFW WKH QXPHUDWRU LPDJH ZLWK ZKLFK WKH ODQGXVH HOHPHQWV RI LQWHUHVW FDQ KDYH UHODWLYH ODUJH 5\ YDOXHV 7KH YDULDELOLW\ IDFWRU )\f LV D IXQFWLRQ RI ERWK WKH FRUUHODWLRQ FRHIILFLHQW Uf DQG WKH FRHIILFLHQWV RI YDULDWLRQ ,I WKH FRUUHODWLRQ EHWZHHQ LPDJHV ; DQG ; DSSURDFKHV SRVLWLYH XQLW\ U f )\ FDQ EH H[SUHVVHG DV )Y &9W &9f >@ ZKLFK LV WKH VJXDUH RI WKH GLIIHUHQFH EHWZHHQ WKH FRHIILFLHQWV RI YDULDWLRQ &9 DQG &9 &RQVHTXHQWO\ WKH YDOXHV RI )\ ZLOO EH YHU\ VPDOO IRU WKRVH ODQGXVH HOHPHQWV ZLWK D VWURQJ SRVLWLYH FRUUHODWLRQ EHWZHHQ ; DQG ; ,I U m WKH YDOXH RI )\ FDQ EH ZULWWHQ DV )Y &9 &9f >@ ZKLFK LV WKH VTXDUH RI WKH VXP RI FRHIILFLHQWV RI YDULDWLRQ

PAGE 124

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f ZLOO DOORZ D ODQGXVH HOHPHQW LQ TXHVWLRQ WR KDYH D UHODWLYH ODUJH )\ YDOXH FUHDWLQJ WKH SRWHQWLDO IRU WKDW ODQGXVH HOHPHQW WR KDYH DQ LQFUHDVHG UDGLRPHWULF YDULDQFH LQ WKH UHVXOWDQW UDWLRHG LPDJH ,Q DGGLWLRQ D QHJDWLYH RU ]HUR FRUUHODWLRQ Uf ZRXOG DOVR PDNH WKH ODQGXVH W\SH LQ TXHVWLRQ DSSHDU EULJKWHU EHFDXVH WKH U &9 &9f FRPSRQHQW LQ HTXDWLRQ >@ LV QRQQHJDWLYH ,W EHFRPHV FOHDU WKDW LW ZLOO QRW EH IHDVLEOH WR XVH WKH UDWLRLQJ PHWKRG LQ DQ HIIRUW WR HQKDQFH WKH UDGLRPHWULF YDULDQFHV RI WKRVH ODQGXVH W\SHV WKDW KDYH D VWURQJ SRVLWLYH FRUUHODWLRQ EHWZHHQ WKH WZR UDWLRLQJ LPDJHV 7R VWDWH DOWHUQDWLYHO\ D UDGLRPHWULF HQKDQFHPHQW E\ WKH UDWLRLQJ PHWKRG FDQ EH DFKLHYHG RQO\ IRU WKRVH ODQGXVH W\SHV ZKRVH FRUUHODWLRQV DUH ZHDN RU QHJDWLYH LQ WKH LPDJHV WR EH UDWLRHG ,W LV ZRUWKZKLOH RI SRLQWLQJ RXW WKDW ERWK WKH QXPHUDWRU DQG GHQRPLQDWRU LPDJHV ; DQG ;f FDQ EH PDQLSXODWHG E\ RWKHU

PAGE 125

PHUJLQJ DSSURDFKHV SUHVHUYLQJ GLIIHUHQFLQJ HWFf LQ D ZD\ WKDW WKH ODQGXVH HOHPHQWV RI LQWHUHVW FDQ DWWDLQ UHODWLYHO\ ODUJH DQG )Y YDOXHV 2QH H[DPSOH RI WKLV PDQLSXODWLRQ LV WKH QRUPDOL]HG GLIIHUHQFH YHJHWDWLRQ LQGH[ +XHWH DQG -DFNVRQ .LGZHOO f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f YDOXHV IRU WKH ODQGXVH HOHPHQW LQ TXHVWLRQ VKRXOG EH XVHG DV WKH QXPHUDWRU LPDJH WR DWWDLQ D UHODWLYH ODUJH 5E YDOXH 2WKHUZLVH LW VKRXOG EH XVHG DV WKH GHQRPLQDWRU LPDJH WR GHWUDFW WKH UDGLRPHWULF TXDOLWLHV RI WKH ODQGXVH HOHPHQW 6HFRQG WKH IHDVLELOLW\ RI UDWLRLQJ LPDJHV IRU LPDJH HQKDQFHPHQW GHSHQGV RQ WKH FRUUHODWLRQ EHWZHHQ WKH UDWLRLQJ LPDJHV 6XFFHVVIXO DSSOLFDWLRQV RI WKH UDWLRLQJ PHWKRG FDQ EH DFKLHYHG RQO\ IRU

PAGE 126

WKH ODQGXVH HOHPHQWV ZKLFK KDYH D QHJDWLYH RU YHU\ ZHDN FRUUHODWLRQ Uf EHWZHHQ WKH UDWLRLQJ LPDJHV 0XOWLUHVROXWLRQ (QKDQFHPHQW 6LQFH PHUJLQJ DFWXDO PXOWLUHVROXWLRQ VDWHOOLWH GDWDVHWV ZDV FDUULHG RXW LQ FKDSWHUV DQG WKLV VHFWLRQ IRFXVHV RQ WKH IDFWRUV WKDW DUH XQLJXH WR PHUJLQJ PXOWLUHVROXWLRQ LPDJHV 7KLV DUUDQJHPHQW ZDV LQWHQGHG WR DGGUHVV WKRVH XQLJXH DVSHFWV EHIRUH HIIRUWV ZHUH PDGH WR GHPRQVWUDWH WKH SURFHVV RI PXOWLUHVROXWLRQ PHUJLQJ XVLQJ D 6327 VDWHOOLWH GDWDVHW 7KH VSDWLDO UHVROXWLRQ GLIIHUHQFH LQ D PXOWLUHVROXWLRQ GDWDVHW UHJXLUHV WKH UHVDPSOLQJ RI DOO LPDJH GDWD WR WKH VDPH SL[HO VL]H EHIRUH EHLQJ PHUJHG 2QH FRQFHUQ LV WKH YDOLGLW\ RI DSSO\LQJ WKH PHUJLQJ SULQFLSOH GLVFXVVHG SUHYLRXVO\ WR WKH UHVDPSOHG LPDJH GDWD ,Q WKH VWDWLVWLFDO FRQWH[W LI WKH HOHPHQWV RI D UDQGRP YDULDEOH DUH HDFK GXSOLFDWHG IRU D FHUWDLQ QXPEHU RI WLPHV WKH QHZ YDULDEOH ZLOO VWLOO DWWDLQ WKH FKDUDFWHULVWLFV RI D UDQGRP YDULDEOH 6LPLODUO\ LI WKH SL[HOV RI D ORZ VSDWLDO UHVROXWLRQ LPDJH DUH HDFK UHVDPSOHG IRU D FHUWDLQ QXPEHU RI WLPHV WKH UHVDPSOHG LPDJH ZLOO VWLOO KDYH WKH FKDUDFWHULVWLFV RI D UDQGRP YDULDEOH +HQFH WKH SULQFLSOH RI PHUJLQJ LPDJHV FDQ EH DSSOLHG WR PXOWLUHVROXWLRQ LPDJH GDWDVHWV DIWHU D UHVDPSOLQJ SURFHGXUH 0XOWLUHVROXWLRQ PHUJLQJ FDQ EH FRQVLGHUHG DV DQ XQLJXH SURFHVV LQ WKDW WKHUH LV QR DOWHUQDWLYH LQ WKH VHOHFWLRQ RI WKH SULPDU\ DQG VHFRQGDU\ LPDJHV IURP WKH PXOWLUHVROXWLRQ

PAGE 127

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f PXVW EH FDXWLRQHG 7KH GLIIHUHQFH LQ VSDWLDO UHVROXWLRQ EHWZHHQ WKH SDQFKURPDWLF DQG PXOWLVSHFWUDO LPDJHV PXVW DOVR EH FRQVLGHUHG )RU LQVWDQFH LI WKH VSDWLDO UHVROXWLRQV KDYH D OLQHDU UDWLR RI WZR RQH ORZ VSDWLDO UHVROXWLRQ SL[HO LQ WKH PXOWLVSHFWUDO LPDJHV ZLOO HQFRPSDVV IRXU VXESL[HOV LQ WKH SDQFKURPDWLF LPDJH )LJXUH f ,I WKH IRXU VXESL[HOV UHSUHVHQW IRXU GLIIHUHQW ODQGXVH REMHFWV WKH PLQLPXP GLIIHUHQFH LQ WKH GLJLWDO QXPEHUV RI WKH IRXU VXESL[HOV LV DQG RU DQ\ IRXU FRQWLJXRXV LQWHJHUV ZLWKLQ WKH UDQJHf ,Q RUGHU IRU DOO RI WKHVH IRXU ODQGXVH REMHFWV WR VKRZ XS LQ D PHUJHG LPDJH D PHUJLQJ FRHIILFLHQW f RI LV UHTXLUHG EHFDXVH RI WKH WUXQFDWLRQ RI LQWHJHU LPDJH GDWD ,I D % YDOXH RI LV XWLOL]HG XS WR WZR RI WKH IRXU ODQGXVH REMHFWV

PAGE 128

FRUUHVSRQGLQJ WR D ORZ UHVROXWLRQ SL[HO ZLOO QRW VKRZ XS LQ D PHUJHG LPDJH ,Q RWKHU ZRUGV XS WR b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f PRUH VSDWLDO REMHFWV FRXOG ORVH WKHLU SUHVHQFH LQ D PHUJHG GDWDVHW 7KLV FRQVWUDLQW LQ VSDWLDO UHVROXWLRQ GLIIHUHQFH ZKLFK ZDV DOVR REVHUYHG E\ 3ULFH f XQGHUOLQHV D OLPLWDWLRQ WR PXOWLUHVROXWLRQ SURFHVVLQJ DV ZHOO DV D FKDOOHQJH WR WKH GHYHORSPHQW RI IXWXUH PXOWLUHVROXWLRQ VHQVLQJ V\VWHPV $ KD]HFRUUHFWLRQ SURFHGXUH LV UHFRPPHQGHG IRU WKH HQWLUH PXOWLUHVROXWLRQ GDWDVHW 7KLV FRUUHFWLRQ HOLPLQDWHV WKH UDGLDQFH D VPDOO IUDFWLRQ RI GLJLWDO FRXQWf FDXVHG E\ WKH DWPRVSKHUH UDWKHU WKDQ E\ VFHQH UHIOHFWDQFH ,W LV XVXDOO\ SHUIRUPHG E\ VXEWUDFWLQJ WKH YDOXH RI HDFK SL[HO ZLWK WKH

PAGE 129

LPDJHZLGH PLQLPXP GLJLWDO QXPEHU W\SLFDOO\ RI ZDWHU DUHDVf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f RI SUHPHUJHG LPDJHV 7KLV XQGHUVWDQGLQJ SURYLGHV WKH EDVLV IRU ERWK HYDOXDWLQJ WKH HIIHFWLYHQHVV RI H[LVWLQJ LPDJH SURFHVVLQJ HIIRUWV LQ GLJLWDOO\ FRPELQLQJ LPDJHV DQG IRU GHYHORSLQJ QHZ PHUJLQJ DSSURDFKHV IRU PRUH HIIHFWLYH XVH RI VDWHOOLWH LPDJH GDWDVHWV IRU UHPRWH VHQVLQJ DSSOLFDWLRQV 7KH SUHVHUYLQJ PHWKRG LV WKH SUHIHUUHG DSSURDFK IRU PHUJLQJ VDWHOOLWH LPDJHV EHFDXVH RI LWV HIIHFWLYHQHVV LQ

PAGE 130

HQKDQFLQJ WKH UDGLRPHWULF TXDOLW\ RI PHUJHG LPDJH GDWD 7KH FRQILQLQJ DSSURDFK LV GHHPHG DV LQHIIHFWLYH ZKLOH WKH GLIIHUHQFLQJ PHWKRG IRU UDGLRPHWULF LPSURYHPHQW LV OLPLWHG WR FLUFXPVWDQFHV ZKHQ WKH LPDJHV WR EH PHUJHG SRVVHVV D VWURQJ QHJDWLYH FRUUHODWLRQ ,Q D PXOWLUHVROXWLRQ GDWDVHW WKH SDQFKURPDWLF LPDJH XVXDOO\ KDV D EURDG ZDYHEDQG WKDW H[WHQGV WR SDUWV RU HYHQ WKH HQWLUH UDQJHV RI WKH PXOWLVSHFWUDO ZDYHEDQGV HJ 6327 GDWDVHWVf 7KLV VSHFWUDO ZDYHEDQG FKDUDFWHULVWLF IRU ZKLFK QRQQHJDWLYH FRUUHODWLRQV DUH XVXDOO\ REVHUYHG EHWZHHQ WKH SDQFKURPDWLF DQG PXOWLVSHFWUDO LPDJHV ZLOO PDNH WKH XVH RI WKH SUHVHUYLQJ DSSURDFK SDUWLFXODUO\ VXLWDEOH IRU PHUJLQJ PXOWLUHVROXWLRQ GDWDVHWV )RU WKLV VDPH UHDVRQ KRZHYHU WKH XVH RI WKH GLIIHUHQFLQJ DSSURDFK ZLOO EH GHWULPHQWDO WR WKH UDGLRPHWULF TXDOLW\ RI PXOWLUHVROXWLRQ PHUJHG LPDJHV :KHQ D PHUJLQJ PHWKRG LV FKRVHQ VXFK DV WKH SUHVHUYLQJ DSSURDFK WKH YDOXH RI PHUJLQJ FRHIILFLHQW ILf ZLOO SOD\ D YLWDO UROH LQ DIIHFWLQJ WKH RYHUDOO TXDOLW\ UDGLRPHWULF VSDWLDO DQG VSHFWUDOf RI D PXOWLUHVROXWLRQ PHUJHG GDWDVHW ,Q WKH FRQWH[W RI ERWK UDGLRPHWULF DQG VSDWLDO HQKDQFHPHQW D ODUJH YDOXH RI PHUJLQJ FRHIILFLHQW % ZLOO EH EHQHILFLDO +RZHYHU WKH XVH RI DQ H[FHVVLYHO\ ODUJH % YDOXH FRXOG FRUUXSW WKH LQWHJULW\ RI PXOWLVSHFWUDO LQIRUPDWLRQ EHFDXVH RI WKH SRVVLELOLW\ RI LQFUHDVLQJ WKH EHWZHHQZDYHEDQG FRUUHODWLRQV DPRQJ WKH PHUJHG LPDJHV 7KH FRUUXSWHG VSHFWUDO VLJQDWXUHV ZLOO GLPLQLVK WKH XVHIXOQHVV RI WKH PHUJHG GDWDVHW IRU UHPRWH

PAGE 131

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f EHWZHHQ WKH WZR UDWLRLQJ LPDJHV ,Q DGGLWLRQ VHOHFWLQJ WKH QXPHUDWRU LPDJH LV FULWLFDO IRU WKH HIIHFWLYHQHVV RI D UDWLRLQJ PHWKRG ,I WKH UDGLRPHWULF TXDOLWLHV RI D ODQGXVH HOHPHQW DUH WR EH HQKDQFHG WKH LPDJH ZKLFK KDV UHODWLYHO\ ODUJH GLJLWDO EULJKWHUf YDOXHV IRU WKH ODQGXVH HOHPHQW LQ TXHVWLRQ VKRXOG EH XVHG DV WKH QXPHUDWRU LPDJH WR DWWDLQ D UHODWLYH ODUJH EULJKWQHVV UDWLR Af 2WKHUZLVH LW VKRXOG EH XVHG DV WKH GHQRPLQDWRU LPDJH WR GHWUDFW WKH UDGLRPHWULF TXDOLWLHV RI ERWK YDULDQFH DQG EULJKWQHVV

PAGE 132

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f 'DWD 6RXUFH DQG (TXLSPHQW 7KH GDWD VRXUFHV DQG HTXLSPHQW XWLOL]HG LQFOXGH D 6327 +59 PXOWLUHVROXWLRQ GDWDVHW DQ $&,5 SKRWRJUDSK\ WZR FRPSXWHU LPDJH SURFHVVLQJ V\VWHPV DQ $UF,QIR *,6 (65, f DQG D SKRWRJUDPPHWULF VWHUHR SORWWHU IRU PDNLQJ SKRWRJUDPPHWULF PHDVXUHPHQWV IRU WKH HVWLPDWLRQ RI FLWUXV FDQRS\ VL]H 6327 ,PDJH 'DWD DQG 6WXG\ $UHD $ PXOWLUHVROXWLRQ VFHQH DFTXLUHG E\ WKH 6327 +59 VHQVRU ZDV XVHG 7KH 6327 VFHQH f KDV DQ DUHD FRYHUDJH RI WKH HQWLUH 6W /XFLH FRXQW\ )ORULGD )LJXUH f DQG FRQVLVWV RI IRXU LPDJHV WKDW ZHUH DFTXLUHG VLPXOWDQHRXVO\ RQ 2FWREHU 2I WKH IRXU 6327 LPDJHV RQH LV SDQFKURPDWLF

PAGE 133

ZKLOH WKH RWKHUV DUH PXOWLVSHFWUDO ZLWK FRUUHVSRQGLQJ VSDWLDO UHVROXWLRQV RI P DQG P UHVSHFWLYHO\ 7KH VSHFWUDO ZDYHOHQJWK XQf UDQJHV DUH IRU WKH SDQFKURPDWLF LPDJH DQG JUHHQf UHGf DQG 1,5f IRU WKH PXOWLVSHFWUDO LPDJHV 7KH SDQFKURPDWLF ZDYHEDQG HQFRPSDVVHV DOPRVW WKH HQWLUH EDQGZLGWK RI WKH JUHHQ DQG UHG ZDYHEDQGV SOXV D VPDOO SRUWLRQ RI WKH 1,5 ZDYHOHQJWK UDQJH Pf )RU HDVH RI H[SODQDWLRQ WKH 6327 JUHHQ UHG 1,5 DQG SDQFKURPDWLF ZDYHEDQGV DUH GHQRWHG DV ZDYHEDQGV +59 +59 +59M DQG 3$1 UHVSHFWLYHO\ 7KH 6327 VFHQH ZDV FOLSSHG WR DQ DUHD RI DSSUR[LPDWHO\ NP E\ SL[HOV RI P VL]Hf ORFDWHG LQ WKH QRUWK FHQWUDO SRUWLRQ RI 6W /XFLH FRXQW\ )LJXUH f 7KLV FOLSSHG VFHQH ZDV GHVLJQDWHG DV WKH VWXG\ DUHD LQ ZKLFK SDVWXUH ODQGV DQG FLWUXV JURYHV ZHUH IRXQG WR EH SUHGRPLQDQW WRJHWKHU ZLWK VRPH LVRODWHG XUEDQ ODQGV DQG UHVLGHQWLDO DUHDV ,Q WKH GLVFXVVLRQV WKDW IROORZ D 6327 LPDJH LV VLPSO\ UHIHUUHG WR WKH FOLSSHG DUHD )LJXUH f 7KH PDLQ XVDJH RI WKLV 6327 VFHQH ZDV WR VWXG\ WKH HIIHFWV RI PXOWLUHVROXWLRQ SURFHVVLQJ RQ ODQGXVH FODVVLILFDWLRQ DQG WKH IHDVLELOLW\ RI GLIIHUHQWLDWLQJ FLWUXV JURYHV EDVHG RQ FDQRS\ VL]H GLIIHUHQFH 6LQFH WKH GLIIHUHQWLDWLRQ RI FLWUXV FDQRS\ FRYHU LV WKH PRVW GLIILFXOW RQ VDWHOOLWH LPDJHV DFTXLUHG LQ VXPPHU VHDVRQV WKH XVH RI WKLV 6327 VDWHOOLWH VFHQH ZLOO UHQGHU DGGLWLRQDO LQVLJKWV LQWR WKH IHDVLELOLW\ RI FODVVLI\LQJ FLWUXV JURYHV XVLQJ UHPRWH VHQVLQJ GDWDVHWV

PAGE 134

NP )LJXUH /RFDWLRQ RI FOLSSHG 6327 PXOWLUHVROXWLRQ GDWDVHW DQG VWXG\ DUHD

PAGE 135

$&,5 3KRWRJUDSK\ $&,5 SKRWRJUDSK\ FRYHULQJ WKH VDPH DUHD DV WKH FOLSSHG 6327 VFHQH ZDV WDNHQ RQ )HEUXDU\ 7KH .RGDN $HURFKURPH FRORU LQIUDUHG ILOP ZDV XVHG DORQJ ZLWK D FP LQFKf IRFDO OHQJWK FDPHUD ZLWK D PLQXVEOXH ILOWHUf IORZQ DW D KHLJKW RI P IWf 7KH ILOP ZDV GHYHORSHG LQWR D VHW RI [ PP LQFK [ LQFKf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f ORFDWHG LQ WKH 5HPRWH 6HQVLQJ $SSOLFDWLRQ /DERUDWRU\ 56$/f RI

PAGE 136

WKH 'HSDUWPHQW RI $JULFXOWXUDO (QJLQHHULQJ DW WKH 8QLYHUVLW\ RI )ORULGD 7KLV LPDJH SURFHVVLQJ SDFNDJH FRQWDLQV H[WHQVLYH LPDJH SURFHVVLQJ FDSDELOLWLHV IRU LPDJH HQKDQFHPHQW LPDJH UHJLVWUDWLRQUHFWLILFDWLRQ ODQGXVH FODVVLILFDWLRQ *,6 DQDO\VHV HWF (5'$6 f 7KH (5'$6 V\VWHP XVHG LV WKH 3& YHUVLRQ f IRU PLFUR FRPSXWHUV ZLWK D 9*$ GLVSOD\ ,Q DGGLWLRQ WR WKH (5'$6 V\VWHP WKH (DUWK 5HVRXUFHV /DERUDWRU\ $SSOLFDWLRQ 6RIWZDUH (/$6f LPDJH SURFHVVLQJ V\VWHP 3& YHUVLRQf ZDV DOVR XVHG *UDKDP HW DO f 7KH SULPDU\ XVDJH RI (/$6 ZDV IRU ODQGXVH FODVVLILFDWLRQ FRPSDULVRQV DV ZHOO DV IRU YDULRXV LQWHUDFWLYH LPDJH GLVSOD\ SXUSRVHV LQ JURXQGWUXWKLQJ FODVVLILHG GDWDVHWV )RU PRUH LQIRUPDWLRQ UHJDUGLQJ WKH WZR HQWLUH LPDJH SURFHVVLQJ V\VWHPV WKH DSSURSULDWH GRFXPHQWDWLRQ *UDKDP HW DO (5'$6 f RI WKH DIRUHPHQWLRQHG VRIWZDUH V\VWHPV VKRXOG EH FRQVXOWHG 7KH $UF,QIR *,6 (65, f V\VWHP ORFDWHG DW WKH VDPH 56$/ ODE ZDV DOVR XWLOL]HG IRU GLJLWL]LQJ RSHUDWLRQV RI JUDSKLFDO PDS GDWD HQWU\ DQG PLVFHOODQHRXV SURFHVVLQJ DQG FRQYHUVLRQV RI LPDJH JULG GDWD 3KRWRJUDPPHWULF 6WHUHR 3ORWWHU $ SKRWRJUDPPHWULF VWHUHR SORWWHU )0$ 0RGHO 0XOWL)RUPDW 3KRWR ,QWHUSUHWDWLRQ 6WDWLRQf ZDV XWLOL]HG WR PDNH SKRWRJUDPPHWULF PHDVXUHPHQWV IURP WKH $&,5 SKRWRJUDSK\ IRU FLWUXV FDQRS\ FRYHU HVWLPDWLRQ 7KH SORWWHU FRQVLVWV RI WZR YLHZLQJ SODWHV RQH DGMXVWDEOH PDJQLI\LQJ YLHZLQJ OHQV

PAGE 137

DVVHPEO\ ZLWK D PD[LPXP PDJQLILFDWLRQ SRZHU D ERG\ IUDPH DQG WZR YHUQLHU PHDVXULQJ GHYLFHV IRU [ DQG \ GLUHFWLRQVf HDFK ZLWK D GHVLJQHG SUHFLVLRQ RI PP )RU WKLV $&,5 SKRWRJUDSK\ WKH SORWWHU SUHFLVLRQ PPf FDQ EH WUDQVODWHG [ PPf LQWR D PP RU FPf KRUL]RQWDO GLVWDQFH RQ WKH JURXQG 3KRWRJUDPPHWULF PHDVXUHPHQWV ZHUH XVHG WR REWDLQ ILHOG SODQWLQJ JHRPHWU\ URZ DQG WUHH VSDFLQJVf DQG WUHH FURZQ GLDPHWHU IRU WKH HVWLPDWLRQ RI FLWUXV FDQRS\ VL]H 3URFHGXUHV IRU 0HUJLQJ 6327 'DWDVHW %HIRUH WKH 6327 PXOWLUHVROXWLRQ LPDJHV ZHUH GLJLWDOO\ PHUJHG VRPH SUHPHUJLQJ SURFHVVLQJ ZDV QHFHVVDU\ ZKLFK LQFOXGHG LPDJH FRUHJLVWUDWLRQ DQG KD]H FRUUHFWLRQV $ PHUJLQJ PHWKRG PXVW EH FKRVHQ DFFRUGLQJ WR WKH 6327 LPDJH GDWD FKDUDFWHULVWLFV D Q DQG Uf WR JHQHUDWH PHUJHG LPDJH GDWD IURP WKH FRUHJLVWHUHG PXOWLUHVROXWLRQ LPDJHV IRU WKH DVVHVVPHQWV RI UDGLRPHWULF HQKDQFHPHQW VSDWLDO LPSURYHPHQW DQG ODQGXVH FODVVLILFDWLRQ 3UHPHUJLQJ 3URFHVVLQJ 7KH PXOWLVSHFWUDO LPDJHV ZLWK D P VSDWLDO UHVROXWLRQ ZHUH HDFK UHVDPSOHG WR D P SL[HO VL]H WKURXJK D GXSOLFDWLRQ DSSURDFK $V D UHVXOW RI WKLV UHVDPSOLQJ HDFK RI WKH SL[HOV LQ DQ RULJLQDO PXOWLVSHFWUDO LPDJH EHFDPH IRXU LGHQWLFDO RQHV LQ WKH UHVDPSOHG GDWDVHW 7KHQ WKH SDQFKURPDWLF LPDJH ZKLFK

PAGE 138

KDG D P VSDWLDO UHVROXWLRQ ZDV FRUHJLVWHUHG WR WKH UHVDPSOHG PXOWLVSHFWUDO LPDJHV %HFDXVH RI DFFXUDF\ FRQFHUQV IRU WRSRJUDSKLFDO PDSV 7KRUSH $6356 f DQG PDS GDWD HQWU\ RSHUDWLRQV %ROVWDG HW DO 7DQ DQG 6KLK Ef WKH LPDJH FRUHJLVWUDWLRQ ZDV GRQH ZLWKRXW XVLQJ DQ DFWXDO JHRJUDSKLFDO UHIHUHQFH V\VWHP HJ 870f $ WRWDO RI PXWXDO SRLQWV ZHUH VHOHFWHG DV WLH SRLQWV EHWZHHQ WKH PXOWLVSHFWUDO DQG SDQFKURPDWLF LPDJHV 7KH URRWPHDQVTXDUH 506f HUURU IRU WKHVH VHOHFWHG SRLQWV ZDV P 7KH PXOWLVSHFWUDO LPDJHV ZHUH WUHDWHG DV D PDVWHU WR ZKLFK WKH SDQFKURPDWLF LPDJH ZDV UHFWLILHG DV D VODYH 6LQFH WKH EHWZHHQZDYHEDQG UHJLVWUDELOLW\ RI WKH 6327 VHQVRU LV P 6327 f WKH FRUHJLVWUDWLRQ RI WKH 6327 LPDJHV ZDV FRQVLGHUHG YHU\ DFFXUDWH ZLWK D 506 HUURU RI P +D]H FRUUHFWLRQ ZDV DOVR DSSOLHG WR WKH FOLSSHG 6327 VFHQH EHIRUH EHLQJ PHUJHG )URP WKH UDZ LPDJH GDWD RI WKH FOLSSHG DUHD WKH PLQLPXP YDOXHV IRU WKH SDQFKURPDWLF UHG JUHHQ DQG 1,5 ZDYHEDQGV ZHUH DQG UHVSHFWLYHO\ 7KHUHIRUH WKH KD]HFRUUHFWLRQ FRHIILFLHQWV ZHUH FKRVHQ DV IRU WKH SDQFKURPDWLF ZDYHEDQG DQG WKH PLQLPXP RI DQG f IRU WKH WKUHH PXOWLVSHFWUDO LPDJHV 7KH SL[HO YDOXHV HDFK ZHUH VXEWUDFWHG E\ IRU WKH SDQFKURPDWLF LPDJH DQG E\ IRU DOO WKH PXOWLVSHFWUDO LPDJHV 7KLV VSHFLILF KD]HFRUUHFWLRQ SURFHGXUH ZDV GRQH WR SUHVHUYH WKH LQWHJULW\ RI VSHFWUDO LQIRUPDWLRQ LQ WKH RULJLQDO PXOWLVSHFWUDO GDWD 7KH VWDQGDUG GHYLDWLRQV IRU WKH JUHHQ UHG 1,5 DQG SDQFKURPDWLF ZDYHEDQGV

PAGE 139

RI WKH KD]HFRUUHFWHG 6327 GDWDVHW DUH SUHVHQWHG LQ 7DEOH $OVR VKRZQ LQ 7DEOH DUH WKH FRUUHODWLRQ FRHIILFLHQWV Uf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f RI DQG IRU WKH JUHHQ UHG DQG 1,5 ZDYHEDQGV 7KHUHIRUH WKH SUHVHUYLQJ DSSURDFK LV FKRVHQ LQ RUGHU WR JHQHUDWH UDGLRPHWULFDOO\ HQKDQFHG PHUJHG LPDJH GDWD IRU LPSURYLQJ WKH GLIIHUHQWLDWLRQ RI ODQGXVH HOHPHQWV 7KH YDOXH RI PHUJLQJ FRHIILFLHQW f IRU WKH VHOHFWHG PHUJLQJ PHWKRG PXVW EH GHWHUPLQHG ZLWK GXH FRQVLGHUDWLRQV WR WKH UDGLRPHWULF TXDOLW\ DQG SRWHQWLDO VSDWLDO LPSURYHPHQW DV ZHOO DV WKH VSHFWUDO LQWHJULW\ RI WKH ILQDO PHUJHG GDWDVHW )URP FKDSWHU LW ZDV QRWHG WKDW WKH PDJQLWXGH RI PHUJLQJ FRHIILFLHQW 5 FDQ KDYH D VWURQJ LPSDFW RQ WKH TXDOLW\ RI D PXOWLUHVROXWLRQ PHUJHG GDWDVHW $ ODUJH YDOXH RI LV EHQHILFLDO WR ERWK WKH UDGLRPHWULF DQG VSDWLDO HQKDQFHPHQWV

PAGE 140

7DEOH 6WDQGDUG GHYLDWLRQ Df PHDQ Qf PD[LPXP DQG PLQLPXP YDOXHV DQG FRUUHODWLRQ FRHIILFLHQWV Uf RI 6327 PXOWLUHVROXWLRQ GDWDVHW :DYHEDQG 0! f Uf 0D[ 0LQ JUHHQf UHGf 1,5f 3 SDQf f§ 1RWH &RUUHODWLRQ FRHIILFLHQWV Uf DUH WR WKH SDQFKURPDWLF LPDJH ZKLFK ZDV XVHG DV VHFRQGDU\ LPDJH GDWD

PAGE 141

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f ZLOO LQFUHDVH WKH H[WHQW RI SDQFKURPDWLF LQIRUPDWLRQ LQ HDFK RI WKH PHUJHG PXOWLVSHFWUDO LPDJHV FUHDWLQJ WKH SRWHQWLDO IRU FRUUXSWLQJ WKH LQWHJULW\ RI PXOWLVSHFWUDO LQIRUPDWLRQ LQ WKH RULJLQDO GDWD :KHQ WKH VSDWLDO UDGLRPHWULF DQG VSHFWUDO FRQVLGHUDWLRQV DUH SXW LQ SHUVSHFWLYH D 5 YDOXH RI ZDV FKRVHQ IRU WKH SUHVHUYLQJ PHWKRG WR JHQHUDWH D PXOWLUHVROXWLRQ PHUJHG GDWDVHW IURP WKH FRUHJLVWHUHG 6327 LPDJH GDWD ,Q DGGLWLRQ D QRUPDOL]HG GLIIHUHQFH YHJHWDWLRQ LQGH[ 1'9,f LPDJH ZDV DOVR JHQHUDWHG XVLQJ WKH P 1,5 +59f DQG P SDQFKURPDWLF 3$1f ZDYHEDQGV WR GHYHORS D QHZ DSSURDFK LQ XVLQJ 6327 LPDJH GDWD IRU YHJHWDWLRQ VWXG\ 7KLV 1'9, LPDJH LV QDPHG DV 1'9,S LQ RUGHU WR GLVWLQJXLVK LW IURP WKH FXVWRPDU\ 1'9, LPDJH .LGZHOO f XVXDOO\ FUHDWHG IURP WKH +59 1,5f DQG +59 UHGf ZDYHEDQGV 7KH 1'9,S IRU D 6327 GDWDVHW LV GHILQHG DV 1,5 3$1 1'9,S >@ 1,5 3$1

PAGE 142

7KH SXUSRVH RI JHQHUDWLQJ WKH 1'9,S LPDJH ZDV WR DVVHVV LWV HIIHFWLYHQHVV LQ GLIIHUHQWLDWLQJ YHJHWDWLRQ VXFK DV FLWUXV FDQRS\ FRYHUV 7KHUH ZHUH WKUHH GDWDVHWV 7DEOH f XVHG IRU IXUWKHU DQDO\VHV LQFOXGLQJ ODQGXVH FODVVLILFDWLRQ DVVHVVPHQW 7KHVH GDWDVHWV DUH GHQRWHG DV f 20'f§RULJLQDO PXOWLVSHFWUDO GDWDVHW RI WKH P PXOWLVSHFWUDO LPDJHV RI WKH JUHHQ UHG DQG 1,5 ZDYHEDQGV f 00'f§PXOWLUHVROXWLRQ PHUJHG GDWDVHW E\ WKH SUHVHUYLQJ DSSURDFK ZLWK IRU HDFK LPDJH DQG f 001'f§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f RI LPDJH GDWD LQ 20' 00' DQG 001' ZHUH REWDLQHG WKURXJK WKH (5'$6 LPDJH SURFHVVLQJ V\VWHP DQG WKHQ FRPSDUHG ZLWK WKRVH RI WKH RULJLQDO GDWD ,Q DGGLWLRQ WKH HVWLPDWHV RI VWDQGDUG GHYLDWLRQ ZHUH DOVR FDOFXODWHG EDVHG RQ WKH FRUUHVSRQGLQJ HTXDWLRQV LQ FKDSWHU DQG WKHQ FRPSDUHG

PAGE 143

7DEOH 0XOWLUHVROXWLRQ GDWDVHWV DQG FRUUHVSRQGLQJ PHUJLQJ HTXDWLRQV 'DWDVHW :DYHEDQG 0HUJLQJ HTXDWLRQ 20' JUHHQf UHGf 1,5f +59 RULJLQDOf +59 RULJLQDOf +59M RULJLQDOf 00' JUHHQf UHGf 1,5f +59 3$1 +59 3$1 +59 3$1 001' JUHHQf UHGf 1'9,Sf +59 3$1 +59 3$1 +59 3$1f +593$1f 1RWH 20' RULJLQDO PXOWLVSHFWUDO GDWDVHW ZKLFK LQFOXGHV WKH RULJLQDO WKUHH P PXOWLVSHFWUDO LPDJHV 00' PXOWLUHVROXWLRQ PHUJHG GDWDVHW JHQHUDWHG E\ WKH SUHVHUYLQJ DSSURDFK ZLWK % IRU HDFK LPDJH 001' PXOWLUHVROXWLRQ PHUJHG DQG 1'9,S GDWDVHW ZKLFK LV VLPLODU WR 00' H[FHSW WKDW WKH PHUJHG 1,5 LPDJH LV UHSODFHG E\ WKH 1'9, GDWD +59M DQG 3$1 DUH PXOWLVSHFWUDO DQG SDQFKURPDWLF LPDJHV UHVSHFWLYHO\

PAGE 144

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f ZHUH DVVLJQHG WR WKH EOXH JUHHQ DQG UHG FRORU SULPDULHV UHVSHFWLYHO\ 7KLV FRORU DVVLJQPHQW ZDV GRQH WR PDNH WKH DSSHDUDQFH RI WKH JHQHUDWHG FRORU FRPSRVLWHV VLPLODU WR WKDW RI DQ $&,5 SKRWRJUDSK\ ZKLFK LV WKH PRVW ZLGHO\ XVHG LQ SKRWRJUDSKLF UHPRWH VHQVLQJ DSSOLFDWLRQV 7KH ,+6 WUDQVIRUP ZDV QRW XVHG EHFDXVH RI LWV XQLYHUVDO DGDSWDELOLW\ RU LQVHQVLWLYLW\ WR D ZLGH UDQJH RI GDWD TXDOLW\ 3HOOHPDQV HW DO &KDYH] HW DO &DUSHU HW DO +DUULV HW DO :HOFK DQG (KOHUV &OLFKH HW DO 'DLO\ DQG +\GDQ HW DO f ZKLFK FRXOG LQWURGXFH DPELJXLW\ WR WKH HYDOXDWLRQ 7KH HYDOXDWLRQ RI VSHFWUDO LQWHJULW\ RI D PHUJHG GDWDVHW ZDV EDVHG RQ FRPSDULVRQV RI FRORU FRPSRVLWH DQG FRUUHODWLRQ DQDO\VHV ,I WKH FRORU FRPSRVLWH RI D PHUJHG GDWDVHW VKRZV D

PAGE 145

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f / [ KI >@ ZKHUH / LV WKH DFWXDO JURXQG GLVWDQFH Pf K LV WKH IO\LQJ KHLJKW Pf I LV WKH IRFDO OHQJWK RI FDPHUD OHQV PPf DQG '

PAGE 146

LV WKH GLVWDQFH QXQf RQ WKH SKRWR ZKLFK LV REWDLQHG E\ \[;Of \@ ZKHUH [ DQG \ DUH SKRWR FRRUGLQDWHV PPf IRU SRLQWV DQG ZKLFK ZHUH UHDG GLUHFWO\ IURP WKH $&,5 SKRWRJUDSK\ WKURXJK WKH VWHUHR SORWWHU 7KH SKRWRJUDPPHWULF DFFXUDF\ RI WKH $&,5 SKRWRJUDSK\ ZDV WHVWHG XVLQJ KLJKZD\ SDYHPHQW ,QWHUVWDWH +LJKZD\ )ORULGD 7XUQSLNH DQG ORFDO URDGVf 7KH SKRWR PHDVXUHPHQWV RI KLJKZD\ SDYHPHQW ZLGWK DW ORFDWLRQV ZHUH REWDLQHG IURP WKH VWHUHR SORWWHU DQG WKHQ FRQYHUWHG WR JURXQG GLVWDQFH XVLQJ HTXDWLRQV >@ DQG >@ $ FRPSDULVRQ RI WKH SKRWRJUDPPHWULF UHVXOWV ZLWK WKH GDWD REWDLQHG IURP WKH ORFDO KLJKZD\ PDLQWHQDQFH RIILFHV LQGLFDWHG D 506 HUURU RI P IWf ZKLFK VXJJHVWHG D YHU\ DFFXUDWH HVWLPDWLRQ IRU WKLV SKRWRJUDPPHWU\ (LJKWHHQ FLWUXV JURYHV ZLWKLQ WKH VWXG\ DUHD )LJXUH f ZHUH VHOHFWHG WKURXJK D YLVXDO LQVSHFWLRQ RI WKH $&,5 SKRWRJUDSKV 7KHVH JURYHV ZHUH XQLIRUP LQ WKDW WKH QXPEHU RI PLVVLQJ RU GHDG WUHHV ZDV IHZ RU ]HUR 3KRWRJUDPPHWULF PHDVXUHPHQWV ZHUH PDGH RQO\ LQ WKH FHQWUDO SRUWLRQ RI HDFK SKRWRJUDSK 7KLV ZDV GRQH WR PLQLPL]H WKH SRWHQWLDO VFDOH GLVWRUWLRQV UHVXOWLQJ IURP FDPHUD OHQV DQG IOLJKW RSHUDWLRQV /LOOHVDQG DQG .LHIHU &XUUDQ f 7KH UDGLXV RI WKH FHQWUDO SRUWLRQ ZDV DERXW PP LQFKHVf FHQWHUHG DW WKH SKRWR SULQFLSDO SRLQW %HFDXVH RI WKH IODW WHUUDLQ LQ VRXWK )ORULGD FRUUHFWLRQV ZHUH QRW QHHGHG IRU WKH HIIHFW RI WRSRJUDSKLF YDULDWLRQV RQ WKH SKRWRJUDPPHWULF PHDVXUHPHQWV

PAGE 147

)RU HDFK VHOHFWHG JURYH WZR WR ILYH URZV ZHUH UDQGRPO\ FKRVHQ IRU WDNLQJ SKRWRJUDPPHWULF PHDVXUHPHQWV ZKLFK LQFOXGHG URZ OHQJWK IRU WKH VHOHFWHG URZV ILHOG ZLGWK DW VHYHUDO ORFDWLRQV DW OHDVW WKUHHf DQG WKH FURZQ GLDPHWHU RI LQGLYLGXDO WUHHV LQ DOO VHOHFWHG URZV 7KH PHDVXUHPHQWV ZHUH XVHG IRU FDOFXODWLQJ ILHOG SODQWLQJ JHRPHWU\ URZ DQG WUHH VSDFLQJVf DQG WKH GLDPHWHU RI WUHH FURZQ 7UHH VSDFLQJ Df ZLWKLQ D URZ ZDV REWDLQHG E\ GLYLGLQJ WKH URZ OHQJWK E\ WKH QXPEHU RI WUHHV LQ D URZ DQG DYHUDJHG RYHU WKH VHOHFWHG URZV LQ D ILHOG H[FOXGLQJ WKUHH WUHHV IURP HDFK RI WKH URZ HQGV 6LPLODUO\ URZ VSDFLQJ Ef ZDV REWDLQHG E\ GLYLGLQJ WKH ILHOG ZLGWK E\ WKH QXPEHU RI URZV LQ WKH JURYH DQG DYHUDJHG RYHU WKH QXPEHU RI PHDVXUHG ORFDWLRQV DW OHDVW WKUHH ORFDWLRQVf DORQJ WKH URZ OHQJWK H[FOXGLQJ WZR URZV IURP HDFK VLGH RI WKH ILHOG 7KH GLDPHWHU RI WUHH FURZQ Gf ZDV EDVHG RQ WKH DYHUDJH RI DOO PHDVXUHG WUHHV LQ D VHOHFWHG JURYH ,Q DGGLWLRQ WKH SKRWRJUDPPHWULF PHDVXUHPHQWV RI WUHH DQG URZ VSDFLQJV ZHUH JURXQGWUXWKHG IRU DFFHVVLEOH VHOHFWHG JURYHV &DQRS\ &RYHU (VWLPDWLRQ 7ZR FDVHV ZHUH HQFRXQWHUHG LQ WKH HVWLPDWLRQ RI FLWUXV FDQRS\ FRYHUV XVLQJ WKH $&,5 SKRWRJUDPPHWULF PHDVXUHPHQWV 7KH ILUVW FDVH ZDV WKDW WUHH FURZQV ZHUH ZLWKLQ WKH DUHD ERXQGHG E\ WUHH VSDFLQJ Df DQG URZ VSDFLQJ Ef ,Q WKLV FDVH SHUFHQWDJH FLWUXV FDQRS\ FRYHU f IRU HDFK VHOHFWHG

PAGE 148

JURYH ZDV HVWLPDWHG E\ WKH IROORZLQJ HTXDWLRQ 7Gfr H ; b >@ D [ E )RU PDWXUH JURYHV ZLWK WUHHV VOLJKWO\ RYHUODSSHG RU WUHH FURZQ ODUJHU WKDQ WUHH VSDFLQJ WKH RYHUODSSLQJ DUHDV $Rf RQ ERWK VLGHV PXVW EH H[FOXGHG )RU WKLV FDVH SHUFHQWDJH FDQRS\ FRYHU ZDV HVWLPDWHG E\ UGfr$ [ b >@ D [ E DQG WKH RYHUODSSLQJ DUHDV $R Pf ZHUH FDOFXODWHG E\ WKH IROORZLQJ HTXDWLRQV $ >UG fDGDr f @ >@ WDQn >G D fD@ S rf >@ ZKHUH D LV WUHH VSDFLQJ Pf E LV URZ VSDFLQJ Pf DQG G LV GLDPHWHU RI WUHH FURZQ Pf /RFDWLRQV RI WKH VHOHFWHG FLWUXV JURYHV LQ WKH 6327 VFHQH ZHUH LGHQWLILHG E\ VFDQ OLQHV DQG SL[HOV LQ HDFK RI WKH WKUHH GDWDVHWV LQFOXGLQJ WKH RULJLQDO RQH ZLWK D P VSDWLDO UHVROXWLRQ )RU HDFK ZDYHEDQG RI D GDWDVHW WKH PHDQ DQG VWDQGDUG GHYLDWLRQ RI JURYHZLGH SL[HO YDOXHV ZHUH REWDLQHG H[FOXGLQJ WKRVH SL[HOV DORQJ ILHOG ERXQGDULHV 7KH UHODWLRQV

PAGE 149

EHWZHHQ HVWLPDWHG FDQRS\ FRYHU DQG LPDJH VSHFWUDO UHVSRQVH ZHUH LQYHVWLJDWHG 7R DVVHVV WKH IHDVLELOLW\ RI GLIIHUHQWLDWLQJ FLWUXV JURYHV EDVHG RQ GLIIHUHQFHV RI FDQRS\ FRYHU WKH YDULDWLRQV RI LPDJH VSHFWUDO UHVSRQVHV RU SL[HO YDOXHVf ZHUH DQDO\]HG IRU DOO VHOHFWHG JURYHV WKURXJK FRLQFLGHQW SORWV RI ILHOGZLGH LPDJH GDWD QsDf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f /DQGXVH &ODVVLILFDWLRQ /DQGXVH FODVVLILFDWLRQ DQDO\VHV ZHUH SHUIRUPHG RQ WKH WKUHH GDWDVHWV OLVWHG LQ 7DEOH 7KH DQDO\VHV ZHUH EDVHG RQ WKH FDSDELOLW\ RI HDFK GDWDVHW WR GLIIHUHQWLDWH WKH VFHQH HQYLURQPHQW WKURXJK VSHFWUDO VLJQDWXUH H[WUDFWLRQ ,Q DGGLWLRQ D *,6EDVHG GLVFUHWH ODQGXVH FODVVLILFDWLRQ WHFKQLJXH ZDV LQWURGXFHG DQG DSSOLHG WR WKH FDQRS\VL]H FODVVLILFDWLRQ RI FLWUXV JURYHV

PAGE 150

3UFOV DQG &RQFHSW &RPSXWHUL]HG ODQGXVH FODVVLILFDWLRQ IURP UHPRWH VHQVLQJ GDWDVHWV LV D WZRVWHS SDWWHUQ UHFRJQLWLRQ SURFHGXUH ZKLFK LQYROYHV D WUDLQLQJ SURFHVV DQG D VRUWLQJ WHFKQLJXH RU FODVVLILFDWLRQ GHFLVLRQ UXOH ,Q RUGHU WR FODVVLI\ D VFHQH RU GDWDVHW WKH VSHFWUDO VLJQDWXUH SDWWHUQV WKDW DUH UHODWHG WR YDULRXV ODQGXVH W\SHV ZLWKLQ WKH VFHQH PXVW EH H[WUDFWHG DQG GHILQHG XVLQJ VWDWLVWLFDO FULWHULRQ HJ PHDQV YDULDQFHV DQG FRYDULDQFHVf LPSOHPHQWHG LQ DQ LPDJH SURFHVVLQJ V\VWHP 7KLV VWHS RI GHILQLQJ VLJQDWXUH SDWWHUQV LV FDOOHG WKH WUDLQLQJ SURFHVV ZKRVH SXUSRVH LV WR WHDFK WKH FRPSXWHU V\VWHP WR UHFRJQL]H WKH VLJQDWXUH SDWWHUQV LQKHUHQW LQ WKH PXOWLZDYHEDQG GDWD ,W LV XVXDOO\ GRQH WKURXJK HLWKHU D VXSHUYLVHG RU DQ XQVXSHUYLVHG DSSURDFK /LOOHVDQG DQG .LHIHU (5'$6 f ,Q D VXSHUYLVHG WUDLQLQJ WKH DQDO\VW GLUHFWV RU VXSHUYLVHV WKH FRPSXWHU LQ GHILQLQJ WKH VLJQDWXUH SDWWHUQV ZLWK WKH KHOS RI KLV SULRU NQRZOHGJH RU H[LVWLQJ LQIRUPDWLRQ DERXW WKH JURXQG 7KH SURFHVV WDNHV SODFH LQ DQ LQWHUDFWLYH IDVKLRQ EHWZHHQ WKH FRPSXWHU DQG WKH DQDO\VW 2QH DSSDUHQW DGYDQWDJH RI D VXSHUYLVHG WUDLQLQJ LV WKDW DFFXUDWH VLJQDWXUH SDWWHUQV FDQ EH JHQHUDWHG IRU WKH ODQGXVH W\SHV IRU ZKLFK WKHUH LV DEXQGDQW H[LVWLQJ LQIRUPDWLRQ +RZHYHU IRU WKRVH ODQGXVH W\SHV IRU ZKLFK WKHUH LV QRW VXIILFLHQW LQIRUPDWLRQ WKH\ DUH XVXDOO\ LJQRUHG RU WUHDWHG DV EDFNJURXQG

PAGE 151

HOHPHQWV 7KH HPSKDVLV LV JLYHQ PDLQO\ WR WKH ODQGXVH W\SHV ZLWK DYDLODEOH LQIRUPDWLRQ ,Q DGGLWLRQ WKH DQDO\VW LV RIWHQ LQFDSDEOH RI LGHQWLI\LQJ WKH VXESDWWHUQV ZLWKLQ D EURDG ODQG XVH W\SH HYHQ WKRXJK WKRVH VLJQDWXUH SDWWHUQV DUH VWDWLVWLFDOO\ VHSDUDEOH DQG PLJKW SRVVHVV VRPH VLJQLILFDQFH &RQVHTXHQWO\ WKHUH LV D JUHDW SRVVLELOLW\ WKDW WKH ZKROH VHW RI VLJQDWXUH SDWWHUQV LQKHUHQW WR D GDWDVHW ZLOO HLWKHU EH LQFRPSOHWH RU VXEMHFWLYH LQ D VXSHUYLVHG WUDLQLQJ ,Q FRQWUDVW WR WKH VXSHUYLVHG DSSURDFK WKH XQVXSHUYLVHG WUDLQLQJ LV YHU\ DXWRPDWHG %DVHG RQ VRPH LQSXW FULWHULRQ VSHFLILHG E\ WKH DQDO\VW WKH FRPSXWHU V\VWHP VHDUFKHV WKURXJK WKH GDWDVHW WR XQYHLO DOO WKH XQLTXH VWDWLVWLFDO SDWWHUQV WKDW DUH LQKHUHQW LQ WKH LPDJH GDWD 7KLV WUDLQLQJ DSSURDFK ZLOO DOORZ WKH GHULYDWLRQ RI D FRPSOHWH VHW RI VLJQDWXUH SDWWHUQV ZKLOH DOLHQDWLQJ WKH OLNHO\ VXEMHFWLYLW\ RI D VXSHUYLVHG WUDLQLQJ 7R FKRRVH RU VHOHFW WKH SURSHU FULWHULRQ RU LQSXW SDUDPHWHUVf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

PAGE 152

SURFHGXUH $ VXPPDU\ RI WKH FRPPRQO\ XVHG FODVVLILFDWLRQ GHFLVLRQ UXOHV LV SUHVHQWHG LQ $SSHQGL[ ZKLFK LQFOXGHV WKH SDUDOOHOHSLSHG FODVVLILHU WKH PLQLPXP GLVWDQFH FODVVLILHU WKH PDKDODQRELV GLVWDQFH FODVVLILHU DQG WKH PRVW ZLGHO\ XVHG PD[LPXP OLNHOLKRRG FODVVLILHU /LOOHVDQG DQG .LHIHU (5'$6 f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f PRGXOH ZDV XVHG ,Q DQ

PAGE 153

XQVXSHUYLVHG VWDWLVWLFDO FOXVWHULQJ SURFHGXUH WKH PRVW LPSRUWDQW SDUDPHWHU LV WKH VFDOHG VSHFWUDOf GLVWDQFH (5'$6 *UDKDP HW DO f ZKLFK GHILQHV WKH VHSDUDELOLW\ FULWHULD IRU DOO VLJQDWXUH SDWWHUQV RI D GDWDVHW ZLWKLQ D PXOWLGLPHQVLRQDO VSDFH ERXQG E\ WKH ZDYHEDQGV 7ZR VLJQDWXUH SDWWHUQV DUH FRQVLGHUHG QRW VHSDUDEOH LI WKHLU VFDOHG GLVWDQFH LV OHVV WKDQ WKH VSHFLILHG YDOXH DXWRPDWLFDOO\ PHUJHGf :KHQ WKH VFDOHG GLVWDQFH LV VHW DW D ODUJH YDOXH WKH QXPEHU RI VHSDUDEOH VLJQDWXUH SDWWHUQV ZLOO EHFRPH VPDOOHU 2Q WKH RWKHU KDQG D VPDOO VFDOHG GLVWDQFH ZLOO DOORZ D WLJKW FOXVWHULQJ PDNLQJ FORVHO\ UHODWHG VLJQDWXUH SDWWHUQV EHFRPH VHSDUDEOH (5'$6 f 7KH (5'$6 67$7&/ PRGXOH ZDV XVHG ZLWK D ODUJH QXPEHU f RI FRQFHLYDEOH VSHFWUDO SDWWHUQV WR HQVXUH WKDW QRQH RI WKH SRWHQWLDOO\ VHSDUDEOH VLJQDWXUH SDWWHUQV ZLOO EH IRUFHG WR PHUJH WR WKH RWKHUV EHIRUH WKH FOXVWHULQJ SURFHVV LV FRPSOHWHG $OVR VHYHUDO YDOXHV RI VFDOHG GLVWDQFH ZHUH XVHG LQ RUGHU WR H[DPLQH WKH FRQVLVWHQF\ DV ZHOO DV WKH GHSHQGDELOLW\ RI D PHUJHG GDWDVHW ,Q RUGHU IRU D VLJQDWXUH SDWWHUQ WR EH VWDWLVWLFDOO\ UHOLDEOH WKH DGHTXDWH VDPSOH VL]H IRU HDFK VLJQDWXUH SDWWHUQ PXVW FRQWDLQ DW OHDVW f [ Qf SL[HOV ZKHUH Q LV WKH QXPEHU RI VSHFWUDO ZDYHEDQGV XVHG 6ZDLQ f )RU LQVWDQFH WKH GHVLUHG VDPSOH VL]H IRU D WKUHHZDYHEDQG GDWDVHW LV DERXW SL[HOV $W WKH FRPSOHWLRQ RI WKH 67$7&/ PRGXOH D VSHFWUDO SDWWHUQ ZLWK D

PAGE 154

VFDOHG GLVWDQFH OHVV WKDQ WKH VSHFLILHG YDOXH LV DXWRPDWLFDOO\ PHUJHG WR LWV FORVHVW QHLJKERU $IWHU VXFK D PHUJLQJ EDVHG RQ WKH VSHFLILHG VFDOHG GLVWDQFH WKRVH SDWWHUQV ZLWK D VDPSOH VL]H OHVV WKDQ SL[HOV ILHOGV LQ DQ (5'$6 WHUPf ZHUH GLVFDUGHG 7KH LQSXW SDUDPHWHUV IRU WKH 67$7&/ PRGXOH DUH VXPPDUL]HG LQ 7DEOH 6LPLODU FOXVWHULQJ SURFHGXUHV DQG SDUDPHWHUV ZHUH DOVR XVHG LQ WKH (/$6 LPDJH SURFHVVLQJ V\VWHP 7075 PRGXOHf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

PAGE 155

7DEOH 3DUDPHWHUV XVHG LQ (5'$6 67$7&/ DQG PRGXOHV IRU VLJQDWXUH H[WUDFWLRQ (/$6 7075 3UHVXPHG QXPEHU RI SDWWHUQV /RZHU ERXQG VWDQGDUG GHYLDWLRQ 8SSHU ERXQG VWDQGDUG GHYLDWLRQ &RHIILFLHQW RI YDULDWLRQ bf 6FDOHG GLVWDQFH XVHGf 0LQLPXP ILHOG WKUHVKROG 3HUIRUP ILQDO PHUJH
PAGE 156

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f RI JUHDWHU LQWHUHVW E\ FRQILQLQJ WKH SURFHVVHV RI FOXVWHULQJ DQG FODVVLI\LQJ WR RQO\ WKH ODQGXVH FDWHJRU\ HJ FLWUXV ODQG XVHf EHLQJ VWXGLHG 7KLV VLJQLILFDQWO\ UHGXFHV WKH WLPH DQG UHVRXUFHV GHYRXUHG WR WKH OHVV LPSRUWDQW ODQGXVH W\SHV 6HFRQG VSHFWUDO VLJQDWXUH SDWWHUQV ZLOO FRQVLVW RI SL[HOV RQO\ IURP WKH ODQGXVH FDWHJRU\ WKDW LV EHLQJ

PAGE 157

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

PAGE 158

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f WR D JULG RI P FHOOV FRPSDWLEOH ZLWK WKH 6327 VDWHOOLWH GDWD 7KLV JULG LV QDPHG DV &,7586 GDWD OD\HU 7KURXJK WKH XVH RI (5'$6 15(&7,)< QRQOLQHDU UHFWLI\f PRGXOH DORQJ ZLWK WKH QHDUHVW QHLJKERU UHVDPSOLQJ PHWKRG WKH WKUHH GDWDVHWV 7DEOH f ZHUH DOVR JHRUHIHUHQFHG WR WKH 870 FRRUGLQDWH V\VWHP LQ RUGHU WR EH JHRJUDSKLFDOO\ FRPSDWLEOH ZLWK WKH &,7586 JULG GDWD OD\HU %HFDXVH DQ LQWHJUDWHG PRGXOH IRU WKH GLVFUHWH FOXVWHULQJ DQG FODVVLILFDWLRQ LV QRW DYDLODEOH LQ HLWKHU WKH (5'$6 RU (/$6 LPDJH SURFHVVLQJ V\VWHPV QRU GRHV LW H[LVW LQ WKH $UF,QIR *,6 V\VWHP VRPH DGGLWLRQDO HIIRUWV ZHUH UHTXLUHG ZKLFK LQFOXGHG FOLSSLQJ WKH FLWUXV DUHDV

PAGE 159

XVLQJ WKH &,7586 JULG OD\HU DQG VHWWLQJ DOO WKH QRQFLWUXV SL[HOV WR ]HUR 7KH UHVXOWDQW GDWDVHWV HDFK 20' 00' DQG 001'f DOORZHG WKH FOXVWHULQJ DQG FODVVLI\LQJ SURFHVVHV WR EH GLUHFWHG WR RQO\ FLWUXV SL[HOV QRQ]HUR SL[HOVf ZKLOH QRQn FLWUXV SL[HOV ZHUH LJQRUHG ,I DQ LQWHJUDWHG PRGXOH IRU GLVFUHWH FODVVLILFDWLRQ ZDV DYDLODEOH WKHVH HIIRUWV WR FOLS DQG PDQLSXODWH WKH LPDJH GDWD FRXOG KDYH EHHQ DYRLGHG $OO WKH DUHDV RXWVLGH WKH FLWUXV ODQG XVH FRXOG DOVR KDYH EHHQ FODVVLILHG LQ MXVW RQH XQLILHG SURFHGXUH )RU LWV KLJK FOXVWHULQJ DFFXUDF\ WKH (5'$6 ,62'$7$ PRGXOH (5'$6 f ZKLFK LV EDVHG RQ WKH LWHUDWLYH VHOIn RUJDQL]LQJ GDWD DQDO\VLV WHFKQLTXH 7RX DQG *RQ]DOH] LQ (5'$6 f ZDV XWLOL]HG WR GHULYH WKH VSHFWUDO VLJQDWXUH SDWWHUQV IURP DOO WKH JURYHV 7KH 67$7&/ PRGXOH ZDV QRW XVHG EHFDXVH RI FRQFHUQV DERXW LWV FOXVWHULQJ SURFHVV WKDW UHOLHV RQ EORFNV RI SL[HOV [ SL[HO DUUD\Vf ZKLFK FRXOG LQWURGXFH SUREOHPV WR WKH ERXQGDU\ DUHDV EHWZHHQ FLWUXV DQG QRQFLWUXV ODQGXVH W\SHV )RU HDFK RI WKH WKUHH GDWDVHWV WKH ,62'$7$ PRGXOH ZDV LQVWUXFWHG WR GHULYH VHYHQ VLJQDWXUH SDWWHUQV ZKLFK ZHUH ODWHU XVHG E\ WKH (5'$6 0$;&/$6 PD[LPXP OLNHOLKRRGf FODVVLILFDWLRQ PRGXOH WR FODVVLI\ DOO WKH FLWUXV SL[HOV LQ HDFK HQWLUH GDWDVHW LQWR VHYHQ VSHFWUDO FODVVHV )RU ERWK WKH ,62'$7$ DQG 0$;&/$6 PRGXOHV WKH QRQFLWUXV SL[HOV ZHUH LJQRUHG DQG WUHDWHG DV D EDFNJURXQG FODVV FODVV ]HURf 7KH (/$6 V\VWHP ZDV QRW XVHG EHFDXVH LWV LPSOHPHQWDWLRQ GRHV QRW

PAGE 160

UHQGHU WKH DOWHUQDWLYH RI LJQRULQJ SL[HOV ZLWK FHUWDLQ YDOXHV HJ ]HURf 7KH GLVFUHWH FODVVLILFDWLRQ WHFKQLTXH LV QRW D VXSHUYLVHG FODVVLILFDWLRQ SURFHGXUH WKRXJK D VXSSOHPHQWDO *,6 GDWDVHW LV XVHG LQ WKH FOXVWHULQJ DQG FODVVLI\LQJ SURFHVVHV :LWKLQ HDFK FDWHJRU\ RI ODQG XVH DOO SRWHQWLDO VXEFODVVHV DUH FOXVWHUHG DQG FODVVLILHG XVLQJ WKH XQVXSHUYLVHG FODVVLILFDWLRQ PHWKRG 7KHUHIRUH WKH VHYHQ VSHFWUDO FODVVHV IRU HDFK GDWDVHW 20' 00' DQG 001'f ZHUH JURXQGWUXWKHG XVLQJ FDQRS\ FRYHU HVWLPDWHV IURP WKH $&,5 SKRWRJUDSK\ DV ZHOO DV GDWD FROOHFWHG GXULQJ ILHOG YLVLWV

PAGE 161

&+$37(5 ',6&866,216 $1' $1$/<6(6 2) 08/7,5(62/87,21 /$1'86( &/$66,),&$7,21 7KH UHVXOWV IURP PHUJLQJ WKH 6327 PXOWLUHVROXWLRQ GDWD DUH GLVFXVVHG LQ WKLV FKDSWHU ZKLFK LQFOXGH WKH UDGLRPHWULF TXDOLW\ RI PHUJHG GDWDVHWV WKH IHDVLELOLW\ IRU D FDQRS\VL]H GLIIHUHQWLDWLRQ RI FLWUXV JURYHV DQG WKH HIIHFW RI PXOWLUHVROXWLRQ SURFHVVLQJ RQ ODQGXVH FODVVLILFDWLRQ (YDOXDWLRQ RI 0HUJHG ,PDJH 7R HYDOXDWH WKH TXDOLW\ RI PHUJHG LPDJHV LPDJH VWDQGDUG GHYLDWLRQV RU UDGLRPHWULF YDULDQFHVf DQG FRORU FRPSRVLWHV RI PHUJHG LPDJH GDWD DUH H[DPLQHG 6LQFH WKH SULPDU\ HPSKDVLV RI PXOWLUHVROXWLRQ SURFHVVLQJ LV WR HQKDQFH WKH PXOWLVSHFWUDO GDWD HYDOXDWLRQV DQG FRPSDULVRQV RI PHUJHG LPDJHGDWDVHWV ZLOO EH PDGH EDVHG RQ WKH VDPH TXDOLW\ IDFWRUV RI WKH FRUUHVSRQGLQJ RULJLQDO PXOWLVSHFWUDO LPDJH 5DGLRPHWULF 4XDOLW\ 7KH VWDQGDUG GHYLDWLRQV Df DQG PHDQ EULJKWQHVV YDOXHV 0f IRU WKH PHUJHG 6327 LPDJHV DUH VXPPDUL]HG LQ 7DEOH $ VXEVWDQWLDO LQFUHDVH LQ LPDJH VWDQGDUG GHYLDWLRQ ZDV REVHUYHG IRU DOO PHUJHG LPDJHV 7DEOH f (YHQ IRU WKH 1,5 ZDYHEDQG ZKLFK KDG D QHDU]HUR FRUUHODWLRQ U f WR WKH SDQFKURPDWLF GDWD 7DEOH f WKH LPDJH VWDQGDUG GHYLDWLRQ

PAGE 162

7DEOH 6WDQGDUG GHYLDWLRQV Df DQG PHDQ EULJKWQHVV YDOXHV +f IRU PXOWLUHVROXWLRQ PHUJHG 6327 LPDJHV :DYHn EDQG 0HUJLQJ PHWKRG t FRHII 0HDQ Qf 6WDQGDUG GHYLDWLRQ Df SDQ UDZ GDWD JUHHQ UDZ GDWD UHG UDZ GDWD 1,5 UDZ GDWD JUHHQ 3D f UHG 3 f 1,5 3 f 1'9,SE 1RWH D f§ 3UHVHUYLQJ PHWKRG ZLWK E f§ 1'9,S LV QRUPDOL]HG GLIIHUHQFH YHJHWDWLRQ LQGH[ XVLQJ SDQFKURPDWLF ZDYHEDQG

PAGE 163

UDGLRPHWULF YDULDQFHf ZDV DOVR LQFUHDVHG LQ WKH PHUJLQJ SURFHVV 1RWH WKDW WKH UDGLRPHWULF HQKDQFHPHQW LQ DOO WKHVH PHUJHG LPDJHV ZDV QRW WKH FRQWHPSODWLRQV RI D FRQWUDVWn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f FRPSXWHG IURP WKH PHUJHG LPDJH GDWD ZHUH IRXQG YLUWXDOO\ LGHQWLFDO WR WKH HVWLPDWHV IURP HTXDWLRQ >@ 7KHVH UHVXOWV QRW RQO\ H[WHQG WKH DSSOLFDWLRQV RI WKH SULQFLSOH RI VWDWLVWLFDO YDULDWLRQ DQDO\VHV RI FRPELQLQJ UDQGRP YDULDEOHV WR VDWHOOLWH LPDJHV ZLWK GLIIHUHQW VSDWLDO

PAGE 164

UHVROXWLRQV EXW DOVR SURYLGH D IHDVLEOH PHDQV WR DVVHVV DQG HYDOXDWH WKH UDGLRPHWULF TXDOLW\ RI SUHPHUJHG PXOWLUHVROXWLRQ GDWDVHWV 6SDWLDO ,PSURYHPHQW DQG 6SHFWUDO ,QWHJULW\ 7KH HYDOXDWLRQ RI VSDWLDO HQKDQFHPHQW LV EDVHG RQ DQ YLVXDO FRPSDULVRQ RI WKH FRORU FRPSRVLWHV EHWZHHQ GDWDVHWV 20' DQG 00' 7DEOH f $IWHU WKH SDQFKURPDWLF GDWD LV PHUJHG WKH FRPSRVLWH RI PHUJHG GDWDVHW 00' LQGLFDWHG D VXEVWDQWLDO LPSURYHPHQWV LQ VSDWLDO GHWDLO $V QRWHG LQ WKH VWXG\ E\ (KOHUV f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f D FRPSDULVRQ RI WKH FRORU FRPSRVLWH RI D PHUJHG GDWDVHW ZLWK WKDW RI WKH RULJLQDO PXOWLVSHFWUDO GDWD f D FRUUHODWLRQ DQDO\VLV EHWZHHQ D PHUJHG LPDJH DQG LWV PXOWLVSHFWUDO FRXQWHUSDUW DQG f D FRPSDULVRQ RI EHWZHHQZDYHEDQG FRUUHODWLRQV DPRQJ WKH LPDJHV ZLWKLQ D GDWDVHW :KLOH WKH FRORU DSSHDUDQFH RI D FRPSRVLWH UHQGHUV DQ HIIHFWLYH

PAGE 165

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f VKRZHG XS LQ EULJKW UHG FRORUV RI YDU\LQJ LQWHQVLWLHV IRU GLIIHUHQW YHJHWDWLRQ FRQGLWLRQV ZKLOH URDGV DQG XUEDQ VWUXFWXUHV ZHUH LQGLFDWHG ZLWK ZKLWH FRORUV DV WKH\ DUH XVXDOO\ REVHUYHG LQ D W\SLFDO $&,5 SKRWRJUDSK\ 7KH KLJK FRUUHODWLRQ EHWZHHQ HDFK PHUJHG LPDJH DQG LWV RULJLQDO PXOWLVSHFWUDO FRXQWHUSDUW 7DEOH f VXJJHVWV WKDW WKHUH LV QR VLJQLILFDQW DOWHUDWLRQV RI LPDJH VSHFWUDO GDWD EHWZHHQ GDWDVHWV 20' DQG 00' ,Q RWKHU ZRUGV WKH GLVSRVLWLRQ RI VSHFWUDO LQIRUPDWLRQ LQ PHUJHG GDWDVHW 00' LV VLPLODU WR WKDW RI GDWDVHW 20' 7KRXJK D VOLJKW LQFUHDVH LQ WKH EHWZHHQ ZDYHEDQG FRUUHODWLRQV ZDV QRWHG IRU GDWDVHW 00' 7DEOH f WKHVH FKDQJHV DUH QHLWKHU VXEVWDQWLDO QRU GHOHWHULRXV WR WKH RULJLQDO PXOWLVSHFWUDO LQWHJULW\ RI GDWDVHW 20' :KHQ WKH IDFWRUV RI UDGLRPHWULF LPSURYHPHQW VSDWLDO HQKDQFHPHQW DQG VSHFWUDO LQWHJULW\ DUH SXW LQ SHUVSHFWLYH WKH FRQFOXVLRQ LV

PAGE 166

7DEOH 6XPPDU\ RI FRUUHODWLRQV EHWZHHQ D PHUJHG LPDJH DQG LWV RULJLQDO PXOWLVSHFWUDO FRXQWHUSDUW :DYHEDQG *UHHQ +59f 5HG +59f 1,5 +59f 1'9,D D D f§ IRU 1'9, DQG 1'9, LPDJHV

PAGE 167

7DEOH %HWZHHQZDYHEDQG FRUUHODWLRQV Uf ZLWKLQ PXOWLUHVROXWLRQ PHUJHG GDWDVHWV 6SHFWUDO ZDYHEDQG 'DWDn VHW 0HUJLQJ PHWKRG :DYHn EDQG JUHHQ UHG 1,5 UDZ GDWD 3DQ 20'D UDZ GDWD UDZ GDWD UDZ GDWD JUHHQ UHG 1,5 00'D 3E f 3 f 3 f JUHHQ UHG 1,5 f§ 1'9,Sf 001'D 3 f 3 f 1'9, JUHHQ UHG 1'9,S F F D f§ 5HIHU WR 7DEOH IRU GDWDVHW GHILQLWLRQ E f§ 3UHVHUYLQJ PHWKRG F f§ 1'9,S LPDJH ZDV XVHG LQVWHDG RI 1,5 ZDYHEDQG IRU WKH FRUUHODWLRQ DQDO\VLV

PAGE 168

WKDW WKH SUHVHUYLQJ DSSURDFK ZLWK f LV DQ HIIHFWLYH PHWKRG IRU PXOWLUHVROXWLRQ SURFHVVLQJ RI 6327 PXOWLUHVROXWLRQ GDWDVHWV IRU UHPRWH VHQVLQJ DSSOLFDWLRQV )URP D EODFNDQGZKLWH GLVSOD\ )LJXUH f WKH 1'9,S LPDJH LQGLFDWHG D JUHDW UHVHPEODQFH WR WKH FXVWRPDU\ 1'9, LPDJH JHQHUDWHG IURP WKH RULJLQDO P PXOWLVSHFWUDO 1,5 DQG UHG ZDYHEDQGV >1RWH 1'9, 1,55HGf1,55HGf@ 7KHVH WZR YHJHWDWLRQ LQGH[ LPDJHV KDG D U f KLJK FRUUHODWLRQ 7DEOH f LPSO\LQJ WKDW WKH LQIRUPDWLRQ RI RQH LPDJH LV YHU\ VLPLODU WR WKH RWKHU ,Q ERWK WKH 1'9,S DQG 1'9, LPDJHV YHJHWDWLYH DUHDV DSSHDUHG DV EULJKW ODUJH 1'9, YDOXHVf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

PAGE 169

1'9, 1,55HGf1,55HGf 1'9,S 1,53$1f1,53$1f )LJXUH &RPSDULVRQ RI 6327 P 1'9, DQG P 1'9,S LPDJHV

PAGE 170

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b WR b EDVHG RQ SKRWRJUDPPHWULF

PAGE 171

HVWLPDWLRQV *URYHV ZLWK FDQRS\ FRYHU OHVV WKDQ b KDYH WUHHV WRR VPDOO WR PHDVXUH RQ WKH $&,5 SKRWRJUDSK\ ZLWK D VFDOH DQG ZHUH QRW VHOHFWHG &DQRS\ FRYHU HVWLPDWLRQ IRU \RXQJ JURYHV VPDOO FDQRS\ FRYHUf UHTXLUHV SKRWRJUDSKV RI D ODUJHU VFDOH HJ f +RZHYHU WKH LUUHJXODU WUHH VKDSH LQ \RXQJ JURYHV FDQ FUHDWH IXUWKHU SUREOHPV IRU PDNLQJ UHOLDEOH PHDVXUHPHQWV 2Q WKH RWKHU KDQG FLWUXV WUHHV LQ PDWXUH JURYHV DUH RYHUJURZLQJ LQWR HDFK RWKHUnV FDQRSLHV :KHQ D JURYH LV RYHUJURZQ LW EHFRPHV LPSRVVLEOH WR LGHQWLI\ WKH VHSDUDWLRQ EHWZHHQ WUHHV IRU PDNLQJ PHDVXUHPHQWV RI WUHH VSDFLQJ DQG WUHH FURZQ VL]H GLDPHWHUf $V D UHVXOW FDQRS\ FRYHUV RXWVLGH WKH WR b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f LV GHVLUDEOH IRU EHWWHU DFFXUDF\ EXW DHULDO SKRWRJUDSK\ DW ODUJH VFDOHV LV H[SHQVLYH SDUWLFXODUO\ ZKHQ D ODUJH FRYHUDJH DUHD LV QHHGHG $OVR LW LV LPSRUWDQW WR UHFRJQL]H WKDW WKH EHQHILW RI SKRWR

PAGE 172

HQODUJHPHQW RU PDJQLILFDWLRQ LV OLPLWHG E\ WKH VSDWLDO UHVROXWLRQ FRQVWUDLQWV RI WKH RULJLQDO SKRWRJUDSKVILOPV 7KHUHIRUH WKH VHOHFWLRQ RI D SKRWR VFDOH IRU FLWUXV FDQRS\ FRYHU HVWLPDWLRQ PXVW EH EDVHG RQ FRQVLGHUDWLRQ RI WKH DFWXDO WUHH FURZQ REMHFWf GLDPHWHU VL]Hf DQG WKH HTXLSPHQW FDSDELOLW\ SUHFLVLRQf *HQHUDOO\ $&,5 SKRWRJUDSKV ZLWK D VFDOH IURP WR FDQ EH FRQVLGHUHG DV DSSURSULDWH IRU FLWUXV FDQRS\ FRYHU HVWLPDWLRQ 5HODWLRQ RI ,PDJH 5HVSRQVH WR &DQRS\ &RYHU 7KH UHODWLRQV EHWZHHQ FLWUXV FDQRS\ FRYHU DQG LPDJH UHVSRQVH IRU WKH JUHHQ DQG UHG ZDYHEDQGV RI WKH RULJLQDO P PXOWLVSHFWUDO GDWDVHW 20' DUH VKRZQ LQ )LJXUHV DQG 7KH GLIIHUHQFH RI FLWUXV FDQRS\ FRYHU GRHV KDYH DQ HIIHFW RQ WKH 6327 VSHFWUDO UHVSRQVHV RI WKH JUHHQ DQG UHG ZDYHEDQGV )LJXUHV DQG f +RZHYHU WKH HIIHFW ZDV QRW SURIRXQG HQRXJK WR UHVXOW LQ ZHOO GHILQHG UHODWLRQVKLSV ,Q RWKHU ZRUGV FLWUXV FDQRS\ VL]H GRHV QRW KDYH D VROLWDU\ FRUUHODWLRQ ZLWK WKH 6327 VSHFWUDO UHVSRQVHV RI WKH JUHHQ DQG UHG ZDYHEDQGV $OVR REVHUYHG LQ )LJXUHV DQG LV DQ LQYHUVH UHODWLRQVKLS EHWZHHQ FDQRS\ VL]H DQG VSHFWUDO UHVSRQVH IRU WKH JUHHQ DQG UHG ZDYHEDQGV 7KH SULPDU\ FDXVH IRU VXFK LQYHUVH UHODWLRQVKLSV ZKLFK ZHUH DOVR REVHUYHG IRU ZKHDW FURSV E\ ,GVR HW DO f ZDV GXH WR WKH UHODWLYHO\ KLJKHU VSHFWUDO UHIOHFWDQFH RI XQGHUO\LQJ VRLOV ,Q SDUWLDO FDQRS\ JURYHV WKH VSHFWUDO UHVSRQVH RI D SL[HO GHSHQGV RQ WKH FROOHFWLYH

PAGE 173

L L L Ua 3HUFHQWLOH FLWUXV FDQRS\ FRYHU &&f )LJXUH (IIHFW RI FLWUXV FDQRS\ FRYHU RQ 6327 JUHHQ ZDYHEDQG UHVSRQVH

PAGE 174

)LJXUH (IIHFW RI FLWUXV FDQRS\ FRYHU RQ 6327 UHG ZDYHEDQG UHVSRQVH

PAGE 175

HIIHFW RI ERWK H[SRVHG VRLOV DQG FDQRS\ FRYHUV $V FRPSDUHG WR YHJHWDWLRQ H[SRVHG VRLOV HVSHFLDOO\ VDQG\ VRLOV LQ VRXWK )ORULGD RUFKDUGVf WHQG WR KDYH VLJQLILFDQWO\ VWURQJ UHIOHFWDQFH LQ WKH YLVLEOH HJ JUHHQ DQG UHGf ZDYHOHQJWK UDQJHV SDUWLFXODUO\ ZKHQ VRLO PRLVWXUH FRQWHQW LV ORZ /LOOHVDQG DQG .LHIHU 6KLK DQG 5HHV f $Q LQFUHDVH LQ FDQRS\ FRYHU ZRXOG VKXW RXW PRUH KLJKUHIOHFWDQFH H[SRVHG VRLOV IURP WKH VHQVRUnV LQVWDQWDQHRXV YLHZLQJ DUHD 7KLV ZLOO UHGXFH WKH RYHUDOO UHIOHFWHG UDGLDQFH IURP WKH WDUJHW SL[HOf $V D UHVXOW RI LQFUHDVHG FDQRS\ FRYHU D VPDOOHU YDOXH RI VSHFWUDO UHVSRQVH GLJLWDO FRXQWf ZDV UHFRUGHG LQ WKH LPDJH ,Q FLWUXV JURYHV LQ VRXWK )ORULGD EDUH VRLOV EHWZHHQ WUHHV DV ZHOO DV LQ WUDIILF WUDFNV DUH H[DPSOHV WKDW KDYH UHODWLYHO\ KLJKHU VSHFWUDO UHIOHFWDQFH WKDQ WUHHV LQ WKH JUHHQ [Pf DQG UHG MXPf ZDYHOHQJWK UDQJHV )RU WKH 6327 SDQFKURPDWLF ZDYHEDQG ZKLFK HQFRPSDVVHV ERWK WKH JUHHQ DQG UHG ZDYHEDQGV ZKLOH H[WHQGLQJ WR D VPDOO SRUWLRQ RI WKH 1,5 ZDYHOHQJWK UDQJH JHQHUDOO\ UHJDUGHG DV [Pf LWV VSHFWUDO UHVSRQVH WR FLWUXV FDQRS\ FRYHU PDLQWDLQHG WKH JHQHUDO FKDUDFWHULVWLFV RI ERWK WKH JUHHQ DQG UHG ZDYHEDQGV )LJXUH f 8QOLNH WKRVH RI WKH JUHHQ DQG UHG ZDYHEDQGV WKH VSHFWUDO UHVSRQVH RI WKH 1,5 ZDYHEDQG GLG QRW LQGLFDWH WR FRUUHODWH WR FLWUXV FDQRS\ FRYHU )LJXUH f )RU WKH 1,5 ZDYHEDQG WKH ODFN RI D SHUFHLYDEOH UHODWLRQVKLS RI VSHFWUDO UHVSRQVH WR FLWUXV FDQRS\ VL]H FDQ EH FDXVHG E\ PDQ\ IDFWRUV LQFOXGLQJ

PAGE 176

)LJXUH (IIHFW RI FLWUXV FDQRS\ FRYHU RQ 6327 SDQFKURPDWLF ZDYHEDQG UHVSRQVH

PAGE 177

, L L L L Ua 3HUFHQWLOH FLWUXV FDQRS\ FRYHU &&f fL )LJXUH (IIHFW RI FLWUXV FDQRS\ FRYHU RQ 6327 1,5 ZDYHEDQG UHVSRQVH

PAGE 178

FDQRS\ LWVHOI DQG XQGHUO\LQJ VRLOV ,Q D VWXG\ RI FRWWRQ FURSV VSHFWUD +XHWH DQG -DFNVRQ f IRXQG WKDW WKHUH LV D VWURQJ LQWHUDFWLRQ EHWZHHQ FDQRS\ FRYHU DQG XQGHUO\LQJ VRLOV IRU SDUWLDO FDQRS\ ILHOGV )RU LQVWDQFH WKH 1,5 VSHFWUDO UHIOHFWDQFH RI H[SRVHG VRLOV LV JHQHUDOO\ ORZHU WKDQ WKDW RI YHJHWDWLRQ /LOOHVDQG DQG .LHIHU 5HHV f ,Q D ODQGXVH FODVVLILFDWLRQ VWXG\ 6KLK f IRXQG WKDW EDUUHQ VRLOV KDG D ORZHU 1,5 UHVSRQVH WKDQ DJULFXOWXUDO ODQGV LQFOXGLQJ FLWUXV JURYHV LQ VRXWK )ORULGD 7KHUHIRUH DQ LQFUHDVH LQ FLWUXV FDQRS\ FRYHU ZRXOG LQFUHDVH WKH UHIOHFWHG UDGLDQFH IURP WKH VHQVRUnV YLHZLQJ DUHD UHVXOWLQJ LQ D ODUJHU LPDJH YDOXH +RZHYHU WKH VSHFWUDO UHVSRQVH RI WKH 1,5 ZDYHEDQG LV QRW LQIOXHQFHG E\ FDQRS\ FRYHU DORQH ,Q WKH 1,5 ZDYHOHQJWK UDQJH WKH UHIOHFWDQFH RI FLWUXV WUHHV YHJHWDWLRQf LV SUHGRPLQDWHO\ UHODWHG WR WUHH KHDOWKJURZWK FRQGLWLRQV :KLOH D KHDOWK\ FLWUXV WUHH H[KLELWV YHU\ KLJK UHIOHFWDQFH D VWUHVVHG RQH ZLOO QRW 6KLK HW DO f ,Q DGGLWLRQ WKH VWDJH RI JURZWK FXOWXUDO SUDFWLFHV HJ KHGJLQJ WRSSLQJ ZHHGLQJ HWFf DQG GLYHUVLW\ RI VRLO VXEVWUDWHV HJ GU\ ZHW GDUN RU EULJKWf FRXOG DOVR FRQWULEXWH LQGLYLGXDOO\ RU FROODERUDWHO\ WR WKH YDULDWLRQV RI WKH 1,5 LPDJH UHVSRQVH IRU JURYHV ZLWK SDUWLDO FDQRS\ FRYHU 7KHUHIRUH WKHVH IDFWRUV WRJHWKHU ZLOO PDNH LW H[WUHPHO\ GLIILFXOW IRU WKH 1,5 ZDYHEDQG WR KDYH D GHILQHG UHODWLRQ WR WKH GLIIHUHQFHV RI FLWUXV FDQRS\ VL]H ,Q VXPPDU\ WKH 6327 LPDJH UHVSRQVH GRHV LQGLFDWH WDQJLEOH LQYHUVH UHODWLRQV WR FLWUXV FDQRS\ VL]H IRU WKH

PAGE 179

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f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s[f IRU HDFK

PAGE 180

VHOHFWHG ILHOG LQ GDWDVHW 20' LV LOOXVWUDWHG LQ )LJXUHV DQG IRU WKH JUHHQ UHG DQG 1,5 ZDYHEDQGV UHVSHFWLYHO\ )URP WKH UHVXOWV SUHVHQWHG LQ )LJXUHV DQG WKUHH FRPPHQWV DUH LQ RUGHU )LUVW WKH QXPEHU RI LPDJH JUD\ VKDGHV ZHUH YHU\ OLPLWHG IRU WKH HQWLUH b UDQJH RI FDQRS\ FRYHU 7KLV VWURQJ FRQWDLQPHQW RI LPDJH JUD\ VKDGHV ZKLFK ZHUH UHVSHFWLYHO\ DERXW DQG IRU WKH JUHHQ UHG DQG 1,5 ZDYHEDQGV QRW RQO\ UHYHDOHG D YHU\ OLPLWHG UHVROYLQJ FDSDELOLW\ RI WKH 6327 LPDJH GDWD IRU WKH HQWLUH b FDQRS\ FRYHU UDQJH EXW DOVR LPSOLHG D JUHDW GLIILFXOW\ IRU D FDQRS\ VL]H GLIIHUHQWLDWLRQ RI FLWUXV JURYHV 7KH OLPLWHG JUD\ VKDGHV WRJHWKHU ZLWK WKH ODFN RI ZHOO GHILQHG UHODWLRQV EHWZHHQ FDQRS\ FRYHU DQG LPDJH UHVSRQVH GLG QRW VXJJHVW OLNHO\ VHSDUDWLRQV ZLWKLQ WKH b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

PAGE 181

*UHHQ ZDYHEDQG UHVSRQVH '&f + Uf§ 3HUFHQWLOH FLWUXV FDQRS\ FRYHU &&f 1RWH '&f§GLJLWDO FRXQW )LJXUH &RLQFLGHQW SORW RI 6327 JUHHQ ZDYHEDQG UHVSRQVH IRU VHOHFWHG FLWUXV JURYHV

PAGE 182

5HG ZDYHEDQG UHVSRQVH '&f 1RWH '&f§GLJLWDO FRXQW )LJXUH &RLQFLGHQW SORW RI 6327 UHG ZDYHEDQG UHVSRQVH IRU VHOHFWHG FLWUXV JURYHV

PAGE 183

1,5 ZDYHEDQG UHVSRQVH '&f 1RWH '&f§GLJLWDO FRXQW )LJXUH &RLQFLGHQW SORW RI 6327 1,5 ZDYHEDQG UHVSRQVH IRU VHOHFWHG FLWUXV JURYHV

PAGE 184

LPDJH UHVSRQVH LQ VRPH UDQJHV RI FDQRS\ FRYHU PXVW EH XQLTXH DV ZHOO DV IUHH IURP GDWD RYHUODSV LQ DW OHDVW RQH ZDYHEDQG ,Q D FLWUXV ILHOG ZLWK SDUWLDO FDQRS\ FRYHU WKH UHVSRQVH YDOXH GLJLWDO FRXQWf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f VXJJHVWLQJ WKDW WKHUH H[LVWHG VLJQLILFDQW YDULDWLRQV RI VRLO FRQGLWLRQ DPRQJ WKH JURYHV $FFRUGLQJ WR +XHWH DQG -DFNVRQ f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

PAGE 185

6WDQGDUG GHY RI JUHHQ UHVSRQVH '&f 1RWH '&f§GLJLWDO FRXQW )LJXUH (IIHFW RI WUHH FURZQ YDULDWLRQV RQ 6327 JUHHQ ZDYHEDQG UHVSRQVH YDULDELOLW\ IRU SDUWLDO FDQRS\ JURYHV

PAGE 186

6WDQGDUG GHY RI UHG UHVSRQVH '&f 1RWH '&f§GLJLWDO FRXQW )LJXUH (IIHFW RI WUHH FURZQ YDULDWLRQV RQ 6327 UHG ZDYHEDQG UHVSRQVH YDULDELOLW\ IRU SDUWLDO FDQRS\ JURYHV

PAGE 187

6WDQGDUG GHY RI 1,5 UHVSRQVH '&f ’ ’ ’ 6WG GHY RI WUHH FURZQ GLDPHWHU Pf 1RWH '&f§GLJLWDO FRXQW )LJXUH (IIHFW RI WUHH FURZQ YDULDWLRQV RQ 6327 1,5 ZDYHEDQG UHVSRQVH YDULDELOLW\ IRU SDUWLDO FDQRS\ JURYHV

PAGE 188

&LWUXV WUHHV WHQGHG WR EH PRUH XQLIRUP LQ JURYHV ZLWK ODUJH FDQRS\ FRYHUV )LJXUH f 7KLV LV SUREDEO\ GXH WR VRPH LQFUHDVHG FXOWXUDO DWWHQWLRQ VXFK DV KHGJLQJ DQG WRSSLQJ SUDFWLFHV $OVR WKH YDULDWLRQ RI JURYHZLGH LPDJH UHVSRQVH ZDV QRW WKH VDPH DFURVV WKH HQWLUH b FDQRS\ FRYHU UDQJH )LJXUHV DQG f 7KH LPDJH UHVSRQVH ZDV VOLJKWO\ OHVV YDULDEOH IRU JURYHV ZLWK FDQRS\ VL]HV JUHDWHU WKDQ b HVSHFLDOO\ IRU WKH JUHHQ DQG UHG ZDYHEDQGV )LJXUHV DQG f :KHQ FDQRS\ FRYHU LQFUHDVHG WKH DUHD RI H[SRVHG VRLOV GHFUHDVHG 7KLV UHGXFHG WKH VWURQJ HIIHFW RI VRLO VXEVWUDWHV ,Q DGGLWLRQ DQ LQFUHDVH LQ FDQRS\ FRYHU ZLOO KDYH OHVV YDULDEOH WUHH FURZQ GLDPHWHU DV LQGLFDWHG LQ )LJXUH &RQVHJXHQWO\ JURYHV RI \RXQJ FLWUXV WUHHV DUH VSHFWUDOO\ PRUH YDULDEOH GXH WR WKH JUHDWHU YDULDELOLW\ LQ ERWK WUHH FURZQ GLDPHWHU DQG H[SRVHG DUHD 5HFDOO DJDLQ WKDW WKH 6327 VDWHOOLWH VFHQH ZDV DFTXLUHG LQ ODWH VXPPHU 2FWREHU f ZKHQ WKH VHDVRQ LV JHQHUDOO\ ZHW DQG SRQGHURXV ZHHGVJUDVVHV DUH VWLOO DFWLYHO\ JURZLQJ +RZHYHU ILHOG FRQGLWLRQV LQ VRXWK )ORULGD DUH JHQHUDOO\ OHVV YDULDEOH LQ ZLQWHU PRQWKV WKDQ LQ WKH VXPPHU EHFDXVH RI WKH GU\ VHDVRQ DV ZHOO DV UHODWLYHO\ LQDFWLYH JURZLQJ RI ZHHGVJUDVVHV LQ WKH ILHOG HQYLURQPHQW 7KHUHIRUH VDWHOOLWH VFHQHV DFTXLUHG LQ GU\ ZLQWHU PRQWKV HJ -DQXDU\ DQG )HEUXDU\f ZRXOG UHQGHU D JUHDWHU SRVVLELOLW\ IRU FLWUXV FDQRS\ FRYHU WR VWDQG RXW VSHFWUDOO\ LQ WKH DUHD WR EH LPDJHG ZKHQ WKH LQIOXHQFH RI VRLO FRQGLWLRQV LV PLQLPL]HG

PAGE 189

&RHI RI YDU &9f RI WUHH FURZQ VL]H f§ )LJXUH &9W && L U 3HUFHQWLOH FLWUXV FDQRS\ FRYHU &&f 5HODWLRQ RI WUHH FURZQ YDULDWLRQ WR FDQRS\ FRYHU GLIIHUHQFH

PAGE 190

(IIHFW RI 0XOWLUHVROXWLRQ 0HUJLQJ )RU WKH 6327 PXOWLUHVROXWLRQ PHUJHG GDWD WKH FRUUHODWLRQ FRHIILFLHQWV Uf IRU WKH UHODWLRQV EHWZHHQ FLWUXV FDQRS\ FRYHU DQG LPDJH UHVSRQVH DUH VXPPDUL]HG LQ 7DEOH 7KHVH UHODWLRQV GLG QRW UHYHDO LPSURYHPHQWV DIWHU WKH SDQFKURPDWLF LPDJH ZDV PHUJHG DQG WKLV ODFN RI LPSURYHPHQW LV DWWULEXWHG WR WKH YDULDELOLW\ RI ILHOG HQYLURQPHQWV 1RWH WKDW LQ HDFK PXOWLVSHFWUDO ZDYHEDQG JUHHQ UHG DQG 1,5f RI WKH RULJLQDO PXOWLUHVROXWLRQ GDWDVHW WKHUH H[LVWHG VLJQLILFDQW YDULDWLRQV RI FRUUHODWLRQ EHWZHHQ WKH SDQFKURPDWLF DQG PXOWLVSHFWUDO LPDJHV DPRQJ WKH VHOHFWHG JURYHV 7DEOH f HYHQ WKRXJK WKHVH JURYHV ZHUH FRQVLGHUHG UHODWLYHO\ XQLIRUP %HFDXVH RI WKHVH YDULDWLRQV RI FRUUHODWLRQ WKH FKDQJHV RI LPDJH GDWD DPRQJ WKH JURYHV ZHUH QRW FRQVLVWHQW ZLWKLQ HDFK ZDYHEDQG 7DEOH f ZKHQ WKH SDQFKURPDWLF ZDYHEDQG LV PHUJHG :KLOH WKH VWDQGDUG GHYLDWLRQ RI LPDJH GDWD LQFUHDVHG IRU VRPH JURYHV LW GHFUHDVHG IRU RWKHUV LQ D PHUJHG LPDJH 7DEOH f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

PAGE 191

7DEOH 6XPPDU\ RI FRUUHODWLRQV EHWZHHQ FLWUXV FDQRS\ FRYHU DQG LPDJH UHVSRQVH IRU PXOWLUHVROXWLRQ PHUJHG LPDJHV :DYHEDQG ([SODQDWLRQ &RUU FRHI Uf 3DQ 2ULJLQDO f *UHHQ 2ULJLQDO f 0HUJHG f 5HG 2ULJLQDO f 0HUJHG f 1,5 2ULJLQDO f 22 0HUJHG f 1'9, 1,5 DQG UHG ZDYHEDQG f 1'9,S 1,5 DQG SDQ ZDYHEDQG f 1RWH 7KH f DQG f VLJQV DUH WR LQGLFDWH SRVLWLYH DQG QHJDWLYH FRUUHODWLRQV UHVSHFWLYHO\ $FWXDO YDOXH LV

PAGE 192

nLH 9DULDWLRQV RI LPDJH GDWD FRUUHODWLRQ Uf EHWZHHQ SDQFKURPDWLF DQG RULJLQDO PXOWLVSHFWUDO ZDYHEDQGV DPRQJ VHOHFW JURYHV &RUUHODWLRQ FRHIILFLHQW Uf WR SDQ LPDJH *UHHQ 5HG 1,5

PAGE 193

7DEOH 6WDQGDUG GHYLDWLRQV Df RI PHUJHG LPDJH GDWD IRU VHOHFWHG FLWUXV JURYHV )LHOG 2ULJLQDO GDWD 0HUJHG LPDJH GDWD VWDQGDUG GHY Df JUHHQ ZDYHEDQGf Uf n rJUHHULf &7SDQf

PAGE 194

7DEOH f§ FRQWLQXHG 2ULJLQDO GDWD 0HUJHG LPDJH GDWD )LHOG VWDQGDUG GHY Df Uf DUHGf &7Af UHG ZDYHEDQGf

PAGE 195

7DEOH f§ FRQWLQXHG )LHOG 2ULJLQDO GDWD 0HUJHG LPDJH GDWD VWDQGDUG GHY Df 1,5 ZDYHEDQGf Uf .LUf DSDQf 1RWH U f§ FRUUHODWLRQ FRHIILFLHQW D f§ VWDQGDUG GHYLDWLRQ ZLWK VXEVFULSWV IRU ZDYHEDQG LQGH[

PAGE 196

,Q VXPPDU\ IRU WKH GLIIHUHQWLDWLRQ RI FLWUXV FDQRS\ FRYHU RQ 6327 PXOWLUHVROXWLRQ LPDJHV IRXU FRQFOXVLRQV DUH UHDFKHG )LUVW WKH SKRWRJUDPPHWULF HVWLPDWLRQ RI FLWUXV FDQRS\ FRYHU LV IHDVLEOH DQG DFFXUDWH XVLQJ $&,5 SKRWRJUDSK\ 7KH PHDVXUDEOH FDQRS\ FRYHU LV FRQVLGHUHG WR EH ZLWKLQ WKH b UDQJH SURYLGHG WKDW WKH SKRWR VFDOH LV SURSHUO\ FKRVHQ IURP WR f 6HFRQG WKH LPDJH UHVSRQVH RI WKH 6327 JUHHQ UHG DQG SDQFKURPDWLF ZDYHEDQGV LQGLFDWHG DQ LQYHUVH UHODWLRQ WR WKH GLIIHUHQFH RI FLWUXV FDQRS\ VL]H +RZHYHU D GHILQDEOH UHODWLRQ WR FLWUXV FDQRS\ VL]H ZDV QRW REVHUYHG IRU WKH 6327 1,5 UHVSRQVH 7KLUG WKH JURYHZLGH VSHFWUDO UHVSRQVH RI b SDUWLDO FDQRS\ ILHOGV YDULHG VLJQLILFDQWO\ DQG WKH YDULDWLRQ LV DWWULEXWHG PDLQO\ WR WKH VRLO VXEVWUDWH YDULDELOLW\ LQ WKH VXPPHU ILHOG HQYLURQPHQW )RU WKLV UHDVRQ LW LV DQWLFLSDWHG WKDW DOWHUQDWLYH VDWHOOLWH VFHQHV DFTXLUHG LQ GU\ ZLQWHU PRQWKV -DQXDU\ DQG )HEUXDU\f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

PAGE 197

XVH FODVVLILFDWLRQ 7KH DQDO\VHV LQYROYHG DOO WKUHH GDWDVHWV 20' 00' DQG 001'f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f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

PAGE 198

7DEOH 6XPPDU\ RI VSHFWUDO VLJQDWXUHV XQYHLOHG E\ (5'$6 67$7&/ PRGXOH 6FDOHG GLVWDQFH 'DWDVHW 20' 00' 001' WY! f R 1RWH 20' RULJLQDO PXOWLVSHFWUDO GDWDVHW ZKLFK LQFOXGHV WKH RULJLQDO WKUHH P PXOWLVSHFWUDO LPDJHV 00' PXOWLUHVROXWLRQ PHUJHG GDWDVHW JHQHUDWHG E\ WKH SUHVHUYLQJ DSSURDFK ZLWK % IRU HDFK LPDJH 001' PXOWLUHVROXWLRQ PHUJHG DQG 1'9,S GDWDVHW ZKLFK LV VLPLODU WR 00' H[FHSW WKDW WKH PHUJHG 1,5 LPDJH LV UHSODFHG E\ WKH 1'9,S GDWD

PAGE 199

VLJQLILFDQWO\ JUHDWHU H[WHQW ZKHQ D PXOWLUHVROXWLRQ PHUJHG GDWDVHW LV XVHG $W WKH VFDOHG GLVWDQFH RI IRU H[DPSOH WKH RULJLQDO GDWDVHW 20'f FRXOG RQO\ GLIIHUHQWLDWH WKH 6327 VFHQH LQWR VSHFWUDO FODVVHV ZKLOH PHUJHG GDWDVHW 00' ZDV DEOH WR VHSDUDWH LW LQWR FODVVHV 7KLV HIIHFWLYHQHVV RI GDWDVHW 00' ZDV FRQVLVWHQW IRU DOO WKUHH FDVHV 7DEOH f 7KH LQFUHDVHG GLIIHUHQWLDWLRQ E\ GDWDVHW 00' LV DQ LUUHIXWDEOH DGYDQWDJH RI XVLQJ PXOWLUHVROXWLRQ PHUJHG GDWD IRU ODQGXVH FODVVLILFDWLRQ HIIRUWV $V D UHVXOW WKH DFJXLVLWLRQ RI LPSURYHG ODQGXVH LQIRUPDWLRQ EHFRPHV LQFUHDVLQJO\ IHDVLEOH WKURXJK D PXOWLUHVROXWLRQ SURFHVVLQJ DSSURDFK 6HFRQG WKHUH LV D OLPLWDWLRQ LQ XVLQJ WKH 1'9,S LPDJH GDWDVHW 001'f IRU ODQGXVH FODVVLILFDWLRQ DSSOLFDWLRQV 7DEOH f ,Q RUGHU WR XQGHUVWDQG WKLV OLPLWDWLRQ WKUHH IDFWRUV PXVW EH FRQVLGHUHG )LUVW WKH 1'9,S PHWKRG LV SULPDULO\ IRU YHJHWDWLRQ HQKDQFHPHQW DQG LWV HIIHFWLYHQHVV LV OLPLWHG WR YHJHWDWLYH DUHDV &KDYH] DQG 0DF.LQQRQ f 7KLV ZLOO PDNH QRQYHJHWDWLYH ODQGV VXFK DV EDUUHQ VRLOV XUEDQ ODQGV DQG ZDWHU ERGLHV LQVHSDUDEOH LQ WKH 1'9,S LPDJH 6HFRQG WKH XVH RI D VFDOLQJ IDFWRU LQ WKH 1'9,S HTXDWLRQ WR VWUHWFK WKH IUDFWLRQDO UHVXOWV WR WKH SRVVLEO\ ODUJHVW UDQJH f FRXOG KDYH H[DJJHUDWHG WKH UDGLRPHWULF LQIRUPDWLRQ RI WKH PHUJHG 1'9,S LPDJH 7KHUHIRUH WKH 1'9,S VWDQGDUG GHYLDWLRQ LV QRW D IDFWXDO LQGLFDWLRQ IRU WKH UDGLRPHWULF LQIRUPDWLRQ SUHVHQW LQ WKH RULJLQDO VFHQH 7KLUG WKH VWXG\ DUHD LV FRYHUHG SULPDULO\ ZLWK YHJHWDWLRQ HJ FLWUXV JURYHV SDVWXUH ODQGVf ZKLOH QRQYHJHWDWLRQ DUHDV ZHUH YHU\ OLPLWHG

PAGE 200

$FFRUGLQJ WR (5'$6 f XVLQJ WKH 67$7&/ PRGXOH ZLWK D VPDOO VFDOHG GLVWDQFH ZLOO DOORZ D WLJKW VHSDUDWLRQ WR GLVFULPLQDWH FORVHO\ UHODWHG FODVVHV )RU WKH VWXG\ DUHD GRPLQDWHG E\ YHJHWDWLYH ODQGV WKLV WLJKW FOXVWHULQJ ZLOO PDNH DOO FORVHO\ UHODWHG YHJHWDWLRQ VLJQDWXUHV GLVWLQJXLVKDEOH UHVXOWLQJ LQ D ODUJH QXPEHU RI VSHFWUDO VLJQDWXUHV 7DEOH f +RZHYHU ZKHQ WKH VFDOHG GLVWDQFH ZDV VHW DW D ODUJHU YDOXH WKH GLIIHUHQWLDWLRQ E\ GDWDVHW 001' EHFDPH D SUREOHP EHFDXVH PDQ\ RULJLQDOO\ VHSDUDEOH VLJQDWXUHV LQ D WLJKW FODVVLILFDWLRQ EHFDPH DVVLPLODWHG ,Q DGGLWLRQ WKH VSHFWUDO VLJQDWXUHV IRU QRQYHJHWDWLYH ODQGXVH HOHPHQWV DUH YHU\ OLPLWHG LQ WKH 1'9,S LPDJH &RQVHJXHQWO\ RQO\ D VPDOO QXPEHU RI VLJQDWXUHV ZHUH XQYHLOHG IRU D VFDOH GLVWDQFH RI 7DEOH f 7KLV SRLQWV RXW WKDW WKH 1'9,S LPDJH LV IHDVLEOH RQO\ LQ D WLJKW FODVVLILFDWLRQ RI YHJHWDWLYH ODQG XVH W\SHV 7KH UHVXOWV IURP WKH (/$6 7075 FOXVWHULQJ PRGXOH DUH FRQVLVWHQW ZLWK WKRVH IURP WKH (5'$6 67$7&/ PRGXOH 7DEOH f WKRXJK WKHVH WZR LPDJH SURFHVVLQJ V\VWHPV KDYH D GLIIHUHQW LPSOHPHQWDWLRQ RI WKH FOXVWHULQJ WHFKQLTXH )RU H[DPSOH PHUJHG GDWDVHW 00' KDG HLWKHU WKH ODUJHVW QXPEHU RI VSHFWUDO FODVVHV IRU D JLYHQ VFDOHG GLVWDQFH RU IRU D JLYHQ QXPEHU RI FODVVHV LW ZRXOG KDYH WKH ODUJHVW VFDOHG GLVWDQFH EHWZHHQ WKH GHULYHG FODVVHV 7KHVH DUH LPSRUWDQW IDFWRUV IRU LPSURYLQJ ODQGXVH FODVVLILFDWLRQV IURP VDWHOOLWH GDWDVHWV

PAGE 201

7DEOH 6XPPDU\ RI VSHFWUDO VLJQDWXUHV XQYHLOHG E\ (/$6 7075 PRGXOH 6FDOHG GLVWDQFH 'DWDVHW 20' 00' 001' 1RWH 20' RULJLQDO PXOWLVSHFWUDO GDWDVHW ZKLFK LQFOXGHV WKH RULJLQDO WKUHH P PXOWLVSHFWUDO LPDJHV 00' PXOWLUHVROXWLRQ PHUJHG GDWDVHW JHQHUDWHG E\ WKH SUHVHUYLQJ DSSURDFK ZLWK IRU HDFK LPDJH 001' PXOWLUHVROXWLRQ PHUJHG DQG 1'9,S GDWDVHW ZKLFK LV VLPLODU WR 00' H[FHSW WKDW WKH PHUJHG 1,5 LPDJH LV UHSODFHG E\ WKH 1'9, GDWD

PAGE 202

*,6 'LVFUHWH &ODVVLILFDWLRQ 7KH VSHFWUDO FODVVHV JHQHUDWHG E\ WKH *,6EDVHG GLVFUHWH FODVVLILFDWLRQ DSSURDFK ZHUH HDFK JURXQGWUXWKHG XVLQJ WKH HVWLPDWHV RI FDQRS\ FRYHU WKH $&,5 SKRWRJUDSK\ DQG ILHOG YLVLWV )RU HDFK RI WKH WKUHH GDWDVHWV RI 20' 00' DQG 001' 7DEOH f D VXPPDU\ RI WKH JURXQGWUXWK IRU WKH VHYHQ VSHFWUDO FODVVHV LV SURYLGHG LQ 7DEOH $V LQGLFDWHG LQ 7DEOH D VSHFWUDO FODVV RI WKH RULJLQDO GDWDVHW 20' FDQ HQFRPSDVV FLWUXV JURYHV IRU D ODUJH UDQJH RI FDQRS\ VL]H )RU H[DPSOH FODVV IRXU YLUWXDOO\ LQFOXGHG HYHU\ PHDVXUHG JURYH ZLWKLQ WKH b FDQRS\ FRYHU UDQJH 7KLV SRLQWV RXW WKDW D FDQRS\VL]H FODVVLILFDWLRQ RI FLWUXV JURYHV LV YHU\ GLIILFXOW XVLQJ WKH RULJLQDO P PXOWLVSHFWUDO GDWDVHW :KHQ PXOWLUHVROXWLRQ PHUJHG GDWDVHWV 00' DQG 001' ZHUH XVHG DQ LPSURYHPHQW ZDV QRWHG 7KH FLWUXV JURYHV DW WKH XSSHU UDQJH RI FDQRS\ VL]H WHQGHG WR EH OHVV PL[HG ZLWK WKRVH DW WKH ORZHU UDQJH DV LQGLFDWHG E\ WKH UHVXOWV RI PHUJHG GDWDVHWV 00' DQG 001' 7DEOH f :KHQ D FRUUHODWLRQ ZDV SHUIRUPHG EHWZHHQ WKH FDQRS\ FRYHUV DQG WKH VSHFWUDO FODVVHV LQ 7DEOH WKH FRHIILFLHQW RI FRUUHODWLRQ Uf ZDV DQG IRU GDWDVHWV 20' 00' DQG 001' UHVSHFWLYHO\ 7KRXJK WKLV LPSURYHPHQW ZDV QRW HQRXJK WR VXEVWDQWLDWH WKH SUDFWLFDOLW\ RI FODVVLI\LQJ FLWUXV JURYHV EDVHG RQ VRPH GLVFUHWH UDQJHV RI FDQRS\ VL]H WKH DGYDQWDJH RI XVLQJ PXOWLUHVROXWLRQ SURFHVVLQJ LV FOHDU 7KH SULPDU\ GLIILFXOW\ LV WKH VXPPHU ILHOG HQYLURQPHQW ZKLFK UHVXOWHG LQ D ODUJH YDULDELOLW\ RI LPDJH GDWD IRU HDFK JURYH +RZHYHU

PAGE 203

7DEOH &DQRS\ FRYHU IRU VSHFWUDO FODVVHV E\ *,6EDVHG GLVFUHWH FODVVLILFDWLRQ WHFKQLTXH 'DWDVHW 20'D 6SHFWUDO FODVV 1R )LHOG,' &DQRS\ bf ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; $ ; ; ; $ ; ; ; ; ; ; ; ; ; $ ; ; ; ; ; ; ; ; $ ; ; ;

PAGE 204

f§ FRQWLQXHG 'DWDVHW 00'D 6SHFWUDO FODVV )LHOG,' &DQRS\b D E F G H I J ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; $ ; ; ; $ ; ; ; ; ; ; ; ; $ ; ; ; ; ; ; ; $ ; ;

PAGE 205

7DEOH f§ FRQWLQXHG 'DWDVHW 001'D 6SHFWUDO FODVV 1R )LHOG,' &DQRS\b $ % F ( ) ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; $ ; ; ; $ ; ; ; ; ; ; ; ; $ ; ; ; ; ; ; ; $ ; f§ 5HIHU WR 7DEOH IRU GDWDVHW GHILQLWLRQ

PAGE 206

IXUWKHU LPSURYHPHQWV DUH H[SHFWHG WKURXJK WKH XVH RI VDWHOOLWH VFHQHV DFTXLUHG LQ GU\ ZLQWHU PRQWKV -DQXDU\ DQG )HEUXDU\f WR PLQLPL]H ILHOG YDULDELOLW\ $OVR LQGLFDWHG LQ 7DEOH LV WKDW WKH FDQRS\VL]H GLIIHUHQWLDWLRQ E\ PHUJHG GDWDVHW 001' ZDV QRW DV HIIHFWLYH DV RQH ZRXOG H[SHFW ,Q D ODWH VXPPHU PRQWK 2FWREHUf LQ VRXWK )ORULGD RUFKDUGV PLVFHOODQHRXV YHJHWDWLRQ HJ ZHHGV DQG JUDVVHV EHWZHHQ URZV DV ZHOO DV EHWZHHQ WUHHVf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

PAGE 207

JURYHV VXJJHVWV WKDW WKHUH H[LVW RWKHU IDFWRUV VXFK DV WKH GLIIHUHQFHV LQ VRLO VXEVWUDWH WUHH KHDOWKJURZWK FRQGLWLRQV WUHH YDULHWLHV DQG FXOWXUDO SUDFWLFHV ZKLFK FRXOG KDYH SOD\HG D YLWDO UROH LQGLYLGXDOO\ DQGRU FROODERUDWHO\ LQ DIIHFWLQJ WKH FDQRS\VL]H GLIIHUHQWLDWLRQ RI FLWUXV JURYHV ,Q DGGLWLRQ WKH VHDVRQDO GLIIHUHQFHV LQ WKH ILHOG HQYLURQPHQW DOVR SOD\ D UROH LQ DIIHFWLQJ WKH FODVVLILFDWLRQ UHVXOWV :LWKRXW VXIILFLHQW LQIRUPDWLRQ RI JURXQGWUXWK LW LV LPSRVVLEOH WR DVVHVV WKH LPSDFWV RI WKHVH IDFWRUV 7KHUHIRUH UHVHDUFK HIIRUWV DUH QHHGHG LQ WKLV UHJDUG LQ RUGHU WR JDLQ PRUH XQGHUVWDQGLQJ DQG WR HYDOXDWH WKH LPSDFWV RI WKHVH IDFWRUV RQ XVLQJ VDWHOOLWH LPDJHU\ GDWD IRU UHJLRQDO FLWUXV ODQGXVH FODVVLILFDWLRQ DQG PRQLWRULQJ

PAGE 208

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f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

PAGE 209

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f WKH GDWD FKDUDFWHULVWLFV U D DQG f RI WKH LPDJHV WR EH FRPELQHG DQG f WKH PHWKRG XVHG WR GLJLWDOO\ PHUJH WKH LPDJH GDWD 7KHVH VDPH FULWHULD FDQ DOVR EH DSSOLHG WR DVVHVVLQJ WKH UDGLRPHWULF TXDOLWLHV RI WKH ODQGXVH W\SHV RI LQWHUHVW LQ D PHUJHG LPDJH 2I WKH WKUHH PHUJLQJ DSSURDFKHV FRQILQLQJ SUHVHUYLQJ DQG GLIIHUHQFLQJf WKH SUHVHUYLQJ PHWKRG LV WKH PRVW HIIHFWLYH DSSURDFK IRU GLJLWDOO\ FRPELQLQJ LPDJH GDWD LQFOXGLQJ WKRVH ZLWK GLIIHUHQW VSDWLDO UHVROXWLRQV 7KH VHOHFWLRQ RI D PHUJLQJ PHWKRG WR DFKLHYH DQ LPDJH HQKDQFHPHQW REMHFWLYH PXVW EH PDGH ZLWK FRQVLGHUDWLRQ RI WKH FRUUHODWLRQ DQG WKH UDGLRPHWULF YDULDQFH GLIIHUHQFH EHWZHHQ WKH LPDJHV WR EH FRPELQHG 7R HQKDQFH WKH UDGLRPHWULF TXDOLW\ RI PHUJHG GDWD WKH SUHVHUYLQJ PHWKRG VKRXOG EH XVHG IRU QRQQHJDWLYHO\ FRUUHODWHG U!f LPDJHV ZKLOH WKH GLIIHUHQFLQJ PHWKRG FDQ RQO\ EH DSSOLHG LQ WKH FDVH ZKHUH WKH LPDJHV WR EH PHUJHG KDYH D VWURQJ QHJDWLYH FRUUHODWLRQ DQG WKH SULPDU\ LPDJH LV EULJKWHU

PAGE 210

DQG KDV D JUHDWHU UDGLRPHWULF YDULDQFH ,Q HYHU\ DVSHFW WKH FRQILQLQJ PHWKRG LV LQHIIHFWLYH DQG LQIHULRU WR WKH SUHVHUYLQJ PHWKRG +HQFH WKH FXVWRPDU\ XVH RI WKH FRQILQLQJ DSSURDFK IRU PXOWLUHVROXWLRQ PHUJLQJ VKRXOG QRW EH FRQWLQXHG 7KH SUHVHUYLQJ PHWKRG ZLWK D PHUJLQJ FRHIILFLHQW IOf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f ODUJH YDULDWLRQV RI LPDJH UHVSRQVH ZHUH REVHUYHG IRU HDFK JURYH VXJJHVWLQJ WKDW VDWHOOLWH VFHQHV DFTXLUHG LQ GU\ ZLQWHU PRQWKV RI -DQXDU\ DQG )HEUXDU\ ZLOO EH PRUH IHDVLEOH IRU FLWUXV FDQRS\ VWXGLHV LQ VRXWK )ORULGD ,Q JHQHUDO WKH 6327 LPDJH UHVSRQVH LV OHVV YDULDEOH IRU FDQRS\ FRYHU JUHDWHU WKDQ b ZKLOH FLWUXV WUHHV DUH PRUH XQLIRUP LQ JURYHV ZLWK KLJKHU SHUFHQWDJH RI FDQRS\ FRYHU 0XOWLUHVROXWLRQ SURFHVVLQJ RI 6327 VDWHOOLWH LPDJHV ZLOO JHQHUDWH ERWK UDGLRPHWULFDOO\ DQG VSDWLDOO\ HQKDQFHG PHUJHG GDWDVHWV ZKLFK LQFUHDVH WKH GLIIHUHQWLDWLRQ RI D VDWHOOLWH

PAGE 211

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f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

PAGE 212

WKH WZR UDWLRLQJ LPDJHV LW ZLOO EH H[WUHPHO\ GLIILFXOW WR HQKDQFH LWV UDGLRPHWULF TXDOLW\ WKURXJK D UDWLRLQJ DSSURDFK ,Q RWKHU ZRUGV VXFFHVVIXO DSSOLFDWLRQV RI ZDYHEDQG UDWLRLQJ FDQ EH DFKLHYHG RQO\ IRU WKRVH ODQGXVH W\SHV ZKLFK KDYH ZHDN RU QHJDWLYH FRUUHODWLRQV EHWZHHQ WKH LPDJHV WR EH UDWLRHG 5HFRPPHQGDWLRQV 7KH XQGHUVWDQGLQJ RI WKH SULQFLSOH DQG WKH UDGLRPHWULF WUDQVIRUPDWLRQV RI PHUJLQJ LPDJHV LQFOXGLQJ ZDYHEDQG UDWLRLQJ SURYLGHV QHZ RSSRUWXQLWLHV IRU XVLQJ VDWHOOLWH LPDJH GDWD WR LPSURYH UHPRWH VHQVLQJ DSSOLFDWLRQV 1RQHWKHOHVV FRQWLQXLQJ UHVHDUFK LV QHHGHG WR IXUWKHU WKH HIIRUWV XQGHUWDNHQ LQ WKLV VWXG\ 7KH FXVWRPDU\ DSSURDFK RI XVLQJ WKH FRQILQLQJ PHWKRG IRU GLJLWDOO\ PHUJLQJ VDWHOOLWH LPDJHV LQFOXGLQJ WKRVH RI PXOWLUHVROXWLRQ GDWDVHWV VKRXOG EH DYRLGHG EHFDXVH RI LWV LQHIIHFWLYHQHVV IRU UDGLRPHWULF DQG VSDWLDO HQKDQFHPHQW 7KH FRQILQLQJ DSSURDFK LV FXUUHQWO\ WKH PRVW FRPPRQO\ XVHG PHUJLQJ PHWKRG IRU PXOWLUHVROXWLRQ SURFHVVLQJ DQG XQIRUWXQDWHO\ FDQ RQO\ JHQHUDWH UDGLRPHWULFDOO\ LQIHULRU PHUJHG LPDJH GDWD ZKLOH FUHDWLQJ D JUHDW SRVVLELOLW\ RI FRUUXSWLQJ WKH VSHFWUDO LQIRUPDWLRQ LQ D PXOWLVSHFWUDO GDWDVHW 7KH PHUJLQJ PHWKRGV SUHVHUYLQJ GLIIHUHQFLQJ DQG UDWLRLQJf GHPRQVWUDWHG LQ WKLV VWXG\ VKRXOG EH H[WHQGHG WR RWKHU GDWDVHWV WR LQFUHDVH WKH XWLOLW\ RI FXUUHQW DQG IXWXUH UHPRWH VHQVLQJ GDWD 7KURXJK DQ HIIHFWLYH GDWD PHUJLQJ DQG

PAGE 213

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

PAGE 214

%HFDXVH FDQRS\ FRYHU LV DQ LPSRUWDQW IDFWRU XVHG LQ PDQ\ HQYLURQPHQWDO DQG YHJHWDWLRQUHODWHG LQYHVWLJDWLRQV WKH SKRWRJUDPPHWULF DSSURDFK IRU FDQRS\ FRYHU HVWLPDWLRQ QHHGV WR EH H[WHQGHG WR RWKHU DJULFXOWXUDO FURSV DQG IRUHVW SODQWDWLRQV WKURXJK IXUWKHU UHVHDUFK HIIRUWV ,Q DGGLWLRQ VDWHOOLWH VFHQHV DFTXLUHG LQ WKH GU\ ZLQWHU PRQWKV RI -DQXDU\ DQG )HEUXDU\ LQ VRXWK )ORULGD VKRXOG EH XVHG IRU FLWUXV FDQRS\ FRYHU VWXGLHV EHFDXVH WKH LQIOXHQFH RI VRLO FRQGLWLRQV ZLOO EH PLQLPL]HG

PAGE 215

$33(1',; $ 5*% &2/25 ',63/$< 7KH 5*% FRORU V\VWHP LV EDVHG RQ WKH FRORU DGGLWLYH WKHRU\ IRU WKH WKUHH SULPDU\ FRORUV UHG JUHHQ DQG EOXHf WR FUHDWH FRORU GLVSOD\ %HFDXVH WKH FRORU DVVRFLDWHG ZLWK D SDUWLFXODU REMHFW GHSHQGV RQ WKH DPRXQWV RI UHG JUHHQ DQG EOXH OLJKWV UHIOHFWHG E\ WKH REMHFW E\ PL[LQJ GLIIHUHQW SURSRUWLRQV RI WKH WKUHH FRORU SULPDULHV WKHUHIRUH DOO WKH FRORUV FDQ EH FUHDWHG /LOOHVDQG DQG .LHIHU f 7R FUHDWH D FRORU GLVSOD\ IRU UHPRWH VHQVLQJ GDWD WKUHH LPDJHV DUH QHHGHG DQG HDFK RI WKHP UHSUHVHQWV RQH RI WKH WKUHH SULPDU\ FRORUV :KHQ WKH WKUHH LPDJHV DUH PL[HG WRJHWKHU E\ WKH GLVSOD\ GHYLFH WKH UHVXOW LV FRORUIXO UHQGLWLRQV IRU WKH LPDJH GDWD %HFDXVH KXPDQ H\HV FDQ GLVFULPLQDWH PDQ\ PRUH FRORUV WKDQ JUD\ VKDGHV /LOOHVDQG DQG .LHIHU *RQ]DOH] DQG :LQW] f LW LV DQ DGYDQWDJH IRU SKRWR LQWHUSUHWHUV WR XVH FRORU SURGXFWV

PAGE 216

$33(1',; % ,+6 75$16)250 )25 ,0$*( ',63/$< 7KH LQWHQVLW\KXHVDWXUDWLRQ ,+6f FRORU WUDQVIRUP LV D VLPXODWLRQ RI WKH SURFHVV RI KXPDQ FRORU SHUFHSWLRQ 8QOLNH WKH ZHOONQRZQ 5*% UHG JUHHQ DQG EOXHf FRORU GLVSOD\ PHWKRG WKH ,+6 WUDQVIRUP XVHV WKH DWWULEXWHV FDOOHG EULJKWQHVV RU LQWHQVLW\ ,f KXH +f DQG VDWXUDWLRQ 6f WR GLVWLQJXLVK RQH FRORU IURP DQRWKHU %ULJKWQHVV UHIHUV WR LQWHQVLW\ RI OLJKW +D\GQ HW DO f RU LOOXPLQDWLRQ %R\QWRQ f DQG LV DVVRFLDWHG ZLWK VSDWLDO LQIRUPDWLRQ &DUSHU HW DO f $ ORZ LQWHQVLW\ ZLOO KDYH D UHODWLYHO\ GDUN GLVSOD\ +XH LV DQ DWWULEXWH DVVRFLDWHG ZLWK WKH GRPLQDQW ZDYHOHQJWK LQ D PL[WXUH RI OLJKW ZDYHV 7KXV KXH UHSUHVHQWV WKH GRPLQDQW FRORU DV SHUFHLYHG E\ DQ REVHUYHU :KHQ DQ REMHFW LV FDOOHG UHG RUDQJH RU \HOORZ LWV KXH LV EHLQJ VSHFLILHG *RQ]DOH] DQG :LQW] f 6DWXUDWLRQ UHIHUV WR WKH UHODWLYH SXULW\ RI KXH PL[HG ZLWK ZKLWH OLJKW 7KH GHJUHH RI VDWXUDWLRQ LV LQYHUVHO\ SURSRUWLRQDO WR WKH DPRXQW RI DGGHG ZKLWH OLJKW *RQ]DOH] DQG :LQW] f 7KH ,+6 WUDQVIRUP WDNHV D WZRVWHS WUDQVIRUPDWLRQ ZKLFK LQFOXGHV D IRUZDUG WUDQVIRUPDWLRQ IURP UDZ 5*% LPDJH GDWD WR WKH + DQG 6 FRPSRQHQWV DQG D UHYHUVH WUDQVIRUPDWLRQ IURP WKH ,+6 FRPSRQHQWV WR 5*% FRORU YDOXHV ,Q SUDFWLFDO LPSOHPHQWDWLRQ RI WKH ,+6 WUDQVIRUP IRU UHPRWH VHQVLQJ GDWD

PAGE 217

WKH IRUZDUG WUDQVIRUPDWLRQ LV DFFRPSOLVKHG E\ WKH IROORZLQJ HTXDWLRQV +D\GQ HW DO f 5 % > %O @ %f, %f >%O@ %f, >%@ ZKHUH 5 % UHSUHVHQW WKH LPDJH GDWD RI WKUHH VSHFWUDO EDQGV UHG JUHHQ DQG EOXHf 7KHQ DQRWKHU VHW RI HTXDWLRQV LV XVHG IRU WKH UHYHUVH WUDQVIRUPDWLRQ IURP WKH + DQG 6 FRPSRQHQWV WR WKH WKUHH FRORU YDOXHV IRU DQ HOHFWURQLF FRORU GLVSOD\ GHYLFH +D\GQ HW DO f U 6 6+f >%@ J 6 6+f >%@ E 6f >%@ ZKHUH U J DQG E UHVSHFWLYHO\ UHSUHVHQW WKH SULPDU\ FRORUV IRU UHG JUHHQ DQG EOXH IRU D HOHFWURQLF FRORU GLVSOD\ GHYLFH 7KH WKUHH SULPDU\ FRORUV DUH XVHG WR GHILQH WKH YLVLEOH FRORUV ZKHQ PL[HG WRJHWKHU ZLWK YDU\LQJ PDJQLWXGH +D\GQ HW DO f 6HYHUDO SRLQWV QHHG WR EH QRWHG ZKHQ XVLQJ WKLV FRORU PRGHO IRU UHPRWH VHQVLQJ GDWD GLVSOD\ SXUSRVHV )LUVW D PD[LPXP RI RQO\ WKUHH LPDJHV FDQ EH GLVSOD\HG LQ RQH WLPH 7KLV LV D GUDZEDFN IRU PXOWLVSHFWUDO GDWDVHWV ZLWK PRUH WKDQ WKUHH VSHFWUDO ZDYHEDQGV 6HFRQG WKH UHVXOWDQW U J DQG Ef YDOXHV GR QRW KDYH DQ\ UHODWLRQV WR WKH SK\VLFDO LPSRUWDQFH RI

PAGE 218

VSHFWUDO LQIRUPDWLRQ 7KHUHIRUH WKH PHUJHG GDWD FDQ RQO\ EH XVHG IRU GLVSOD\ SXUSRVH DQG DQ\ PXOWLVSHFWUDO DQDO\VHV UHODWHG WR WKH WUDQVIRUPHG LPDJH GDWD ZLOO EH LUUHOHYDQW 7KLUG WKH LPDJH GLVSOD\ GRHV QRW UHQGHU DQ\ TXDQWLWDWLYH LQIRUPDWLRQ IRU GLIIHUHQW ODQGXVH W\SHV LQ WKH LPDJH 6XFK LQIRUPDWLRQ LV WRWDOO\ OHIW XS WR WKH XVHU RU SKRWRn LQWHUSUHWHU WR GHWHUPLQH )LQDOO\ WKH ,+6 WUDQVIRUP LV RQO\ DQ DWWHPSW WR PDNH GLVSOD\ FRORUV SOHDVDQW WR WKH KXPDQ H\HV UDWKHU WKDQ DQ LPDJH SURFHVVLQJ SURFHGXUH ZKLFK VKDUSHQV LPDJH GDWD 3HOOHPDQV HW DO f 7KH ,+6 WUDQVIRUP PHWKRG KDV EHHQ VXFFHVVIXOO\ XVHG LQ PDQ\ VWXGLHV HJ +D\GQ HW DO &DUSHU HW DO *UDVVR f WKDW DLPHG DW LPSURYLQJ LPDJH LQWHUSUHWDWLRQ WKURXJK FRORU HQKDQFHPHQW +RZHYHU WKH SK\VLRSV\FKRORJLFDO SURFHVV RI KXPDQ FRORU SHUFHSWLRQ LV QRW \HW IXOO\ XQGHUVWRRG *RQ]DOH] DQG :LQW] f

PAGE 219

$33(1',; & 352*5$0 &2'(6 72 813$&. $9+55 /$& '$7$ $ 7XUER& FRPSLOHU LV QHHGHG WR FRPSLOH WKH IROORZLQJ SURJUDP FRGHV )RU GHWDLOHG LQIRUPDWLRQ UHJDUGLQJ KRZ WKH /$& GDWD LV SDFNHG FRQVXOW WKH 7,526 PDQXDO .LGZHOO f 7KH WKH ELW DUUDQJHPHQW IRU WKUHH ELW SL[HOV LV DV ELWV ‘ !O SL S S SL S S SL S S EO E E E E EO E E E 1RWH EOE EDQGV WKURXJK SOS SL[HOV WKURXJK rrrr FXW KHUH DFWXDO SURJUDP FRGHV EHJLQ QH[W OLQH rrrrrrr LQFOXGH VWGLRK! LQFOXGH FRQLRK! LQFOXGH VWGOLEK! PDLQf ^ ORQJ 6NLS" XQVLJQHG LQW L5HDG/LQH3L[HO&RXQW3,33,, XQVLJQHG LQW 287>@>@ XQVLJQHG FKDU ,1>@1DPH>@GXP\ ),/( rILQ rIRXW 1DPH>@ SULQWI?Q (QWHU LQSXW /$&f ILOH QDPH f ILQ IRSHQFJHWV1DPHfUEf LIILQ 18//f UHWXUQ SULQWI?Q 6NLS E\WHf UHFRUGV RI LQSXW ILOH f VFDQIbOG t6NLSf 6NLS 6NLSr LI6NLSf UHWXUQ 1DPH>@ SULQWI?Q (QWHU RXWSXW ILOH QDPH f IRXW IRSHQFJHWV1DPHfZEf LIIRXW 18//f UHWXUQ

PAGE 220

SULQWI?Q %HJLQ XQSDFNLQJ LQSXW ILOH f /LQH 5HDG 3L[HO &RXQW UHZLQGIOf LI6NLS!f IVHHNIO6NLS6((.B6(7f IVHHNILQ6((.B&85f r 6NLS ILUVW E\WHV r ZKLOHIHRIILQff ^ IUHDG,1ILQf r UHDG E\WH SL[HOV r 5HDG 5HDGO &RXQW &RXQWO GXP\ ,1>@ ,O GXP\ m GXP\ ,1>@ GXP\ GXP\ !! GXP\ 3O f GXP\ ,1>@ GXP\ GX[Q\ ,O GXP\ m GXP\ ,1>@ GXP\ GXP\ } GXP\ 3 f GXP\ ,1>@ GXP\ GXP\ m ,O GXP\ m ,1>@ 3 f VZLWFK5HDGf ^ FDVH r LI ILUVW E\WH r 287>@>3L[HO@ 3 287>@>3L[HO@ 3 287>@>3L[HO@ 3 EUHDN FDVH r LI VHFRQG E\WH r 287>@>3L[HO@ 3 287>@>3L[HO@ 3 3L[HO 3L[HOO 287>@>3L[HO@ 3 EUHDN

PAGE 221

FDVH r LI WKLUG E\WH r 287>@>3L[HO@ 3 287>@>3L[HO@ 3 287>@>3L[HO@ 3 EUHDN FDVH r LI IRXUWK E\WH r 287>@>3L[HO@ 3 3L[HO 3L[HOO 287>@>3L[HO@ 3 287>@>3L[HO@ 3 EUHDN FDVH r LI ILIWK E\WH r 287>@>3L[HO@ 3 287>@>3L[HO@ 3 287>@>3L[HO@ 3 3L[HO 3L[HOO 5HDG EUHDN ` LI&RXQW f ^r LI E\WH UHDGV RU RQH VFDQ r IRUL L Lf IZULWH287>L@IRXWf IVHHNILQ6((.B&85f 3L[HO 5HDG &RXQW r EHJLQ D QHZ OLQH r /LQH /LQHO LI/LQHb f SULQWI?Q )LQLVK OLQH bGf/LQHf ` ` FOUVFUf SULQWI?Q?Q 2XWSXW ILOH LV ZULWWHQ LQ D EDQG LQWHUOHDYH E\f SULQWI?Q OLQH RU %,/ ELW GDWD IRUPDW 7KH HQWLUH VFHQHf SULQWI?Q KDV bG VFDQ OLQHV DQG EDQGV /LQHf SULQWI?Q 7KHUH DUH SL[HOV SHU VFDQ?Qf IFORVHDOOf H[LWf f

PAGE 222

$33(1',; &/$66,),&$7,21 '(&,6,21 58/(6 7KH FODVVLILFDWLRQ GHFLVLRQ UXOHV LPSOHPHQWHG LQ ODQGXVH FODVVLILFDWLRQ SURFHGXUHV IRU VDWHOOLWH UHPRWH VHQVLQJ GDWDVHWV KDYH EHHQ ZHOO HVWDEOLVKHG DQG GRFXPHQWHG 7KHVH GHFLVLRQ UXOHV QDPHO\ LQFOXGH WKH SDUDOOHOHSLSHG FODVVLILHU WKH PLQLPXP GLVWDQFH FODVVLILHU WKH PDKDODQRELV GLVWDQFH FODVVLILHU DQG WKH PD[LPXP OLNHOLKRRG FODVVLILHU /LOOHVDQG DQG .LHIHU 7KRPDV HW DO (5'$6 f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

PAGE 223

WKH VSHFWUDO ZDYHEDQGV LQ D GDWDVHW WKH SDUDOOHOHSLSHG ERXQGDULHV GHILQHG E\ WKH XSSHU DQG ORZHU GDWD OLPLWV HJ D UHFWDQJXODU LQ D WZRZDYHEDQG VSDFHf LV XQDEOH WR DGHTXDWHO\ GHVFULEH WKH VODQWHG RU HORQJDWHG FOXVWHULQJ WHQGHQF\ RI LPDJH GDWD RI WKDW VSHFWUDO FODVV /LOOHVDQG DQG .LHIHU f ,Q WKLV UHJDUG WKH SDUDOOHOHSLSHG FODVVLILHU LV QRW VHQVLWLYH WR WKH FRUUHODWLRQV RI LPDJH GDWD EHWZHHQ VSHFWUDO ZDYHEDQGV ZLWKLQ D VSHFWUDO FODVV %HFDXVH RI LWV IDVW LPSOHPHQWDWLRQ WKH SDUDOOHOHSLSHG FODVVLILHU LV RIWHQ XVHG DV D ILUVWSDVV SURFHVV LQ D PRUH LQYROYHG FODVVLILFDWLRQ SURFHGXUH (5'$6 f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f 7KHUHIRUH LW LV LQVHQVLWLYH WR WKH LPDJH GDWD YDULDWLRQV DPRQJ GLIIHUHQW VSHFWUDO FODVVHV $V D UHVXOW D SL[HO LV PRUH OLNHO\ WR EH DVVLJQHG WR WKH FODVVHV ZKLFK KDYH VPDOOHU GDWD YDULDWLRQV RU DUH PRUH FORVHO\ FOXVWHUHG

PAGE 224

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f (XFOLGHDQ GLVWDQFH %\ WKLV PRGLILFDWLRQ D SL[HO LV DV OLNHO\ WR EH DVVLJQHG WR WKH FODVVHV ZLWK D ODUJH GDWD YDULDELOLW\ DV WR WKRVH ZLWK VPDOO LPDJH GDWD YDULDQFHV 7KH 0D[LPXP /LNHOLKRRG &ODVVLILHU 7KH PD[LPXP OLNHOLKRRG FODVVLILHU RSHUDWHV XQGHU WKH DVVXPSWLRQ WKDW WKH LPDJH GDWD RI HDFK VSHFWUDO ZDYHEDQG DUH QRUPDOO\ GLVWULEXWHG *DXVVLDQ GLVWULEXWLRQf ZKLFK LV JHQHUDOO\ DFFHSWDEOH IRU PRVW UHPRWH VHQVLQJ GDWDVHWV /LOOHVDQG DQG .LHIHU f 8VLQJ WKH LPDJH GDWD RI WUDLQLQJ VDPSOHV D SDUDPHWULF VWDWLVWLFDO DSSURDFK LV XQGHUWDNHQ WR SUHSDUH D PXOWLYDULDWH SUREDELOLW\ GHQVLW\ IXQFWLRQ IRU HDFK VSHFWUDO FODVV LQ D PXOWLVSHFWUDO GDWDVHW 7KDPRV HW DO f 7KHQ WKH OLNHOLKRRG YDOXHV RU SUREDELOLWLHV IRU D FDQGLGDWH SL[HO WR HDFK RI WKH VSHFWUDO FODVVHV DUH FDOFXODWHG DQG WKH FDQGLGDWH SL[HO LV DVVLJQHG WR

PAGE 225

WKH FODVV WR ZKLFK LW KDV WKH KLJKHVW SUREDELOLW\ 7KH GHWHUPLQDWLRQ RI D FDQGLGDWH SL[HO WR D VSHFWUDO FODVV LV EDVHG RQ WKH OLNHOLKRRG SUREDELOLW\ RI WKDW SL[HO UDWKHU WKDQ RQ WKH (XFOLGHDQ GLVWDQFH PLQLPXP GLVWDQFH RU 0DKDODQRELV GLVWDQFHf RU WKH ORZHU DQG XSSHU GDWD OLPLWV 3DUDOOHOHSLSHG FODVVLILHUf 7KH PD[LPXP OLNHOLKRRG FODVVLILHU LV WKH VORZHVW EXW WKH PRVW DFFXUDWH GHFLVLRQ UXOH DPRQJ WKH FODVVLILHUV

PAGE 226

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f %R\QWRQ 50 +XPDQ FRORU YLVLRQ +ROW 5LQHKDUW DQG :LQVWRQ 1HZ
PAGE 227

&OLFKH ( %RQQ DQG 3 7HOOHW ,QWHUJUDWLRQ RI WKH 6327 SDQFKURPDWLF FKDQQHO LQWR LWV PXOWLVSHFWUDO PRGH IRU LPDJH VKDUSQHVV HQKDQFHPHQW 3KRWRJUDPPHWULF (QJLQHHULQJ DQG 5HPRWH 6HQVLQJ f &ROHPDQ 7/ / *XGDSDWL DQG 'HUULQJWRQ 0RQLWRULQJ IRUHVW SODQWDWLRQV XVLQJ /DQGVDW WKHPDWLF PDSSHU GDWD 5HPRWH 6HQVLQJ RI (QYLURQPHQW &ROZHOO 51 DQG &( 3RXOWRQ 6327 VLPXODWLRQ LPDJHU\ IRU XUEDQ PRQLWRULQJ $ FRPSDULVRQ ZLWK /DQGVDW 70 DQG 066 LPDJHU\ DQG ZLWK KLJK DOWLWXGH FRORU LQIUDUHG SKRWRJUDSK\ 3KRWRJUDPPHWULF (QJLQHHULQJ DQG 5HPRWH 6HQVLQJ f &XUUDQ 33ULQFLSOHV RI UHPRWH VHQVLQJ /RQJPDQ ,QF 1HZ
PAGE 228

E /DQGVDW WHFKQLFDO QRWHV 6HSWHPEHU )RUEHV %OYG /DQKDP 0' (DUWK 5HVRXUFH 'DWD $QDO\VLV 6\VWHP (5'$6f )LHOG JXLGH PDQXDO IRU SF YHUVLRQ f (5'$6 ,QF %XIRUG +LJKZD\ 6XLWH $WODQWD *$ (QYLURQPHQWDO 6\VWHP 5HVHDUFK ,QVWLWXWH (65,f $UF,QIR PDQXDOV (QYLURQPHQWDO DQG 6FLHQWLILF 5HVHDUFK ,QVWLWXWH 5HGODQGV &$ )XNXVKLPD 7 DQG 0XUDRND 6LPSOH PRGHO WR SUHGLFW ZDWHU TXDOLW\ LQ -DSDQHVH ODNHV 3URF RI WKH ,QWL $VVRF IRU 7KHRUHFWLFDO DQG $SSOLHG /LPQRORJ\ f *LOOHVSLH $5 $% .DKOH DQG 5( :DONHU &RORU HQKDQFHPHQW RI KLJKO\ FRUUHODWHG LPDJHV 'HFRUUHODWLRQ DQG +6, FRQWUDVW VWUHWFKHV 5HPRWH 6HQVLQJ RI (QYLURQPHQW *RQ]DOH] 5& DQG 3 :LQW] 'LJLWDO LPDJH SURFHVVLQJ QG HG $GGLVRQ:HVOH\ 3XE &RPSDQ\ 5HDGLQJ 0$ *UDKDP 0+ %* -XQNLQ 07 .DOFLF 5: 3HDUVRQ DQG %5 6H\IDUWK (DUWK UHVRXUFHV ODERUDWRU\ DSSOLFDWLRQV VRIWZDUH XHU UHIHUHQFH YRO t ,, 5HSRUW 1R (DUWK 5HVRXUFHV /DERUDWRU\ 1DWLRQDO 6SDFH 7HFKQRORJ\ /DERUDWRULHV 1DWLRQDO $HURQDXWLFV DQG 6SDFH $GPLQLVWUDWLRQ *UDVVR '1 $SSOLFDWLRQV RI WKH ,+6 FRORU WUDQVIRUPDWLRQ IRU VFDOH JHRORJLF PDSSLQJ $ ORZ FRVW 6327 DOWHUQDWLYH 3KRWRJUDPPHWULF (QJLQHHULQJ DQG 5HPRWH 6HQVLQJ f +DUULV -5 5 0XUUD\ DQG 7 +LURVH ,+6 WUDQVIRUP IRU WKH LQWHJUDWLRQ RI UDGDU LPDJHU\ ZLWK RWKHU UHPRWHO\ VHQVHG GDWD 3KRWRJUDPPHWULF (QJLQHHULQJ DQG 5HPRWH 6HQVLQJ f +D\GQ 5 *: 'DNOH +HQNHO DQG -( %DUH $SSOLFDWLRQ RI WKH ,+6 FRORU WUDQVIRUP WR WKH SURFHVVLQJ RI PXOWLVHQVRU GDWD DQG LPDJH HQKDQFHPHQW 3URFHHGLQJV RI WKH ,QWL 6\PS RQ 5HPRWH 6HQVLQJ RI $ULG DQG 6HPL $ULG /DQGV &DLUR (J\SW -DQXDU\ +XHWH $5 DQG -DFNVRQ 6RLO DQG DWPRVSKHUH LQIOXHQVHV RQ WKH VSHFWUD RI SDUWLDO FDQRSLHV 5HPRWH 6HQVLQJ RI (QYLURQPHQW

PAGE 229

,GVR 6% 55HJLQDWR DQG 5' -DFNVRQ $OEHGR PHDVXUHPHQW IRU UHPRWH VHQVLQJ RI FURS \LHOGV 1DWXUH f -DFNVRQ /. DQG 6DXOV )UXLW FURSV IDFW VKHHW 7KH VZHHW RUDQJH )& ,QVW RI )RRG DQG $JULH 6FL 8QLY RI )ORULGD *DLQHVYLOOH )/ )UXLW FURSV IDFW VKHHW *UDSHIUXLW )& ,QVW RI )RRG DQG $JULH 6FL 8QLY RI )ORULGD *DLQHVYLOOH )/ -XGG '% DQG :\V]HFKL &RORU LQ EXVLQHVV VFLHQFH DQG LQGXVWU\ UG HGLWLRQ -RKQ :LOH\ t 6RQV ,QF 1HZ
PAGE 230

1RYRWQ\ 9 DQG &KHVWHUV +DQGERRN RI QRQSRLQW SROOXWLRQ VRXUFHV DQG PDQDJHPHQW 9DQ 1RVWUDQG 5HLQKROG &RPSDQ\ 1HZ
PAGE 231

6SRWOLJKW 6327 ,PDJH &RUSRUDWLRQ 1HZVOHWWHU 6327 ,PDJH &RUSRUDWLRQ 5HVWRQ 9$ 0DUFK 6ZDLQ 3+ )XQGDPHQWDOV RI SDWWHUQ UHFRJQLWLRQ LQ UHPRWH VHQVLQJ LQ 3+ 6ZDLQ DQG 60 'DYLV HGLWRUV 5HPRWH VHQVLQJ 7KH TXDQWLWDWLYH DSSURDFK 0F*UDZ+LOO ,QF 1HZ
PAGE 232

:RQJ )+ DQG 5 2UWK 5HJLVWUDWLRQ RI 6HDVDW/DQGVDW FRPSRVLWH LPDJHV WR 870 FRRUGLQDWHV 3URF RI WKH WK &DQDGLDQ 6\PS RQ 5HPRWH 6HQVLQJ +DOLID[ 1RYD 6FRWLD 0D\ =REULVW $/ 5%ODFNZHOO DQG :' 6WURPEHUJ ,QWHJUDWLRQ RI /DQGVDW 6HDVDW DQG RWKHU JHRGDWD VRXUFHV 3URFHHGLQJV RI WKH WK $QQXDO 6\PS RQ 5HPRWH 6HQVLQJ RI (QYLURQPHQW (QYLURQPHQWDO 5HVHDUFK ,QVWLWXWH RI 0LFKLJDQ $QQ $UERU SS

PAGE 233

*/266$5< D PHUJLQJ FRHIILFLHQW IRU SULPDU\ LPDJH PHUJLQJ FRHIILFLHQW IRU VHFRQGDU\ LPDJH 5F PHUJLQJ FRHIILFLHQW IRU PLQLPXP YDULDQFH LQ PHUJHG LPDJH E\ FRQILQLQJ PHWKRG G PHUJLQJ FRHIILFLHQW IRU HTXDO YDULDQFH LQ PHUJHG LPDJH E\ GLIIHUHQFLQJ PHWKRG [ PHDQ IRU LPDJH RQH RU YDULDEOH RQH + PHDQ IRU LPDJH WZR RU YDULDEOH WZR 0F PHDQ IRU PHUJHG LPDJH E\ FRQILQLQJ PHWKRG G PHDQ IRU PHUJHG LPDJH E\ GLIIHUHQFLQJ PHWKRG [S PHDQ IRU PHUJHG LPDJH E\ SUHVHUYLQJ PHWKRG 0U PHDQ IRU PHUJHG LPDJH E\ UDWLRLQJ PHWKRG 0\ PHDQ IRU PHUJHG LPDJH RU PHUJHG YDULDEOH
PAGE 234

QRUPDOL]HG YDULDQFH IRU PHUJHG LPDJH
PAGE 235


PAGE 236

20' RULJLQDO PXOWLVSHFWUDO GDWDVHW 3$1 SDQFKURPDWLF LPDJH RU DYHEDQGf 5%9 UHWXUQ EHDP YLGLFRQ 5*% UHG JUHHQ DQG EOXH 506 URRWPHDQVTXDUH HUURUf 56$/ 5HPRWH 6HQVLQJ $SSOLFDWLRQV /DERUDWRU\ 6$5 V\QWKHWLF DSHUWXUH UDGDU 63& VWDWH SODQH FRRUGLQDWH V\VWHPf 6327 )UHQFKf 6\VWHPH 3UREDWRLUH GH n2EVHUYDWLRQ GH OD 7HUUH 7,5 WKHUPDO LQIUDUHG 70 WKHPDWLF PDSSHU 870 XQLYHUVDO WUDQVYHUVH PHUFDWRU FRRUGLQDWH V\VWHPf 86*6 8QLWHG 6WDWHV *HRORJLFDO 6XUYH\

PAGE 237

%,2*5$3+,&$/ 6.(7&+ 7KH DXWKRU ZDV ERUQ DQG UDLVHG LQ D FRXQWU\VLGH LQ *XDQJGRQJ 3URYLQFH 7KH 3HRSOHn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

PAGE 238

, FHUWLI\ WKDW KDYH UHDG WKLV VWXG\ DQG WKDW LQ P\ RSLQLRQ LW FRQIRUPV WR DFFHSWDEOH VWDQGDUGV RI VFKRODUO\ SUHVHQWDWLRQ DQG LV IXOO\ DGHTXDWH LQ VFRSH DQG TXDOLW\ DV D GLVVHUWDWLRQ IRU WKH GHJUHH RI 'RFWRU RI 3KLORVF 6XQ )X 6O
PAGE 239

7KLV GLVVHUWDWLRQ ZDV VXEPLWWHG WR WKH *UDGXDWH )DFXOW\ RI WKH &ROOHJH RI (QJLQHHULQJ DQG WR WKH *UDGXDWH 6FKRRO DQG ZDV DFFHSWHG DV SDUWLDO IXOILOOPHQW RI WKH UHTXLUHPHQWV IRU WKH GHJUHH RI 'RFWRU RI 3KLORVRSK\ 'HFHPEHU :LQIUHG 0A3KLO

xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E5YR77M5H_NK1J4B INGEST_TIME 2011-09-29T18:06:53Z PACKAGE AA00004730_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES


MULTIRESOLUTION PROCESSING OF SATELLITE IMAGES AND
GEOGRAPHIC INFORMATION SYSTEMS TECHNIQUES FOR
LAND-USE CLASSIFICATION
By
YURONG TAN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1994

Copyright 1994
by
Yurong Tan

ACKNOWLEDGEMENTS
This research was performed using the facilities of the
Remote Sensing Applications Laboratory (RSAL) of the
Department of Agricultural Engineering at the University of
Florida. The author is grateful for the assistance provided
by the RSAL director, Dr. Sun F. Shih; RSAL manager, Orlando
Lanni; and RSAL assistants, Jonathan D. Jordan, Chih-Hung Tan,
and Bruce E. Myhre. The author is also grateful for the
comments and review of this manuscript by Dr. Donald L. Myhre
of the Soil and Water Science Department at the University of
Florida.
The author extends his appreciation to each of the
members of his advisory committee, Dr. Brian J. Boman, Dr.
Edward P. Lincoln, Dr. Allen R. Overman, and Dr. Byron E. Ruth
for their comments and advice rendered during this research,
particularly to the committee chairman, Dr. Sun F. Shih of the
Department of Agricultural Engineering at the University of
Florida, for the guidance and support provided throughout the
course of his graduate study at the University of Florida.
The greatest gratitude of the author goes to his wife,
Siru, who always shared the joy as well as frustrations and
provided unconditional support in every aspect during this
seemingly endless process. The author is in debt to his son,
Guolong, for the patience he undertook while this research was
being actively pursued.
iii

Lastly, the author acknowledges that this research would
not have been completed without the continuous support and
encouragement from his loving parents.
iv

TABLE OF CONTENTS
ACKNOWLEDGEMENTS iii
LIST OF TABLES vii
LIST OF FIGURES ix
ABSTRACT xii
CHAPTERS
1 INTRODUCTION 1
Overview 1
Statement of Research Problem 3
Concept of Multiresolution Processing 8
2 OBJECTIVES OF RESEARCH 13
3 REVIEW OF LITERATURE 14
Conventional Image Enhancement 14
Multiresolution Enhancement 20
Color Composite Generation 20
Radiometric Enhancement 27
Other Enhancement Methods 36
Summary: Assessment of Problems 40
4 PRINCIPLE OF MERGING IMAGES 46
Principle of Merging Images 46
Assumptions 47
Arithmetic of Random Variables 48
Confining Method 53
Preserving Method 63
Differencing Method 69
Summary: Principle of Merging Images 73
5 DEMONSTRATION OF MERGING METHODS 76
Satellite Image Data 76
Variance of Merged LAC Images 81
Comparison of Merged LAC Images 91
Ratioing of Satellite Images 106
Multiresolution Enhancement 113
Summary: Appraisal of Merging Methods 116
6 MATERIALS AND METHODOLOGY FOR
MULTIRESOLUTION LAND-USE CLASSIFICATION 119
Data Source and Equipment 119
v

SPOT Image Data and Study Area 119
ACIR Photography 122
Image Processing Systems 122
Photogrammetric Stereo Plotter 123
Procedures for Merging SPOT Dataset 124
Pre-merging Processing 124
Generating Merged Dataset 126
Evaluation of Merged Data 129
Image Response and Citrus Canopy Cover 132
Photogrammetric Measurement 132
Canopy Cover Estimation 134
Land-use Classification 136
Précis and Concept 137
Extracting Signature Patterns 139
GIS-base Discrete Classification 141
7 DISCUSSIONS AND ANALYSES OF
MULTIRESOLUTION LAND-USE CLASSIFICATION 148
Evaluation of Merged Image 148
Radiometric Quality 148
Spatial Improvement and Spectral
Integrity 151
Image Response and Citrus Canopy Cover 157
Estimation of Citrus Canopy Cover 157
Relation of Image response to
Canopy Cover 159
Differentiation of Canopy Cover 166
Effect of Multiresolution Merging 177
Land-use Classification 183
Potential for Signature Extraction 184
GIS Discrete Classification 189
8 CONCLUSIONS AND RECOMMENDATIONS 195
Research Conclusions 195
Recommendations 199
APPENDICES
A RGB COLOR DISPLAY 202
B IHS TRANSFORM FOR IMAGE DISPLAY 203
C PROGRAM CODES TO UNPACK AVHRR LAC DATA 206
D CLASSIFICATION DECISION RULES 209
REFERENCES 213
GLOSSARY 220
BIOGRAPHICAL SKETCH 224
vi

LIST OF TABLES
Table Facia
1-1 Available sources of Landsat and SPOT resource
satellite data and system characteristics 5
4-1 Summary of the characteristics of different
merging approaches 75
5-1 Wavelength characteristics of NOAA-11
AVHRR LAC images 77
5-2 standard deviation (a), normalized variance
(a2), mean (n), maximum and minimum values
of NOAA-11 AVHRR LAC images 80
5-3 Offset constant (C) used in the differencing
method for merging LAC images 82
6-1 Standard deviation (a) , mean (/¿) , and maximum
and minimum values, and correlation coefficients
(r) of SPOT multiresolution dataset 127
6-2 Multiresolution datasets and corresponding
merging equations 130
6-3 Parameters used in ERDAS STATCL and ELAS
TMTR modules for signature extraction 142
7-1 Standard deviation (a) and mean brightness
values (/i) for multiresolution merged SPOT
images 149
7-2 Summary for correlations between a merged image
and its original multispectral counterpart 153
7-3 Between-waveband correlations (r) within
multiresolution merged datasets 154
7-4 Summary for corelations between citrus
canopy size and image response for
multiresolution merged images 178
7-5 Variation of image data correlation (r)
between panchromatic and original
multispectral wavebands among selected groves ... 179
vii

7-6 Standard deviations (a) of merged image
data for selected citrus groves 180
7-7 Summary of spectral signatures unveiled
by ERDAS STATCL module 185
7-8 Summary of spectral signatures unveiled
by ELAS TMTR module 188
7-9 Canopy cover for spectral classes by GIS-
based discrete classification technique 190
viii

LIST OF FIGURES
Figure Fags
1-1 Schematics of merging multiresolution
satellite images 9
3-1 Schematics of principal component analysis
for multispectral datasets 18
4-1 Relation of radiometric variance to merging
coefficient (B) and correlation coefficient
(r) for the confining method 57
4-2 Effect of variance difference on the
radiometric quality of merged images
for the confining method 61
4-3 Relation of radiometric variance to merging
coefficient (B) and correlation coefficient
(r) for the preserving method 66
4-4 Effect of variance difference on the
radiometric quality of merged images
for the preserving method 68
5-1 Location of clipped NOAA-11 AVHRR LAC images .... 79
5-2 Comparison between actual and estimated
radiometric variance for merged LAC
images (case I) 83
5-3 Comparison between actual and estimated
radiometric variance for merged LAC
images (case II) 84
5-4 Comparison between actual and estimated mean
digital count for merged LAC images (case I) .... 85
5-5 Comparison between actual and estimated mean
digital count for merged LAC images (case II) ... 86
5-6 Original clipped NOAA-11 LAC images of
red and NIR wavebands 93
5-7 Merged LAC images by the preserving
method (case I) 94
IX

5-8 Merged LAC images by the preserving
method (case II) 96
5-9 Merged LAC images by the confining
method (case I) 97
5-10 Merged LAC images by the confining
method (case II) 98
5-11 Merged LAC images by the differencing
method (case I) 100
5-12 Merged LAC images by the differencing
method (case II) 101
5-13 Summary (mosaic) of merged LAC images for
three methods (case I) 104
5-14 Summary (mosaic) of merged LAC images for
three methods (case II) 105
6-1 Location of clipped SPOT multiresolution
dataset and study area 121
7-1 Comparison of SPOT 20-m NDVI and 10-m
NDVIp images 156
7-2 Effect of citrus canopy cover on SPOT green
waveband response 160
7-3 Effect of citrus canopy cover on SPOT red
waveband response 161
7-4 Effect of citrus canopy cover on SPOT
panchromatic waveband response 163
7-5 Effect of citrus canopy cover on SPOT NIR
waveband response 164
7-6 Coincident plot of SPOT green waveband
response for select citrus groves 168
7-7 Coincident plot of SPOT red waveband
response for select citrus groves 169
7-8 Coincident plot of SPOT NIR waveband
response for select citrus groves 170
7-9 Effect of tree crown variations on SPOT
green waveband response variability for
partial canopy groves 172
x

7-10 Effect of tree crown variations on SPOT
red waveband response variability for
partial canopy groves 173
7-11 Effect of tree crown variations on SPOT
NIR waveband response variability for
partial canopy groves 174
7-12 Relation of citrus tree variations to
canopy cover difference 176
xi

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
MULTIRESOLUTION PROCESSING OF SATELLITE IMAGES AND
GEOGRAPHIC INFORMATION SYSTEMS TECHNIQUES FOR
LAND-USE CLASSIFICATION
By
Yurong Tan
December, 1994
Chairman: Dr. Sun Fu Shih
Major Department: Agricultural Engineering
Combining multiresolution images to improve land-use
information assessment is an important subject in remote
sensing applications. The problem in finding effective
methods for multispatial processing must be resolved through
the development of new procedures for merging satellite
images. The effect of combining image data on the quality of
merged datasets must also be assessed toward land-use
classification applications and multispectral analyses.
In digitally merging satellite images, the statistical
variation analyses for combining random variables can be used
to understand the various forms of image data merging and
assess the radiometric quality of pre-merged images. The
selection of an effective merging approach must be made with
consideration of both the correlation and radiometric variance
difference between the combining images and the merging
coefficients. Merging images is a radiometric transformation
xii

among the various land-use types in a scene. This principle
can be used to collaborate Landsat MSS, Landsat TM, SPOT, and
other satellite data for broader applications.
To generate enhanced datasets, the preserving approach
should be used for non-negatively correlated images, and the
differencing approach for those with negative correlations.
The commonly used, but ineffective confining method should be
avoided. The efficacy of waveband ratioing is limited to the
land-use elements with weak/negative correlations and larger
values in the numerator image.
The preserving method with a 6=0.5 coefficient was
effective in generating both spatially and radiometrically
enhanced SPOT multiresolution merged datasets which
consistently rendered significantly more spectral signatures
from a satellite scene. This enhanced differentiation
provides a greater amount of information for applications
including land-use classification and image interpretation.
The photogrammetric estimation of citrus canopy cover is
feasible and accurate. Except for the NIR waveband, citrus
canopy cover is inversely related to SPOT image spectra of
partial canopy groves, suggesting a strong influence of soil
substrate on satellite image response. The canopy-size
classification of citrus groves was improved through the
combined use of merged SPOT dataset and GIS-based
classification techniques. Citrus groves with a higher
percentage of canopy cover had more uniform trees and less
variable spectral responses.
xiii

CHAPTER 1
INTRODUCTION
Overview
Information about land use plays an increasingly
important role in the management and preservation of natural
resources. For instance, land-use data are used in the
operations of water resources management which range from
water-use permitting to the development and implementation of
regional planning and management strategies. In environmental
and water quality monitoring, land-use activities are often
indicative of the source and type of pollutants (Novotny and
Chesters, 1981; Fukushima and Muraoka, 1988) , particularly
from agricultural and urban lands (USEPA, 1984; Pionke and
Urban, 1985) . In many cases, it is the change of land use
that creates immense environmental concerns. Agricultural
land-use data are needed to forecast and monitor production as
well as to assess damage caused by diseases and natural
catastrophic events. Also, land-use data are used in many
other ways including forest management (Coleman et al., 1990),
urban development and planning (Colwell and Poulton, 1985),
hydrological investigations, and applications of geographic
information systems (Ehlers, 1989; Piwowar et al., 1990; Tan
and Shih, 1991a). Therefore, the availability of quality and
timely land-use information becomes an indispensable factor
1

2
which prescribes our efforts in better managing natural
resources.
Traditionally, land-use data are collected through aerial
photography, ground surveys, and existing maps. While these
methods are reliable and accurate, they are expensive and
time-consuming. In addition, the process of traditional
methods is tedious, and therefore often provides land-use data
that are years out of date, while data availability becomes a
limiting factor in some cases. When a large coverage area is
needed, the difficulties involved increase in magnitude as
well as in complexity. Fortunately, the synoptic coverage and
periodic availability of satellite remote sensing data provide
an excellent opportunity for the acquisition of timely land-
use data and the monitoring of extensive land-use activities.
This significantly amplifies our ability to understand the
effects of land use types and to manage the impacts and
consequences resulting from the change of land use activities.
With increasing environmental awareness, more careful planning
and monitoring of land-use activities becomes an important
consideration in all levels of resources management.
To derive land-use information from satellite data, a
land-use classification procedure is used within an automated
computer image processing system. Such procedures generate
statistically similar spectral classes which are then related
to different land-use types (Lillesand and Kiefer, 1979;
Thomas et al., 1987) through a ground-truthing process. To

3
improve the acquisition of land-use information from space,
continuous research efforts are underway in the development of
both new sensing systems (Engel, 1986; Spotlight, 1991; EOSAT,
1992a, 1992b) and image processing techniques.
Statement of Research Problem
Obtaining land-use data or land-use information by
satellite remote sensing requires a significant improvement
both in accuracy and in specificity in order to be used
operationally in many applications (Lo et al., 1986; DeGloria
et al., 1986). For instance, day-to-day operations in water
resources management seldom use satellite-based land-use data,
mainly because of the lack of desired specificity or details.
One facet to the solution of this problem is to improve the
quality of raw data through advanced sensing technology and
sensor system design. This has been initiated by the
development of new sensing systems which will be onboard
Landsat-7 (EOSAT, 1992a, 1992b) and the French Systeme Probatoire
de 1 'Observation de la Terre (SPOT) resources satellite four
referred to as SPOT-4 (Spotlight, 1991). Equally important is
the development of data processing techniques to analyze and
classify the remotely sensed data so that improved land-use
information becomes feasible in practical applications.
Combining multispectral satellite data that have
different spatial resolutions to extract more subtle land-use
information has become an important component in image

4
processing techniques. In the process, the spectral and
spatial advantages rendered by different sensing systems
(Table 1-1) are combined complementarily into a merged
dataset. This provides an unparalleled opportunity that
expands our ability beyond using any of the original
individual datasets to acquire land-use information. Because
of the challenge of future sensor systems which will provide
multiresolution sensing as well as onboard registration
capabilities (Spotlight, 1991; EOSAT, 1992a, 1992b) and the
tremendous amount of image data already captured by satellite
sensors operating over a wide range of spatial resolutions and
spectral wavebands (Shih, 1984; Moore, 1989; Ehlers, 1989),
merging multiresolution satellite images creates an immense
opportunity to make contributions to the improvement of
current land-use data acquisition from space. As a result,
multiresolution processing is anticipated to be a very
powerful image processing technique in future remote sensing
applications.
To date, much research work remains to be done in order
to effectively use multiresolution satellite imagery for
resources management. For instance, finding effective methods
to digitally merge multiresolution datasets continues to be
the central problem in multiresolution processing. A good
merger will be able to take full advantage of the spectral and
spatial benefits of multiresolution images so that resultant
merged datasets will have incomparable radiometric quality

Table 1-1. Availabe sources of Landsat and SPOT resource satellite data and system
characteristics.
Spectral characteristics Spatial
Type of resolution
Sensor Band# Wavelength (/i) Color (m)
Landsat-1 and Landsat-2
RBVa
1
0.475-0.575
Blue-green
76
2
0.580-0.680
Yellow-red
76
3
0.690-0.830
Red-infrared
76
MSSb
4
0.50 -0.60
Green
76
5
0.60 -0.70
Red
76
6
0.70 -0.80
Near infrared
76
7
0.80 -1.10
Near infrared
76
Landsat-3
RBVa
Camera
0.505-0.750
Panchromatic
40
MSSb
4
0.5 - 0.6
Green
76
5
0.6 - 0.7
Red
76
6
0.7 - 0.8
Near infrared
76
7
0.8 - 1.1
Near infrared
76
8
10.4 -12.6
Thermal infrared
234
TMC
1
2
3
Landsat-4, Landsat-5
0.52 Blue
0.61 Green
0.69 Red
0.45
0.53
0.62
30
30
30
U1

Table 1-1
continued
Type of
Sensor
MSSb
HRVf
Spectral characteristics
Spatial
resolution
(m)
Band#
Wavelength(n)
Color
4
0.78 - 0.91
Near infrared
30
5
1.57 - 1.78
Intermediate infrared
30
6
10.42 -11.66
Thermal infrared
120
7
2.08 - 2.35
Intermediate infrared
30
1
0.50 -0.60
Green
76
2
0.60 -0.70
Red
76
3
0.70 -0.80
Near infrared
76
4
0.80 -1.10
Near infrared
76
Landsat-6C and Landsat-7
0.50 - 0.90
Panchromatic
15
1
0.45 - 0.52
Blue
30
2
0.53 - 0.61
Green
30
3
0.62 - 0.69
Red
30
4
0.78 - 0.91
Near infrared
30
5
1.57 - 1.78
Intermediate infrared
30
6
10.42 -11.66
Thermal infrared
120
7
2.08 - 2.35
Intermediate infrared
30
SPOTe-l, SPOT-2, and SPOT-3
0.51 - 0.73
Panchromatic
10
0.50 - 0.59
Green
20
0.61 - 0.68
Red
20
0.79 - 0.89
Near infrared
20
1
2
3

Table 1-1 — continued.
Type of
Sensor
Spectral characteristics
Spatial
resolution
(m)
Band#
Wavelength(n)
Color
■ orUl 4 “
HRVf
0.61 - 0.68
Panchromatic
10
1
0.50 - 0.59
Green
20
2
0.61 - 0.68
Red
20
3
0.79 - 0.89
Near infrared
20
4
1.58 - 1.75
Intermediate infrared
20
Source: modified from Shih, 1984; Spotlight, 1991; and EOSAT, 1992a; 1992b.
a Return beam vidicon camera.
b Multispectral scanner.
c To be replaced by Landsat-7 because of failure to reach orbit.
d Thematic mapper.
6 (French) Systeme Probatoire de 1 'Observation de la Terre (SPOT).
f High resolution visible.
Note: Operation of Landsat 1
Landsat 2
Landsat 3
Landsat 4
Landsat 5
Landsat 6
Landsat 7
SPOT 1
SPOT 2
SPOT 3
SPOT 4
7/23/1972 - 1/06/1978
1/22/1975 - 2/25/1982
3/05/1978 - 3/31/1983
7/16/1982 - present.
3/01/1984 - present.
launched in 1993, but failed to reach obit,
identical to Landsat 6 and to be launched in 1997.
2/22/1986 - 12/30/1990
1/22/1990 - present.
?/?/1992 - present.
To be launched in 1995.

8
and enhanced spatial information. These quality factors of
image data are vital not only to the utility of the merged
datasets for potential applications, but also to any remote
sensing efforts that attempt to improve our capability in
monitoring land-use resources. Therefore, this research was
focused on the techniques for combining multiresolution
satellite images as well as on the utility of multiresolution
processing for land-use classification and image
interpretation.
Concept of Multiresolution Processing
Multiresolution processing is an image processing
technique used to combine or merge multispectral images that
have different spatial resolutions. One of the images to be
combined will have a high spatial resolution or a smaller size
of picture element (pixel), and a panchromatic waveband, while
the others will be multispectral (or multi-waveband), but with
a relatively lower spatial resolution, or a larger pixel.
These images of different spatial resolutions are digitally
merged to reconstruct a new set of images that can inherit the
spectral and spatial characteristics of both the multispectral
and panchromatic images. The process is schematically
illustrated in Figure 1-1.
The purpose of multiresolution processing is to generate
a new set of images with enhanced spectral and spatial
qualities by taking the spectral and spatial advantages of the

Multispectral images
Merged multispectral
images
10 m
XMSS „
XMSSk
XMSSia
xmss14
Figure 1-1. Schematics of merging multiresolution satellite images.

10
images to be combined. The spatial and spectral virtues of
the original multiresolution image data are utilized
complementarily. As a result, the merged dataset becomes
spectrally as well as spatially more powerful for remote
sensing applications.
One example of multiresolution processing is to merge the
SPOT high resolution visible (HRV) panchromatic and
multispectral images that have respective 10-m and 20-m
spatial resolutions (Cliche et al., 1985; Carper et al.,
1990). The panchromatic image with a 10-m resolution can
reveal subtle spatial details of scene objects, but its usage
for multispectral analyses (land-use classification) is
hampered by its very broad spectral waveband. The 20-m
multispectral data with three spectral wavebands are more
useful for land-use classification, however a high spatial
resolution multispectral dataset is more desirable for
extracting subtle information from the scene. When such
multiresolution images are merged, the spectral and spatial
advantages are combined into a new set of images which are
multispectral and with a 10-m spatial resolution. As a
result, the new merged dataset will have a greater potential
for remote sensing applications.
There are two major steps involved in the process of
multiresolution processing. The first deals with the co¬
registration of the multiresolution images. This can be done
with two different approaches. The first one is to simply

11
project all images to a mutual geographic reference system
which can be either the latitude-longitude system, or the
universal transverse mercator (UTM) system, or the state plane
coordinate (SPC) system. The second approach is to treat one
of the images as a master and the rest as slaves. After
selecting a number of tie points that are mutual to all images
including the master one, the slave images are rectified to
the master image. In the second approach, no actual
geographical coordinate system (e.g. UTM) is utilized and the
slave images are referenced relative to the master image.
Usually, this relative approach produces a smaller error of
co-registration because transitional reference (e.g. maps) and
digitizing operations for map data entry are not involved. To
register multiresolution images, it is also necessary to
invoke an image resampling procedure before or during the
registration process. Virtually all image processing software
packages provide the facilities for image resampling and
registration operations.
The second step involves the use of mathematical
manipulations to digitally combine, pixel by pixel, the
numerical image data. This is a very critical step because
the spectral, radiometric, and spatial qualities of the merged
dataset depend on the selection of a good combining algorithm.
At the end, a new set of multispectral images are generated
which are radiometrically, spatially, and spectrally enhanced.
While the combining algorithms reported in the literature vary

12
considerably, their introduction is the results of
speculations and arbitrary elaborations because the basic
principle of digitally merging satellite images is not well
understood. Therefore, it has become essential to explore and
to understand the principle of image data manipulations so
that the techniques of multiresolution processing can be
developed to effectively enhance satellite remote sensing
applications including land-use classification.

CHAPTER 2
OBJECTIVES OF RESEARCH
The main objective of this research was to study the
principle of digitally merging satellite images and to develop
techniques for combining multiresolution satellite datasets,
as well as to evaluate the utility of multiresolution
processing for satellite-based land-use classifications. The
specific objectives included:
1. To formulate the principle of digitally combining
multispectral satellite images including those with different
spatial resolutions.
2. To develop techniques and methods for digitally
merging multiresolution satellite images.
3. To study the effects of multiresolution processing
on the spectral, spatial, and radiometric qualities of merged
multispectral datasets.
4. To study the effects of canopy sizes of citrus trees
on the spectral responses of SPOT satellite data as well as to
investigate the feasibility of a canopy-size differentiation
of citrus crops on satellite images.
5. To investigate the utility and benefits of combining
multiresolution satellite images for land-use classifications,
particularly for citrus crops.
13

CHAPTER 3
REVIEW OF LITERATURE
Because of the multispectral capabilities of contemporary
satellite sensing systems, a geographic area can be imaged
simultaneously with a number of spectral wavebands, resulting
in a multi-image scene or dataset. In the discussions
throughout this dissertation, a scene includes all the images
acguired for one geographic area at one time, while an image
is meant to represent the numerical data of only one spectral
waveband.
Conventional Image Enhancement
Over the years that remote sensing data have become
widely used, many technigues for image enhancement have been
well developed and standardized in image processing software
systems. Therefore, an in-depth discussion for each of these
techniques seems inappropriate. However, a brief review of
those techniques which were involved or used in many previous
research efforts to combine multiresolution satellite images
would be useful to the understanding of continued discussions.
Those techniques included the contrast stretching, spatial
filtering, and principal component analysis.
A contrast-stretching procedure is an image processing
procedure used to arbitrarily rescale a set of image gray
14

15
shades to a larger range or to a full range (0-255) for
increasing image contrast. The gray shades of an original
satellite image of Landsat, SPOT, and other satellites usually
spread over a portion of the available 0-255 dynamic range (or
sometimes called data depth). As a result, such images with
cramped gray shades do not have conspicuous tonal gradations.
After a contrast-stretching process, the image values (often
called image digital counts) of relatively dark pixels are
scaled back further, while those of bright pixels are scaled
up. As a result, original dark pixels will become darker
while the bright ones become brighter in a contrast-stretched
image (Gonzalez and Wintz, 1987). Very often, this simple
procedure can produce satisfactory results for image
interpretation. Note that the increase in image tonal
contrast by a contrast-stretching procedure gives a false
sense that the procedure can improve the image radiometric
quality.
The contrast-stretching procedure can be applied to a
portion of the existing image gray shades (Thomas et al.,
1987) or to a subimage area (Gonzalez and Wintz, 1987) for a
selective enhancement. Also, there are linear and nonlinear
contrast stretching methods (Lillesand and Kiefer, 1979;
Thomas et al., 1987) and the procedure is performed for each
image or waveband independently.
A spatial filtering procedure includes both the high-pass
and low-pass filters which are often used to remove or to

16
emphasize certain visual effects of a digital image. For
instance, a low-pass filter is used for image smoothing and
noise elimination while a high-pass filter is for edge
enhancement (Lillesand and Kiefer, 1979). The simplest form
of a low-pass filter is to replace the value of a pixel by the
average computed from its neighborhood (e.g. 3 x 3 pixel
array). By replacing a pixel's value with its neighborhood
average, the large values (such as noises) will be compressed
while the small values are inflated or exaggerated (Lillesand
and Kiefer, 1979). As a result, a low-pass filtered image
will appear smoother and have less contrast. In the case of
a high-pass filter, the value of a pixel will be added to or
subtracted from by its deviation from the average of its
neighborhood (e.g. 3 x 3 array), depending on its relative
magnitude with respect to the defined neighborhood average.
Therefore, boundary pixels which usually have the largest
deviations will become either much darker or brighter. Often,
the deviations are doubled or even tripled in order to make
edges or linear features more conspicuous (Lillesand and
Kiefer, 1979). The operation of a spatial filtering procedure
(high-pass or a low-pass) is performed independently for each
image or waveband. An important point in spatial filtering is
that the resultant image data are radiometrically altered by
such filtering procedures.
As compared to the methods of both contrast stretching
and spatial filtering, principal component analysis (PCA) is

17
a procedure which involves a multi-dimensional transformation
for a set of multispectral images. In the process, the multi¬
waveband data are transformed from the original coordinate
system formed by the spectral wavebands into one defined by
new synthesized wavebands. There are several usages for a PCA
procedure. First, it can be used to reduce the dimensionality
of multi-waveband datasets (Thomas et al., 1987). For
instance, when a PCA transform is applied, the image data of
a two-waveband dataset can be effectively represented by the
first principal component (PCI) as shown in Figure 2-1, thus
reducing the dataset to essentially one dimension (or one
synthesized waveband). The second usage is to increase the
image contrast as well as the separability for land-use
elements (Lillesand and Kiefer, 1979). For instance, the
image data variance encompassed by the PCI component (Figure
2-1) is greater than either of those for the two original
wavebands. Therefore, the image of the PCI component will
have more contrast as well as greater separation among the
different land-use elements in the image. The third usage of
a PCA procedure is for the decorrelation of multispectral
images (Gillespie et al., 1986). In such a case, a PCA
transform is followed by a contrast-stretching procedure
applied to the PC components, particularly the PC2 component
as shown in Figure 2-1. Then, the first (PCI) and second
(PC2) components are together retransformed back to their
original multispectral space. In a decorrelated dataset, the

i
o
ü
-p
T5
G
XI
Q)
>
(d
td
P
-P
O
cu
a
w
Spectral waveband one
Figure 2-1. Schematics of principal component analysis for multispectral datasets.
03

19
identities for the various types of spectral elements may be
significantly different from those of the original images
(Gillespie et al., 1986).
If the PCA procedure is applied to a multispectral image
dataset with n wavebands, the image data transformation will
take place within a n-dimensional space. The results are that
the amount of radiometric information represented by the
first, the second, . . . and the nth component will be in a
decreasing order. Also, the transformed components can each
be contrast-stretched (Lillesand and Kiefer, 1979) to further
enhance the tonal gradations of transformed images. The PCA
transform is usually carried out before initiating land-use
classification procedures to reduce data dimensionality as
well as to enhance the radiometric separability of spectral
classes. Thomas et al. (1987) presents in-depth discussions
about PCA transforms which are exemplified by using a Landsat
multispectral scanner (MSS) dataset.
Finally, it is worthwhile to point out that the
procedures of contrast stretching, spatial filtering, and
principal component analysis will not enhance or improve the
spatial resolution of the original images. In addition, a
contrast-stretching procedure will not increase the actual
number of gray shades in an image, even though the radiometric
variance of stretched image data is increased.

20
Multiresolution Enhancement
Combining the spatial and multispectral advantages of
multiresolution satellite images for various resource
management applications has inspired great interests in the
remote sensing community. To merge satellite images with
different spatial resolutions, both image co-registration and
arithmetical data manipulations are required. If the images
are already co-registered, the primary methods to manipulate
the image data can be summarized into two broad approaches
which include the generation of color composites and the
enhancement of radiometric quality of merged images. Note
that to generate a color composite usually requires three
images for the blue, green, and red primary colors of a
display device.
Color Composite Generation
The most commonly used methods for generating color
renditions from image datasets are the well-known RGB (red,
green, and blue) color display system (Appendix A) and the
intensity-hue-saturation (IHS) color transform (Appendix B).
For multiresolution datasets, the RGB system is simple and
easy to use, but the resultant color composites often have a
blocky appearance, particularly when the spatial resolution
difference is large. Recently, the IHS transform has gained
popularity mainly because of its effectiveness to produce more
balanced color products for a wide range of datasets. To

21
generate a color composite from a multiresolution dataset, the
IHS method first takes a forward transformation from the low
spatial resolution images of three wavebands into the
intensity (I), hue (H), and saturation (S) components
(Appendix B). Then, a reverse transformation is carried out
to convert the I, H, and S components to the RGB values in
order to generate color composites through a RGB color display
device. The high spatial resolution image is merged in the
process by replacing the I component during the reverse
transformation (Haydn et al., 1982; Carper et al., 1990).
Note that a color composite by either the RGB system or the
IHS transform uses a maximum of only three spectral channels
and successful results often depend on a tedious trial-and-
error process.
Daily et al. (1979) were among the first to recognize the
importance of multiresolution processing of satellite data for
remote sensing applications. An airborne radar image with a
10-m spatial resolution was co-registered with Landsat 80-m
MSS images in an effort to improve geological interpretation
for a desert environment. The superior textural variations of
the radar image along with a 10-m spatial resolution were
utilized to complement the low contrast as well as the low
spatial resolution of Landsat MSS data which, in turn,
compensated for the drawbacks of radar shadows. Through a
direct RGB color display method, color composites generated
from the co-registered dataset were able to delineate subtle

22
geologic units through a visual image interpretation. Using
a similar approach, Wong and Orth (1980) also generated useful
color composites from Seasat synthetic aperture radar (SAR)
and Landsat MSS images which have 4 0-m and 80-m spatial
resolutions, respectively. These two early studies underlined
the benefits in the unified use of satellite data acquired by
completely different sensing systems (multispectral vs. radar)
for improving the interpretability of remote sensing images.
When the RGB color display system is used, satellite
images do not readily define or fit into the red, green, and
blue primary colors (Harris et al., 1990). In other words,
the images can not simply substitute the red, green, and blue
primaries in the RGB display system because of the spectral
incompatibility which could lead to serious color distortions
and poor-quality composites (Haydn et al., 1982; Harris et
al., 1990; and Carper et al., 1990). As a result, the IHS
color perception system has become the widely adopted approach
to resolve the color distortion problems encountered in the
RGB display of multispectral images. The entire process of an
IHS transform for multiresolution processing takes four steps
which include (i) co-registration of multiresolution images,
(ii) a forward transformation from three multispectral images
to the three IHS components, (iii) a reverse transformation
from the IHS components to RGB values, usually with the
replacement of the intensity component by the high spatial
resolution image, and (iv) display the results through a RGB

23
color display system. For the IHS system, the intensity or
brightness of a scene is a function of illumination (Boynton,
1979). Therefore, the intensity component should encompass a
broader range of wavelength (Haydn et al, 1982) and is
extensively associated with the spatial relations of scene
objects (Judd and Wyszechi, 1975). For this reason, the
intensity component is always assumed to be replaced by the
high spatial resolution panchromatic image in the reverse IHS
transformation.
Zobrist et al. (1979) were among the first to apply the
IHS transform to satellite data for image enhancement. In the
study, Landsat MSS 80-m and meteorological Seasat 25-m radar
images were used. The intensity component transformed from
the Landsat MSS data was simply replaced by the 25-m radar
image. Then, an IHS reverse transformation was taken to
create color composites.
Haydn et al. (1982) further demonstrated the utility of
the IHS transform for image enhancement. Landsat MSS, Landsat
return beam vidicon (RBV), and the Heat Capacity Mapping
Mission (HCMM) thermal infrared (TIR) images with respective
spatial resolutions of 80 m, 30 m, and 600 m were merged
between the RBV and MSS and between the MSS and HCMM images.
A direct replacement of the transformed intensity component by
the corresponding high spatial resolution image was employed
in the reverse transformation for each case. Also, ratioed
data between spectral wavebands was demonstrated for the use

24
of the IHS transform. For example, while the intensity
component was transformed from Landsat MSS wavebands four,
five, and seven (denoted respectively as MSS4, MSS5, and
MSS7), the H and S components were substituted, respectively,
by the MSS5/MSS4 and MSS5/MSS6 ratioed data. Substantial
enhancement in color composites was observed. The IHS color
transform was adopted in the entire study because the direct
RGB color model produced confusing and low quality image
presentations. Using a similar methodology, Welch and Ehlers
(1987) were able to produce enhanced color composites from
Landsat (30 m) thematic mapper (TM) and SPOT HRV 10-m
panchromatic images.
Very different approaches for using the IHS transform
have also been reported. A color composite was created from
a Seasat mono-band radar image (Daily, 1983) . Both the strong
and weak radar responses related to sloping targets and
vegetation features were extracted, respectively, by high-pass
and low-pass filters, and then used as the hue and saturation
components while the original radar image was used directly as
the intensity component for the IHS transform. The color
composite was able to reveal major structural features
invisible in the original black-and-white radar image. Harris
et al. (1990) took a step further when combining Landsat 30-m
TM and 10-m airborne radar images. In two instances, the high
spatial resolution image was used directly as the intensity
component, while the hue components were created from a

25
combination of Landsat TM wavebands two, four, and seven
(denoted as TM2, TM4, and TM7) or of Landsat TM wavebands two,
five, and seven (denoted as TM2, TM5, and TM7). However, the
saturation component was held at a constant value (150). In
another instance of the same study by Harris et al. (1990),
the radar image was used as the intensity component and the
geological units (numerical codes) in a digitized map as the
hue component, while the saturation component was held at a
constant (150). Based on a visual assessment, the study
concluded that the color composites were able to define
lithological and structural features that were absent from
existing geological maps. These two studies by Daily (1983)
and Harris et al. (1990) not only opened a new dimension in
the use of the IHS transform for remote sensing applications,
but also demonstrated the effectiveness and compatibility of
the IHS transform for a broad range of data characteristics
including satellite images and digital maps.
The use of the IHS transform can be extended to include
the imagery digitized from an aerial color infrared (ACIR)
photography (Grasso, 1993) . In the study, a digitized ACIR
high spatial resolution (10 m) image was merged with Landsat
MSS and Landsat TM data to enhance geological interpretation.
The intensity components transformed from either Landsat MSS
or Landsat TM images were directly replaced by the ACIR image
during the IHS reverse transformation. The color composites,
which had a 8x linear spatial resolution factor, were still

26
useful for geological mapping. Also in the study, a different
approach in utilizing the IHS transform was demonstrated in
which the digitized ACIR image was used as the intensity
component, the Landsat TM ratio data (TM5/TM7) as the
saturation component while the hue component was held at a
constant value (96). The results were very useful for
delineating the high and low clay content areas. Note that
the high and low TM5/TM7 ratios were essentially used to
regulate the level of color saturation (S component) so that
high clay content areas would show more vivid colors than its
counterparts. However, results also showed that the colors of
these composites could change very rapidly by just varying the
hue component with a moderate magnitude. Though the concept
of the latter example is somewhat different from the previous
one by Harris et al. (1990) who emphasized the color diversity
(H component) rather than the color purity (S component), good
guality color composites can still be produced by the IHS
transform. This indicates that the IHS color transform has
tremendous flexibilities in adapting to a wide variety of
geographic data.
In summary, when applying the RGB and IHS methods to
generate color composites, it has been demonstrated that image
interpretability can be significantly improved through a
unified use of multiresolution datasets. This is particularly
evident for the IHS transform which is capable of producing
quality color composites under a broad range of circumstances.

27
Also, several studies have illustrated that the IHS transform
seems to possess a virtually universal adaptability to
geographic data. The multiresolution merged results in the
form of color composites are indispensable for many remote
sensing applications which involve image interpretation.
However, to generate color composites is not the ultimate goal
of multiresolution processing of satellite imagery data. The
radiometric quality of merged images is far more important
than a color display and vital to the potential of post¬
merging applications such as land-use classification. In
addition, a severe disadvantage for color composites is that
tremendous efforts are needed to extract quantitative land-use
information from the color products while a maximum of only
three spectral wavebands can be handled at one time.
Radiometric Enhancement
In the radiometric enhancement approach, arithmetical
algorithms are used to digitally combine the multiresolution
image data in order to generate merged images which can
achieve the purpose of multiresolution processing. Direct
substitution of the high spatial resolution image for the RGB
color display system often created color composites with
blocky appearances because of the spatial resolution
differences. To overcome such a weakness, digital
manipulations of the image data have become necessary. In a
study by Cliche et al. (1985), simulated SPOT HRV panchromatic

28
and multispectral images from an airborne dataset, which had
11 spectral wavebands, were digitally merged, pixel by pixel,
using the following methods
I. MIj = A. * (PAN * HRVj)* + Bj [3-1]
II. MI,. = A. * (PAN * HRVj) + B,. [3-2]
III. MI, = A, * (PAN * HRV,)* + B, [3-3a]
MI2 = A2 * (PAN * HRV2)'a + B2 [ 3-3b]
MI3 = A3 * (0.25PAN + 0.75HRV3) + B3 [3-3c]
where MI,, is the merged multispectral images, i (in methods I
and II and subscripts 1-3 in method III) is waveband index,
PAN and HRV are, respectively, the simulated SPOT panchromatic
and multispectral images, and A,, and B,. are coefficients or
scaling factors to maintain the merged data within the 0-255
dynamic range.
From the color composites generated through the use of
the RGB color display system, the study concluded that, while
the improvement on spatial resolution was apparent for all
three methods, method (III) produced the best color composite.
The improvement by method (III) was attributed to the use of
different merging algorithms which helped preserve the SPOT
HRVj near infrared information. For method (II), the pixel
values were low and concentrated, resulting in dark and no¬
contrast merged images. Because of the high correlations in
the merged images between the near infrared and visible

29
wavebands, method (I) produced wash-out images. Even though
all these merging methods were based on arbitrary speculations
and the results were displayed using the RGB system, the
potential benefits of digitally merging image datasets were
indicated with improved spatial information.
In digitally merging multiresolution images, speculations
for a combining approach do not bring about consistent
results. In an effort to find a general approach that does
not depend on arbitrary elaborations, Price (1987) contended
that the high correlations between the panchromatic and both
the multispectral green and red wavebands within a SPOT
multiresolution dataset could be utilized to estimate the
corresponding high spatial resolution multispectral merged
images. In the study, the original SPOT 10-m panchromatic and
20-m multispectral images were artificially degraded, by
averaging, to 20-m panchromatic (P20) and 4 0-m multispectral
(M40) images, respectively. Then, the whole approach took two
steps. The 20-m multispectral merged images (MI) were first
estimated from the degraded panchromatic P20 data by a
regression eguation
MIi = Ai * P20 + Bi + D [3-4]
where MIi is the estimated multispectral image i based on the
degraded (20-m) panchromatic image, A1 and B. are regression
coefficients determined from the degraded panchromatic P20 and
the original 20-m spatial resolution multispectral image, and

30
D is a correction factor to balance the numerical sum of
estimated subpixels with the recorded value of a low
resolution pixel (M40) . If the sum of the estimated digital
counts of subpixels did not equal the recorded value of the
low resolution pixel in question, a correction was applied.
The estimated 20-m images from the degraded (40-m)
panchromatic waveband were able to retain 99% of the variances
of the original 20-m images of the green and red wavebands.
However, a potentially serious problem could have existed with
a high correlation between the two estimated images because
they both depended on the same identical panchromatic data.
In fact, the multispectral images were used only as
complementary information through a correction procedure.
A different approach was undertaken to estimate the SPOT
near-infrared (NIR) image which in general does not correlate
well with the panchromatic waveband. The (estimated) merged
20-m NIR image (MI3) was first obtained from a lookup table
created by both the degraded 2 0-m panchromatic (P20) and the
original 20-m NIR images. Then correction was applied similar
to those used for the green and red wavebands. Results
indicated that only 75% of the radiometric variance of the
original NIR image was retained during the merging process.
Though the broad spectral bandwidth of the panchromatic image
encompasses part or even the entire range of the multispectral

31
green and red wavebands, it is impossible that the portion of
image digital count for a merged high spatial resolution image
can be separated from a panchromatic pixel. The difficulty is
analogous to isolating from a jar of oil the part that came
from a particular peanut. In addition, the process of spatial
degradation (by averaging pixels) could smooth out or compress
the radiometric information in the original image data.
To explore the utility of digital manipulations for
datasets acquired by multiple sensors, Landsat MSS and Shuttle
imaging radar A-band (SIR-A) images were digitally merged in
a lithological mapping study (Chavez et al., 1983). However,
the high spatial resolution of the 40-m radar image was not
utilized to its advantage for enhancing the spatial resolution
of the Landsat 80-m MSS images. Instead, the spatial
resolution of the radar image was artificially degraded for
compatibility with that of the Landsat MSS data. From the
results of various arithmetical manipulations including
addition, subtraction, ratioing, and difference-ratioing of
the co-registered SIR-A and Landsat MSS image data, it was
concluded that the addition and ratioing methods were useful
for discriminating some geologic units while the applicability
of the subtraction method is limited only to negatively
correlated images. The results by Chavez et al. (1983) have
two important implications. First, digital manipulations of
image data can be extended to include those images acquired by
different sensing systems. Second,
the arithmetical

32
manipulations of image data can be applied to images with
different spatial resolutions as well as those which have the
same spatial resolution.
Digital merging multiresolution images has been used in
efforts to further enhance the results of an IHS transform.
In order to more effectively use the IHS transform, the
selection of a proper intensity or brightness component is
very critical to the guality of color display (Boynton, 1979).
A low intensity component could result in severe image
degradations (Judd and Wyszechi, 1975; Haydn et al., 1982).
In the case of a low intensity value, corrections are needed
for the hue and saturation components (Judd and Wyszechi,
1975) or for the intensity component (Boynton, 1979; Haydn et
al., 1982; Gillespie et al. , 1986). However, by applying such
correction procedures, the final image is very difficult to
interpret because the original colors can be altered
significantly (Zobrist et al., 1979).
The importance of finding the most effective method to
generate the intensity component for the IHS transform for
merging multiresolution datasets has been recognized by some
researchers, including Carper et al. (1990). Instead of
adopting the direct replacement of the panchromatic image for
the intensity component, Carper et al. (1990) conducted some
experiments on different merging methods in order to find the
best intensity component. In addition to many previous
studies that relied on imagery data acquired on different

33
dates or even in different years, simultaneously-acquired SPOT
10-m panchromatic and 20-m multispectral images were used.
This was done to eliminate the contribution of temporal
information which could introduce some difficulty to the
assessment of the benefits of an IHS transform. Carper et al.
(1990) proposed the following set of merging algorithms to
calculate the intensity components.
Ia = (PAN + RHV3)/2 [3-5]
Ib = (PAN * PAN * HRV3)1/3 [3-6]
Ic = (2 * PAN + HRV3)/3 [3-7]
Id = (PAN * HRV3)1/2 [3-8]
I0 = (HRV1 + HRV2 + HRV3)/3 [3-9]
where I, with alphabetical subscripts for method index, is the
calculated intensity component to replace the original
intensity component IQ transformed from the 20-m multispectral
images, PAN is the SPOT panchromatic image, and HRV is the
multispectral data with numerical subscripts for waveband
index. The study concluded that the weighted average method
(Ic) consistently produced results as good as or better than
the others. The effectiveness of this weighted average method
(Ic) was attributed to the greater histogram similarity
between the calculated (Ic) and the original (Io) intensity
components. However, some points in the results were left

34
undiscussed. For instance, while the histogram of Ic
correlated extremely well to that of the panchromatic image
except with a moderate shift to higher values, it did not have
any resemblance to that of the original HRV3 image. This
indicated that the coefficient (2/3) for the PAN image in
equation [3-7] significantly exaggerated the effect of the
panchromatic image in the Ic component, implying not only a
duplication of the panchromatic information, but also a
significant loss of radiometric information for the HRV3 image
in the merging process. In addition, the great similarity
between the histograms of intensity Ic and the panchromatic
image suggested that a direct replacement of the intensity
component (IQ) by the panchromatic image, as used in many
other studies, is workable in an IHS transform.
In response to a broad array of diverse approaches which
have been used to merge multiresolution datasets, several
methods to combine multiresolution images were evaluated by
Chavez et al. (1991) using statistical, visual, and graphical
comparisons. More specifically, those different combining
methods included the IHS transform, the PCA method, and the
high-pass (spatial) filtering (HPF). For the Landsat TM and
SPOT panchromatic datasets used in the study, a contrast¬
stretching procedure was applied to the SPOT panchromatic
image in an attempt to increase (arbitrarily scale up) the
radiometric variance. Then, in the IHS method, the intensity
component transformed from Landsat TM images was simply

35
replaced by the contrast-stretched panchromatic image during
the IHS reverse transformation. In the PCA method, the
stretched panchromatic image was assumed to be similar to the
first principal component transformed from the Landsat TM
images of all six wavebands (excluding the TIR waveband),
while in the HPF method, a high-pass filter was applied to the
contrast-stretched panchromatic image to extract the high
frequency spatial information which was merged to each of the
six Landsat TM images through a pixel-by-pixel addition
method.
Color composites generated by all three methods were
subjected to visual comparisons. Statistical correlation
analyses were conducted between the first principal component
of Landsat TM six-waveband data, the IHS intensity component
and the contrast-stretched panchromatic image. Spectral
signatures from five selected land-use types were graphically
compared between the original Landsat TM data and the merged
datasets by the IHS transform and HPF method. Chavez et al.
(1991) concluded that, though the IHS method produced the best
color composite among the three methods, it distorted the
spectral characteristics of the merged images the most. For
the HPF method, the merged images possessed the spectral
characteristics comparable to those of the original Landsat TM
data. The distortion of spectral information by the IHS
method was attributed to the fact that the customary
assumption of similarity between the IHS intensity component

36
and the panchromatic image is not always valid. When one
examines the implicit spectral requirements (in a decreasing
order of spectral bandwidth for the I, H, and S components) by
the IHS transform as discussed by Haydn et al. (1982), it is
not surprising to recognize that the distortions of spectral
integrity would be inevitable in the transformed I, H, and S
components. Note that the requirement for decreasing spectral
bandwidths for the I, H, and S components would generally
result in the numerical values of those components being in
the same order. In using the IHS transformed data for post¬
merging applications other than color composites, these
distortions of spectral information cause a serious concern
about the utility and effectiveness of a merged dataset for
multispectral analyses.
Other Enhancement Methods
There were some other cases in which multiresolution
merging was used for purposes other than image enhancement.
It is worthwhile to discuss these methods because of their
pertinence to the subject of merging multiresolution datasets.
The practical importance of digitally merging multiresolution
datasets for image data compression purpose was investigated
by Schowengerdt (1980). He contended that the data volume for
storage and transmission can be significantly reduced if a
high spatial resolution multispectral dataset can be
constructed by combining a high spatial resolution image with

37
a relatively low spatial resolution multispectral dataset.
With that argument in mind, the spatial resolution of the
Landsat MSS images of wavebands four (green), six (NIR), and
seven (NIR) with the original 80-m spatial resolution was
artificially degraded by a linear factor of three to a 240-m
spatial resolution dataset. The original 80-m resolution
image of waveband five (red) remained unchanged and was used
as the high spatial resolution image. Assuming that an image
consists of both spectral and spatial components, the
following merging eguations were proposed
MI. = MSSj + k(- * H5 [3-10]
and
k, = <*,- / a5 [3-11]
where MIi is the reconstructed image, i (and subscript 5) is
waveband index, H5 is the high freguency spatial information,
and a is the image-wide standard deviation. The high
freguency spatial component (H5) was obtained by a subtraction
between the low-pass and the high-pass filtered images of
waveband five. New images with a 80-m spatial resolution were
reconstructed through pixel-by-pixel manipulations using
equations [3-10] and [3-11]. Visual evaluation of the
reconstructed images indicated that a great deal of high
frequency information (edges) could be restored except for
vegetation-dominated areas where a reverse tonal appearance

38
was indicated. Waveband five was selected as the high spatial
resolution image because it had the greatest contrast. This
selection of waveband five would make the kj values by
equation [3-11] smaller than 1.0 because a5 is the largest.
Consequently, equation [3-10] implicitly emphasizes the
multispectral images, making it possible for the merged
datasets to maintain the spectral characteristics of the
original multispectral data.
The utility of an IHS transform for image data
compression was also studied by Haydn et al. (1982) using
Landsat MSS wavebands four (green) , five (red) , and seven
(NIR). The hue and saturation components transformed from the
three Landsat MSS images were each arbitrarily degraded. The
spatial resolution was reduced by linear factors of two, four,
and six which corresponded to data compression factors of
four, sixteen, and thirty-six, respectively. Color composites
were regenerated for each data compression factor using the
degraded H and S components along with the original I
component. Visual comparisons of the regenerated color
composites to that of the three original wavebands did not
indicate substantial quality deterioration except for the case
which had a data compression factor of thirty-six or a 6x
linear resolution factor.
A half-pixel shifting method to improve the effective
spatial resolution of remote sensing data was studied by Dye
and Wood (1989) . They argued that, for a given pixel in a

39
scene imaged twice over a time period, both its numerical
value and geographic location would not be identical because
of the potential offset (error) in sampling the pixel by the
sensor. Therefore, if one of the two images in a dataset is
artificially offset half a pixel before the two images are
combined together, the resultant merged image will increase
its spatial resolution by a linear factor of two. From the
viewpoint of data sampling technique, this method is very
interesting. However, in the remote sensing monitoring of
land-use activities, the concept may not be valid or even
logical when considering the time lapse in image acquisition
and the spectrally dynamic changes in natural environments.
In a study using artificial as well as satellite images,
Albertz and Zelianeos (1990) pointed out the following
requirements necessary for this half-pixel shifting method to
be successful: (1) the scene must be imaged several times—
preferably more than four; (2) there will be no significant
changes in the scene environments (spectrally static objects);
and (3) image geo-referencing or co-registration must be very
accurate in order to have the precise half-pixel offset.
With the advent of geographic information systems (GIS)
techniques, various types of geographical data including
existing map data and multi-date imagery data have been
integrated during an image processing scheme. However, the
main purpose of such image processing efforts is to detect
changes rather than to improve the spatial and radiometric

40
qualities of the final results. To improve agricultural land-
use classification, Lo et al. (1986) combined two Landsat MSS
scenes acquired in different growing seasons. The two scenes
were co-registered and some waveband ratioing was undertaken
before invoking land-use classification procedures. Using
this multitemporal approach, the land-use classification by an
unsupervised classification scheme was improved from 84% to
86%. However, it is arguable that the information accumulated
from the two scenes and the use of more spectral wavebands
would definitely be a factor contributing to the improvement
of classification results. A similar study for corn-soybean
field classifications was conducted by Badhwar et al. (1982)
using Landsat MSS data.
There are many other examples that involved the use of
satellite imagery data and thematic overlay techniques. For
instance, the study by Walsh et al. (1990) combined Landsat TM
images with digital elevation model (DEM) data to study the
hydrological processes in rugged terrain environments, and
that by Shih (1988) who combined Landsat MSS data with the
digitized version of the United States Geological Survey
(USGS) land use/land cover maps within a GIS environment for
land-use classification comparisons.
Summary: Assessment of Problems
Many studies have been made to develop image processing
techniques to combine multiresolution images for remote

41
sensing applications. Opportunities exist to improve the
interpretability of satellite image datasets for the
management and monitoring of natural resources and the
environment. In summary, these efforts have demonstrated the
following aspects.
1. The IHS transform is a powerful and effective method
for generating true color composites of good quality under a
broad range of data characteristics. The effectiveness of the
IHS transform has indicated a virtually universal adaptability
to any geographic datasets. As compared to the direct RGB
color display system, the IHS transform is superior because it
can overcome the incompatibility of spectral information
content of satellite multispectral images. This makes the IHS
transform more likely to produce well balanced color
composites that are more suitable for image interpretation.
However, the effectiveness of the IHS transform has misled
many to believe that it is a powerful image processing
technique that can actually sharpen the image data.
Unfortunately, it is not. The process is only for the display
of colors for human aesthetic pleasure. The merged images by
the IHS transform are not useful for multispectral analyses
because of the inferior radiometric quality and corrupted
spectral integrity.
2. Many combining methods have been developed that vary
significantly in the basic principle as well as in the
complexity of merging algorithms. These methods can be

42
categorized as: (1) linear combination of images, (2)
principal component analysis, (3) regression technigue which
is similar to linear combination, and (4) multiplication or
product (including square-root of product). Though arbitrary
and largely dependent on speculation, these methods provide
knowledge about merging multiresolution images. The studies
by Schowengerdt (1980), Cliche et al. (1985), Price (1987),
Carper et al. (1990), and Chavez et al. (1991) suggest that
combining multiresolution images by linear combination of
images would have a greater potential for multiresolution
processing. The multiplication and principal component
analysis methods are perceived as ineffective.
3. The lack of understanding of the principle of
multiresolution processing is ubiquitous, resulting in wide
speculation for merging algorithms. The fundamental problem
is that the effects of combining multiresolution images on the
radiometric, spatial, and spectral qualities of a merged
dataset were not well understood when a merging algorithm was
introduced. Frequently, efforts resulted in radiometrically
inferior and spectrally corrupted merged datasets. A good
merger should take full advantage of the spatial and spectral
benefits of the multiresolution images to create a merged
dataset.
4. The main attention of research efforts was given to
image color display rather than to the radiometric and spatial
enhancement and, the spectral integrity of merged datasets.

43
In remote sensing applications, achieving the best color
display is necessary and often very useful for many
applications, but it is not the ultimate nor the only goal of
combining multiresolution datasets. Instead, the merged
images should be sharpened radiometrically while the spectral
integrity is preserved to enhance the utility of merged
datasets.
5. Visual assessment, which is necessary for evaluating
the quality of color composites, is adopted in most cases as
the only technigue for determining the gualities of merged
datasets. However, the subjectivity and great variability of
the technigue make many of the efforts inconclusive.
6. One other problem not discussed in the literature is
the accuracy of image co-registration. In order to merge
multiresolution images correctly, an accurate co-registration
is required, particularly for high spatial resolution datasets
as well as for images which are not taken simultaneously. For
instance, if two images are not co-registered accurately, a
pixel of one land-use type will be merged with a different
land-use type and the merged pixel belongs to neither of the
original land-use elements. This makes the merged dataset
very difficult or even impossible to interpret and analyze.
Therefore, both the precision of intermediate references (e.g.
maps) and the methods of entering (or digitizing) reference
coordinates must also be addressed (ASPRS, 1990; Bolstad et
al, 1990; and Tan and Shih 1991b). For the current map

44
standard, which is 0.5 mm (1/47 inch) times the reciprocal of
map scale (APSRS, 1990; Bolstad et al. , 1991), the
geographical error for the USGS 7.5 minute series maps
(1:24,000) is about 13 m and the digitizing process could
introduce additional errors of significant magnitude (Tan and
Shih, 1991b). Therefore, it will be necessary to utilize
high-precision techniques such as the global positioning
system (GPS) to bypass the intermediate reference (map) as
well as manual digitizing operations in order to achieve a
high accuracy registration or to use datasets acquired by a
satellite sensor equipped with onboard co-registration
capability.
7. To merge multi-date images creates another problem in
evaluating the techniques of multiresolution processing.
Because of the dynamic change of scene environments, it is
difficult to analyze the merged data due to the intermingling
of image spectral information with the temporal effects. This
is particularly important for agricultural lands, as well as
natural environments, because they can change rapidly within
a short period of time. When multi-date scenes are combined,
the merged dataset will naturally contain more information
than any of the original ones. Therefore, it will be
difficult to objectively assess the possible improvement as
well as to evaluate the processing techniques. While the
temporal effects could be used for improving land-use

45
classifications (Badhwar et al. 1982; Lo et al., 1986), it
does create difficulties in evaluating the technique.
Fortunately, future satellite sensor systems can provide
simultaneous multiresolution sensing capabilities as well as
onboard image co-registration techniques (Spotlight, 1991;
EOSAT, 1992a; 1992b). Therefore, the problems with multidate
merging and image co-registration will no longer be a concern
to the user community of future satellite remote sensing data.

CHAPTER 4
PRINCIPLE OF MERGING IMAGES
This chapter is focused on the principle of merging
satellite remote sensing images. After the fundamental
principle is presented and discussed, three merging methods
are examined. However, the demonstrations and discussions of
the effectiveness of the merging methods are provided in
chapter 5 using actual satellite images.
Principle of Merging Images
Merging multiresolution images requires the use of
arithmetical manipulations to digitally combine the image
data. An effective merging approach will take full advantage
of the spectral, spatial, and radiometric merits of the images
to be combined to generate merged image data with enhanced
qualities. To develop successful merging methods for remote
sensing applications of multiresolution image datasets, an
adequate understanding of the fundamental principle for
digital manipulations of image data is essential. Therefore,
to assist such efforts in exploring this principle, it is
advantageous to conceptualize remote sensing image data so
that the factors affecting the spatial, radiometric, and
spectral qualities of merged images can be identified,
evaluated, and assessed.
46

47
Assumptions
A digital image can be considered as a set of repetitive
digital numbers that are constrained to a spatial arrangement
which is determined by the relations of objects present in the
scene. In virtually all image processing efforts, this
spatial arrangement is not important because it serves only to
reveal where an object or activity is identified rather than
to indicate how and why the decision is made in the process.
Therefore, a digital image is similar to a random variable.
The numerical values of a remote sensing image, which are
often called digital counts (DC), have a distribution depicted
by the image histogram.
The radiometric variance of an image is an important
indicator of the image radiometric quality, and like a random
variable, it can be assessed by the variance of image data.
For a given scene environment, a larger radiometric variance
indicates that scene activities are recorded in more detail.
Throughout this dissertation, the term "radiometric variance"
will exclusively refer to those image data that have not been
subjected to procedures such as spatial filtering and
contrast-stretching discussed in chapter 3.
The assumption that an image is similar to a random
variable will allow the statistical variation analyses of
random variable manipulations to be applicable to image data.
From previous research efforts by Cliche et al. (1985); Price
(1987); and Carper et al. (1990), the method of linear

48
combination of images was considered to have the greatest
potential for multiresolution processing. Therefore,
attention will be given to these combining methods, which will
include summation and differencing of image data. To better
understand the benefits as well as to assess the drawbacks
from manipulating remote sensing images, the arithmetical
functions of summation and differencing of random variables
for statistical variation analyses will be briefly reviewed.
Such a review is necessary in order to understand the existing
merging technigues as well as to develop new merging methods
so that remote sensing images can be manipulated more
productively. For the purpose of clarity, continuing
discussions will be limited to the circumstance of merging two
random variables or images, though three or more variables can
be manipulated at one time. Also, images with the same
spatial resolution will be examined first before proceeding to
the discussion of multiresolution merging.
Arithmetic of Random Variables
It is necessary to examine the arithmetical functions of
random variables to effectively investigate the various forms
of digital manipulations of image data and to assess the
results of such manipulations. According to Mood et al.
(1974) and Mendenhall et al. (1986), combining (both summing
up and differencing) two random variables X1 and X2 with means
and ¿i2 and variances a,2 and a22, respectively, will create

49
a merged variable (Y) which is expressed in a general form of
Y = a X, ± 8 X2. [4-1]
This new variable Y will have a mean value (ny)
Hy = a ± 6 M2 [4-2]
and a variance {a2)
a 2 = a2 a 2 + R2 a2 ± 2 a R cov(X,, X2) [4-3]
where a (>0) and 6 (>0) are numerical constants and cov(X1. X2)
is the covariance between X1 and X2. In digitally combining
images, Y is the merged image, X1 and X2 represent images one
and two to be combined, and the corresponding constants a and
R are often called weighting factors or merging coefficients.
The covariance cov (X1. X2) term in equation [4-3] can be
written as (Mendenhall et al., 1986)
cov(X1. X2) = r a1 a2 [4-4]
where a1 and a2 are the standard deviations and r is the
correlation coefficient for X1 and X2. The value of r can be
negative or positive depending on the actual relationship
between variables X1 and X2. Substituting the covariance of
equation [4-4] into equation [4-3] will yield
a2 = a2 a2 + R2 a2 ± 2 a R r a1 a2 [4-5]
which is the equation for calculating/estimating the variance
of a merged variable based on the merging coefficients, the

50
variances (or standard deviations), and the correlation
coefficient for X1 and X2.
For a merged image, the quality factor of greatest
concern is the contrast (or gray shades), and the contrast of
an image is directly related to the variance of image
radiometric data. For instance, an image will have no
contrast if its radiometric variance is zero. Therefore,
attention in the continuing discussion will be given to the
variance (ay2) of merged variable Y. From equation [4-5], the
factors that collectively affect the radiometric variance or
contrast of a merged image are the weighting coefficients a
and 6, the correlation coefficient (r), and the variances (a^
and a22) of the two images to be combined.
To assist the efforts in examining the effects of these
various factors on the variance (uy2) of merged variable Y, it
would be advantageous to reduce the number of the involved
elements in equation [4-5]. One method to achieve that is to
normalize the variances of X1 and X2 to unity (1.0) using the
following equation
o* + ct22 = 1 [4-6]
where a,2 and a22 are the normalized variances for X1 and X2,
respectively. If the condition of+o**0 is satisfied, o* and
a22 are defined, respectively, as
a
2
[4-7]

51
and
2
2
[4-8]
For easy comparisons, let a2 also be normalized to (of+o22) by
the following equation
CT
2
2
Y
a,
[4-9]
where a 2 is the normalized variance of Y. Note that the
—y
normalized values are a relative measure for the variances of
X,,, X2, and Y. Dividing equation [4-5] by (o2+o2) and making
rearrangements through the use of equations [4-6], [4-7], [4-
8], and [4-9] will yield
2 = a2 a 2 + B2 (1 -o2)
± 2 a B r a1 J (±-g_y¿) .
[4-10a]
Because the variances of X, and X2 are normalized to unity,
equation [4-10a] can also be written as
a 2 = a2 (l-a22) + B2 a2
± 2 a 6 r a2 J (l-o_2¿)
[4-10b]
where
= J{°f)
[4-lla]
°2 = J{°2¿) ♦
[4-llb]

52
Three benefits result from normalizing the variances of X1 and
X2. These benefits are (1) reduction of the number of the
involved factors in equation [4-5]; (2) relief from getting
involved with actual image data for conceptual discussions;
and (3) easy comparison of the variance of the merged variable
with those of the original variables. It becomes clear that
equation [4-10a] (or [4-10b]) is the basic relation that
reflects the effects of the various factors (a, B, r, and a)
on the radiometric variance or contrast (ay2) of a merged
image.
A comparison of the relations between equations [4-1] and
both [4-10a] and [4-10b] reveals that the only distinction
between summation and differencing of two variables is the ±
sign for the last terms in equations [4-10a] and [4-10b].
Therefore, in the context of evaluating the variance of the
merged variable, differencing two negatively correlated
variables (r<0) is technically identical to summing up two
positively correlated ones (r>0). Because merged image data
must be positive, differencing two images may require the
addition of a positive constant (C) to the end of equation [4-
1] such that
Y = aX1-6X2 + C [4-12]
in order to avoid negative image data. However, from the
relations of equation [4-10], the constant C in equation [4-
12], which is usually determined by a pre-merging scanning of

53
the given image data, will not affect the radiometric variance
of the differenced image.
In practical applications where two images are given, the
radiometric variances (a.,2 and o22) and the correlation
coefficient (r) are known. The only factors that need to be
determined for equation [4-1] are the merging coefficients a
and 6. From the relations of eguation [4-10] and based on the
given factors a2, a2, and r, the selection of appropriate
merging coefficients a and 6 for eguation [4-1] is the key
factor that affects the radiometric variance of merged image
data. To assess the impacts of these merging coefficients (a
and B) on the radiometric variance of merged images, three
approaches for digitally combining images will be discussed.
In addition, of the two images (X1 and X2) to be combined, X,
will be denoted as the primary image and X2 as the secondary
image in order to distinguish their relative importance in the
merging process. When actual image data are used, the primary
image (X.,) will be assumed to contain primary information
while the secondary image (X2) is used as the supplementary
data for improving the primary image.
Confining Method
The first method to be discussed is the confining method
which is defined mathematically as
Yc = a X1 + B X2
[4-13]

54
where Yc is the merged image by the confining method, X1 and
X2 are, respectively, the primary and secondary images, and a
and 6 are weighting coefficients. An unique aspect in
combining images is to keep the merged image data within the
0-255 dynamic range (or 8-bit data depth). One approach to
accomplish that requirement is to choose the weighting
coefficients a and R in equation [4-13] such that
a + R = 1 [4-14a]
which can be written alternatively in the following forms of
a = 1 - R [4-14b]
and
R = 1 - a. [4-14c]
Because the merged image data is automatically confined to the
0-255 dynamic range, this merging method is called the
confining approach.
Let o2 and o22 denote the normalized radiometric
variances for the primary (X^ and secondary (X2) images,
respectively. Because the general purpose to combine images
is to use the complementary secondary image data for improving
the primary image, the weighting coefficient R for the
secondary image will be of greater interest. For this reason,
the relation of equation [4-14b] is preferred and by
substituting it into equation [4-13], the following relation

55
is obtained as
Yc = (1-6) X, + 6 X2. [4-15]
In comparing equation [4-15] with the relations between
equations [4-1] and [4-10a] (or [4-10b]), the normalized
variance (o^2) of merged image Yc can be estimated by the
following equation
oj = (1-6)2 g2 + 62(l-a12)
+ 2r(1-6)6 a1 J(l-gf) . [4-16a]
Since the variances of X1 and X2 are normalized to unity,
equation [4-16a] can also be written as
gj = (1-6)2 (1 -g2) + 62 g2
+ 2r(1-6)6 g2 7(1 -g2¿) . [4-16b]
The following relations for the normalization of variances are
also needed in order to use equation [4-16a] or [4-16b]
g* + g22 = 1 [4-17]
a, = J(o{) [4-i8]
0-2 = 7W). [4-19]
From equations [4-16a] and [4-16b], the radiometric variance
(gc2) of an image merged by the confining method is influenced
only by the secondary image coefficient 6. The value 6 will

56
have a direct impact on <7c2 — a measure of the radiometric
quality of a merged image by the confining method. In
combining multiresolution images, selecting an appropriate R
value is particularly important because it not only affects
the radiometric variance, but also indirectly impacts the
spectral information of the entire merged dataset. For
instance, if a large R is used to merge a panchromatic image
to each image in a multi-waveband dataset, all the images in
the resultant merged dataset will be very similar to each
other.
Assuming that the variances of the primary (X1) and
secondary (X2) images are equal or close to each other, the
relation of gc2 as a function of weighting factor R is depicted
in Figure 4-1 for the confining method. Although the graphs
in Figure 4-1 can tilt somewhat from one side to the other in
response to the variance difference between the primary and
secondary images, four important observations can be made for
the confining method.
First, the radiometric variance of a merged image by the
confining method is likely to be smaller than that of either
the primary and secondary image data. A smaller radiometric
variance implies that the merged image by the confining method
will have low contrast and inferior radiometric data.
Second, the state (positive or negative) as well as the
strength of correlation between the primary and secondary
image images also has a strong effect on the radiometric

Normalized variance of merged data
Note: a + & = 1.
Figure 4-1. Relation of radiometric variance to merging coefficient (6) and
correlation coefficient (r) for the confining method.
ui
vj

58
variance of a merged image. If the primary image is
negatively correlated to the secondary image, the loss of
radiometric information in the merged image (Yc) will be even
more detrimental as shown in graphs (4) and (5) of Figure 4-1.
The negative correlation (r<0) creates a negating effect on
the variances of the primary image when the secondary image
data is digitally merged. Consequently, the resultant merged
image will have low or even no contrast depending on the
strength of the correlation as well as the use of R values
(Figure 4-1). As mentioned earlier, adding up negatively
correlated images is similar to subtracting positively
correlated ones or vice versa. If two negatively correlated
images are differenced instead of summed together as done by
Chavez et al. (1983), the loss of radiometric information in
the merged image can be alleviated. In this circumstance, the
results of graphs (4) and (5) will be changed to those of
graphs (2) and (1) in Figure 4-1, respectively.
Third, a ftc exists at which the radiometric variance of
merged data will be at minimum. That is, the merged image
with 6c value will have least contrast. Therefore, the use of
such a R value must be avoided when using the confining
method. The value of Rc can be obtained by first taking the
derivative of equation [4-16a] (or [4-16b]) with respect to R
<*(£c2) ? ?
-2 (1-6) + 2fi(l-a12)
dfi
+ 2r a1 y(l-a,¿) (l-2fi)
[4-20]

59
and then setting the first derivative to equal to zero such as
0 = -2 (1-6C) a,2 + 2fic(l-a12)
+ 2ra1 7(1 -of) (l-26c). [4-21]
Through the use of equations [4-7], [4-8], [4-9], and [4-17],
the Bc value can be estimated by the following equation
a * - ra1 a2
Bc = — ; [4-22]
+ a2z - 2 r a, a2
where a* and a22 are the variances (a1 and o2 are the standard
deviations) of the primary and secondary images, respectively.
Note that the range of valid values for 6 is 0 to 1. If 6c is
outside the 0-1 range, the minimum radiometric variance of a
merged image will not exist within that range. Obtaining the
Bc value before merging the images will give a first
assessment on the variance of a merged image. For instance,
if Bc < 0, the radiometric variance of merged data is an
increasing function with 6, implying that an improvement for
image contrast is possible. If Bc « 1.0, the variance of
merged data will decreases as B increases. As a result, the
contrast of the merged image will deteriorate. By
substituting Bc into equation [4-15a] (or [4-15b]) and by
using the relations of equations [4-7], [4-8], [4-9], and [4-
17], the minimum variance (am2) for an image merged by the
confining method can be estimated as

<712 °2Z (1 - r2)
60
2 r a.
[4-23]
Caution should be exercised in using equation [4-23] to
estimate the minimum radiometric variance of a merged image.
If 6C is not within the 0-1 range, the estimated minimum
radiometric variance is a false value that cannot exist for a
merged image.
Fourth, as & continues to increase beyond the 6c value,
the variance of merged image Yc is approaching that of the
secondary image data. This will make the merged image more
and more similar or even identical to the secondary image as
a result of large fi values, which has been indicated by Carper
et al. (1990). In the case of merging a high resolution
panchromatic image to a set of multispectral images, all the
resultant merged images will be highly correlated among each
other because of the excessively redundant panchromatic data.
Consequently, the spectral integrity (or signatures) of the
merged dataset will be corrupted and the effectiveness of the
merged multispectral data for differentiating land-use
elements will be reduced.
The variance difference between the primary and secondary
images can also have an effect on the radiometric variance of
a merged image as shown in Figure 4-2. For instance, if the
primary image has a larger variance relative to that of the
secondary image, the merged image will have less contrast
regardless of the state of correlation. This is illustrated

Normalized variance of merged data
Note: r = correlation coefficient.
Figure 4-2. Effect of variance difference on the radiometric quality of merged
images for the confining method.

62
by graphs (1) and (3) of Figure 4-2. If the primary image has
a smaller variance, the radiometric information in the merged
image will either increase or decrease depending on the
magnitude of the variance difference as well as the state of
correlation between the two images as shown by graphs (2) and
(4) in Figure 4-2. Note that only when the primary image has
a very small variance relative to that of the secondary image
and the correlation between the two images to be combined is
high and positive, will an image merged by the confining
method have an enhanced contrast. This indicates that (1) the
confining method is not an effective merging approach for
digitally combining images and (2) the determination of a B
value for the confining method can not be arbitrary nor
independent of the factors such as the variance difference and
the correlation between the two combining images.
The way by which the merging coefficients are determined
(a+fi=l) for the confining method has one important implication
of the compromising effect on the quality of the primary and
secondary images. The use of a larger R value to emphasize
the effect of the secondary image is made at the concession of
the primary image variance because of a smaller a value. As
shown in Figure 4-2, this concession of the primary image data
can be beneficial or detrimental. If the secondary image has
a relatively larger variance, this compromising effect is
beneficial to improve the primary image as shown by graphs (2)
and (4) in Figure 4-2. On the other hand, the effect will be

63
deleterious to the radiometric quality of a merged image as
illustrated by graphs (1) and (3) in Figure 4-2.
In summary for the confining approach (a+B=l), the
following observations are as follows. (1) The resultant
merged image will likely have a smaller radiometric variance
or lower contrast unless the primary image has a very small
variance relative to that of the secondary image and the
correlation between the two combining images is high and
positive. (2) There may exist a Rc value at which the
radiometric variance or contrast of the merged image will be
minimum, therefore, the selection of 13 values close or equal
to J3c should be avoided. (3.) Two images with a negative
correlation should be differenced rather than summed in order
to minimize the loss of radiometric information. (4) In
general, the contrast (or variance) and brightness of an image
merged by the confining method can be considered as a
compromise for each of these two quality factors between the
primary and secondary images.
Preserving Method
For most satellite imagery, the spread of image digital
data does not extend throughout the entire 0-255 dynamic
range. For a typical agricultural scene, the data spread is
about 40% of the 0-255 range in Landsat imagery (Price, 1984)
while a much smaller range is often found for SPOT images.
Therefore, the utility of the 8-bit data depth for these

64
images has not been fully utilized. In merging satellite
images, such a deficiency can be turned into an advantage by
maintaining the primary image unchanged (a=l) while the
secondary image data is merged. Hence, this method is called
the preserving approach.
By using the preserving approach to combine images, the
following merging algorithm is used
Yp = X, + 6 X2 [4-24]
where B is weighting coefficient, Yp is the merged image, and
X1 and X2 have been defined previously. Let a 2 and g_2 denote
the normalized variances for the primary and secondary images,
respectively. A comparison of the relations between equations
[4-1] and [4-10a] (or [4-10b]) indicates that the normalized
variance (£p2) of an image merged by the preserving method can
be estimated by
Op2 = a,2 + 62(l-a12) + 2r6 a, . [4-25a]
Since the variances of the primary (X^ and secondary (X2)
images are normalized to unity, equation [4-25a] can also be
written as
Op2 = (l-a22) + B2 o2 + 2rB a2 J(l-az¿) . [4-25b]
In both equations [4-25a] and [4-25b], 6 is the weighting
coefficient and r is the correlation coefficient for the
primary (X.,) and secondary (X2) images. Note that the variance

65
of merged image Yp is normalized to o2+o2. Also, the
relations of equations [4-17], [4-18], and [4-19] are needed
when using equation [4-25a] (or [4-25b]) for assessing the
radiometric variance of a merged image. As mentioned earlier,
the only distinction between summation and differencing of two
images is the ± sign for the last term of equation [4-25a] (or
[4-25b]). Thus, differencing two negatively correlated images
(r<0) is identical to summing up two positively correlated
ones (r>0).
Figure 4-3 shows the normalized variance ar 2 of merged
images by the preserving method as a function of both the
merging coefficient (6) and the correlation coefficient (r).
When the primary and secondary images are not negatively
correlated, the variance of an image merged by the preserving
method is an increasing function with merging coefficient R as
shown in graphs (1) through (3) of Figure 4-3. This implies
that the radiometric variance (contrast) of an image merged by
the preserving method will surely improve, provided that the
correlation coefficient is r>0. Unlike the confining method,
which tends to make a compromise between the secondary and
secondary images, the preserving method does not subdue
(because a=l) the radiometric variance of the primary image
during the merging process. Consequently, the merged data are
always enhanced even when the images to be combined are not
correlated (r=0) as shown in graph (3) of Figure 4-3.
The results from combining two negatively correlated
images are also shown by graphs (4) and (5) of Figure 4-3.

Normalized variance of merged data
Note: a=l, and fi>0.
Figure 4-3. Relation of radiometric variance to merging coefficient (6) and
correlation coefficient (r) for the preserving method.

67
Apparently, any improvement on the radiometric variance of
merged image Yp is unlikely, particularly when the correlation
coefficient r«-l. However, such negatively correlated images
can be differenced. This will reverse the results to those of
summing up two positively correlated images as depicted by
graphs (1) and (2) of Figure 4-3. This differencing approach
will alleviate or even avoid the loss of image contrast in the
merged data.
The radiometric variance difference between the primary
and secondary images also has an effect on the radiometric
variance of a merged image (Figure 4-4). However, the effect
does not cause a negative impact on the radiometric variance
of merged data. The image contrast will always improve, and
the extent of improvement is inversely related to the
magnitude of the variance of the primary image. When the
radiometric variance of the primary image is relatively small,
the improvement on the merged image is more notable as
illustrated by graphs (1) and (3) of Figure 4-4. If the
radiometric variance of the primary image is relatively large,
the radiometric improvement might not be so apparent,
particularly when the correlation between the two combining
images is near zero (r«0) as shown by graph (4) of Figure 4-4.
It needs to be pointed out that large values of 6 can not
used for the preserving approach. Otherwise, a scaling factor
must be introduced to equation [4-24] in order to keep the
merged image data within the 0-255 range. In this case, the

Normalized variance of merged data
Note: r = correlation coefficient.
Figure 4-4. Effect of variance difference on the radiometric quality of merged
images for the preserving method.

69
use of an additional scaling factor will make the preserving
method less effective or even similar to the confining method.
In summary, several observations are made for the
preserving approach: (1) if the correlation coefficient (r)
between the primary and secondary images is non-negative
(r>0), the image contrast in the merged data will surely be
enhanced by the preserving method; (2) as compared to that of
the confining method (a+B=l), the effect of the variance
difference between the two combining images will not create a
negative impact on the radiometric variance of a merged image
by the preserving method, provided that the correlation is
non-negative (r > 0) ; (3.) the preserving method, which does
not subdue (a=l) the primary image in the digital merging
process, will make it less likely that the spectral signatures
of the original multispectral dataset will be altered or
corrupted in a merged dataset; (4) two images with a strong
negative correlation (r»-l) should be differenced instead of
summed together in order to avoid a potential loss of
radiometric information in the merged image; and (5) the
preserving method has both a much smaller sensitivity to the
strength of correlation and a larger range of R values to use
because a minimum variance does not exist provided that r>0.
Differencing Method
From previous discussions on both the confining and the
preserving methods, it is known that, in order to enhance the

70
radiometric variance of merged image data from negatively
correlated wavebands (r<0), the differencing method must be
used. To ensure that the merged data will be positive, a
constant must be added to the merged data. Therefore, the
following relation will be used as the merging equation for
two negatively correlated images
Yd = X1 — R X2 + C [4-26]
where R (>0) is a weighting coefficient, C (>0) is a constant
to avoid negative merged data, Yd is the merged (differenced)
image, and X1 and X2 have been defined previously.
Let a/ and o22 denote the normalized variances for the
primary and secondary images, respectively. By comparing
equation [4-26] with the relationship between equations [4-1]
and [4-10a] (or [4-10b]), the normalized radiometric variance
(a/) of a merged image by equation [4-26] can be estimated by
gj = (1 -a22) + B2a22 - 2rfl g2 J(l-g/) . [4-27a]
Since the variances of primary and secondary images are
normalized to unity, equation [4-27a] can also be written as
aj- = g* + B2(l-a12) - 2rB a, 7(1-0;/) . [4-27b]
In both equations [4-27a] and [4-27b], r is the correlation
coefficient for the primary and secondary images and R is a
weighting coefficient. Note that the variance of the merged
image is normalized to the sum of the variances (o/to/) of

71
the primary and secondary images. Again, the relations of
normalization equations [4-17], [4-18], and [4-19] are needed
in order to use equation [4-27a] (or [4-27b]) for estimating
the radiometric variance of a pre-differenced image.
Because the last term in equation [4-27a] (or [4-27b]) is
negative and the correlation coefficient (r) is also negative,
the relation of equation [4-27a] (or [4-27b]) is identical to
that of equation [4-25a] (or [4-25b]) of the preserving method
discussed previously. Therefore, additional information for
the effects of 6 values, correlation coefficient, and variance
difference on the radiometric variance of merged data can be
found in the previous section for the preserving method with
reference to both Figures 4-3 and 4-4.
In order for an image merged by the differencing approach
to have an improved radiometric variance, it is essential that
the last two terms in equation [4-27a] (or [4-27b]) be > 0.
That is
B2 o2 - 2r6 o, ct2 > 0. [4-28]
Hence, if both 6*0 and a2*0, a critical 6d value for the
differencing method can be obtained as
ñd *
2 r a1
—2
[4-29]
According to the relations of equations [4-17] through [4-19],
equation [4-29] can be rewritten as (a2*0)

72
Rd > 2 r ay/a2 [4-30]
where a1 and o2 are the standard deviations for the primary
(X1) and secondary (X2) images, respectively. If a 6 value is
greater than Bd, the variance of a merged image by the
differencing method will increase. Otherwise, the merged
(differenced) image will have a decreased radiometric
variance.
It must be pointed out that the relative magnitudes of
the combining image data can have a serious impact on the
tonal appearance of the merged image. Assuming that the
primary image (X^ has relatively higher values (brighter)
than the secondary image (X2) , a subtraction by R X2 in
equation [4-26] will be less likely to create negative values
in the merged data. Therefore, a small constant is needed for
equation [4-26]. This will maintain the tonal gradations of
the primary image, and as a result the bright areas in the
primary image remain bright while the dark areas remain dark
in the merged data. When the secondary image has relatively
larger values, the component of R X2 in equation 4-26] will not
be small in comparison to the primary image (X^ data. This
will likely create negative values of large magnitude in the
merged data, requiring the use of a large constant in equation
[4-26] to offset these negative values. Consequently, the
areas with low values (e.g. water bodies) will have relatively
large image values in the merged data because of the use of a
large constant in equation [4-26]. This could make these dark

73
areas appear bright in the merged image (Yd) , suggesting that
the tonal gradations of the original primary image have been
altered. Thus, it must be cautioned that the differencing
method may invert the merged image.
Summary: Principle of Merging Images
The principle of merging images has been discussed under
the assumption that an image is similar to a random variable
with regard to digital manipulations for statistical variation
analyses. Three fundamental approaches, which include the
confining, the preserving, and the differencing methods, have
been put forth for digitally merging image data.
Understanding these methods for digitally merging images
is essential for manipulating remote sensing data. Such an
understanding will render useful guidelines for evaluating the
existing methods as well as for developing new effective
approaches in future image processing efforts for remote
sensing applications.
When two images are digitally combined, the radiometric
improvements on the merged image will depend on three factors
which include (1) the selection of a merging method or merging
algorithm; (2) the correlation (r) between the two combining
images; and (3) the variance difference (a1 and o2) between the
primary and secondary images. The confining approach should
be avoided because of its ineffectiveness for radiometric
enhancement. Unfortunately, this merging approach is the most

74
widely used method (Cliche et al., 1985; Carper et al., 1990).
The preserving method is recommended for merging positively
correlated images while the differencing approach is for those
with a strong negative correlation. In addition, the image
with a brighter appearance should be chosen as the primary
image (X,) for the differencing method in order to avoid a
potential of altering the tonal appearance in the merged
(differenced) image.
A summary for the effectiveness of the three merging
approaches is provided in Table 4-1 for an easy comparison.
Actual satellite images will be utilized in chapter 5 to
demonstrate the results discussed throughout this chapter.

75
Table 4-1. Summary of the characteristics of different
merging
approaches.
Radiometric
improvement
on merged image
When
Confining
Preserving
Differencing
i : r>0 and
ct1 » a2
No
Yes
No
a, « o2
No
Yes
No
o1 « o2
Yes(if r«l)
Yes
No
ii: r<0 and
a1 » a2
No
No
Yes
a1 « a2
No
No
Yes
a1 « a2
No
No
Yes
Note: r = correlation coefficient.
a1 = standard deviation of primary image.
a2 = standard deviation of secondary image.

CHAPTER 5
DEMONSTRATION OF MERGING METHODS
The main objective in this chapter was to verify and
demonstrate the results of the three merging methods discussed
in chapter 4. To begin the process, the radiometric variance
and mean brightness of merged images by the three methods were
examined using the results from an actual satellite dataset.
The visual appearance in both image contrast and brightness
for the merged images were also evaluated.
Satellite Image Data
A satellite scene by the advanced very high resolution
radiometer (AVHRR) on a National Oceanographic and Atmospheric
Administration (NOAA) series satellite was acquired for this
demonstration. The satellite scene had five images recorded
at the 14:05h U.S. eastern standard time on December 14, 1989
by the AVHRR sensor onboard the NOAA-11 satellite. The NOAA
satellite scene consisted of two reflective (red and near-
infrared or NIR) and three thermal infrared (TIR) spectral
wavebands with wavelength characteristics shown in Table 5-1
(Kidwell, 1991). The scene had a local area coverage (LAC) of
the entire south-eastern region of the United States and all
the images of the five spectral wavebands have the same
spatial resolution of about 1,000 m (Kidwell, 1991).
76

77
Table 5-1. Wavelength characteristics of NOAA-11 AVHRR LAC
images.
Waveband#
Wavelength
range
(Mm)
Spatial
resolution
Ia
0.58 -
0.68
(red)
1000 m
2a
0.725 -
1.10
(NIRb)
1000 m
3
3.55 -
3.93
(TIRC)
1000 m
4
10.30 -
11.30
(TIRC)
1000 m
5
11.50 -
12.50
(TIRC)
1000 m
Source: Kidwell, 1991.
a — used in this study.
b — near infrared.
c — thermal infrared.

78
The original NOAA-11 LAC scene contained image data in a
10-bit data-depth format where every three pixels were packed
to a 32-bit word (Kidwell, 1991). A program, which runs on a
PC computer environment, was developed (Appendix C) to unpack
as well as to rescale (linearly) these 10-bit data to a 8-bit
data format for compatibility with PC-based image processing
systems as well as display device. For this research, the LAC
scene was clipped to the region of the Florida peninsula
(Figure 5-1) and only the red and NIR images of the clipped
scene were used. The images of the TIR wavebands were
excluded to avoid confusions from merging thermal data. In
the discussions that follow, a NOAA-11 LAC image is simply
referred to the clipped data unless otherwise stated. The
main usage of this clipped LAC scene was for the verifications
of the three different merging methods discussed in chapter 4.
For ease of explanation, the red waveband was arbitrarily
named as LAC1 while the NIR waveband was denoted as LAC2. The
mean, standard deviation, normalized variance, maximum, and
minimum values of the LAC1 (red waveband) and LAC2 (NIR
waveband) images are presented in Table 5-2. The two selected
LAC images were positively correlated with a correlation
coefficient (r) of 0.577.
Because of the noted difference in the radiometric
variances between the two LAC images (Table 5-2), the use of
LAC1 and LAC 2 for the primary and secondary images was
alternated for each of the three merging methods. In case I,

79
Figure 5-1. Location of clipped NOAA-11 AVHRR LAC images.

80
Tables 5-2. Standard deviation (a), normalized variance (a2),
mean (/x) , maximum and minimum values of NOAA-11
AVHRR LAC images.
Waveband
a
g}
max
min
LAC1
20.54
5.108
0.2286
138
14
(0.58-0.68 fm)
LAC 2
26.35
9.383
0.7714
125
11
(0.725-1.10 Mm)

81
LAC2 was used the primary image and LAC1 as the secondary
image, and in case II, LAC1 and LAC2 were used, respectively,
as the primary and secondary images. The purpose of this
alternative use for the LAC1 and LAC2 images was to assess the
effect of variance difference between the combining images on
the radiometric variance of merged data. In the differencing
method, the constants (C) used in equation [4-26] are provided
in Table 5-3 for both case I and case II. These constant
values, which were determined by a scanning of the original
image data, were used to avoid negative merged image data in
the differenced LAC images for the corresponding R values.
Variance of Merged LAC Images
The normalized radiometric variances of merged LAC images
by the three methods are presented in Figures 5-2 (case I) and
5-3 (case II). In addition, the mean values (brightness) of
these merged LAC images are presented in Figures 5-4 and 5-5
for case I and case II, respectively. The points in these
four figures are the results computed from the actual merged
image data, while the lines represent the estimates obtained
through the equations in chapter 4. While the estimates of
radiometric variance were obtained through equations [4-15],
[4-25], and [4-27] along with the normalized variances (Table
5-2) and a correlation coefficient (r) of 0.577, the mean
digital count (Figures 5-4 and 5-5) were estimated using
equations [4-13], [4-24], and [4-26] for each corresponding

82
Table 5-3. Offset constant (C) used in the differencing
method for merging LAC images.
& value
Case
0.1 0.2 0.3 0.4 0.5 0.6
0.7
0.8
0.9
1.0
I
3 7
11
15
20
24
II
3
5
8
10
13

Normalized variance of image data
Merging coefficient (B) for secondary image
Note:
i. Primary image is LAC2; secondary image is LAC1.
ii. Methods: (C)—confining; (D)—differencing; and
(P)—preserving.
Figure 5-2.
Comparison between actual and estimated radiometric variance
for merged LAC images (case I).
CD
w

Normalized variance of image data
Merging coefficient (B) for secondary image
Note: i. Primary image is LAC1; secondary image is LAC2.
ii. Methods: (C)—confining; (D)—differencing; and
(P)—preserving.
Figure 5-3. Comparison between actual and estimated radiometric variance
for merged LAC images (case II).

Merging coefficient (ñ) for secondary image
Note:
i. Primary image is LAC2; secondary image is LAC1.
ii. Methods: (C)—confining; (D)—differencing; and
(P)—preserving.
Figure 5-4. Comparison between actual and estimated mean digital count
for merged LAC images (case I).
00
U1

Merging coefficient (fi) for secondary image
Note: i. Primary image is LAC1; secondary image is LAC2.
ii. Methods: (C)—confining; (D)—differencing; and
(P)—preserving.
Figure 5-5.
Comparison between actual and estimated mean digital count
for merged LAC images (case II).
00
(Ti

87
merging method. The letters P, C, and D in Figures 5-2
through 5-5 denote the preserving method, the confining
method, and the differencing method, respectively. From the
results shown in Figures 5-2 through 5-5 for all the three
methods and B values used, four observations are in order.
First, the principle of statistical variation analyses
for combining random variables can be applied in assessing the
radiometric quality (variance and brightness) of a pre-merged
image. This provides the basis for understanding the various
forms of digital manipulations of satellite image data and for
assessing the effectiveness of an image processing effort in
remote sensing applications. In practical applications when
two images are given, the values of correlation, radiometric
variance, and mean digital (brightness) for the images to be
merged are known. Therefore, the overall quality in both
radiometric variance (contrast) and brightness of a merged
image can be evaluated based on the merging method and
coefficient (B). This pre-merging evaluation will lead to
more efficient approaches because unproductive efforts can be
eliminated.
Second, an image contains many subvariables representing
the various land-use types distributed throughout the entire
scene. Note that the subvariables do not usually possess the
same correlation, radiometric variances, and mean data values
in the images of a multispectral dataset. When a merging
algorithm is used to digitally combine the entire images, the

88
changes in both radiometric variance and brightness might not
be the same among the land-use elements. While some land-use
elements will benefit with an improvement in radiometric
information, others could have a guality detraction. Even for
those land-use elements with an enhancement, the extent of
improvement in both contrast and brightness will not be
identical. Therefore, digitally merging satellite images is
not simply a methmatical procedure. It is a transformation of
radiometric information from the combining images into the
merged data. Unfortunately, such a radiometric transformation
was overlooked in previous efforts in image data merging.
Third, the non-uniform changes in radiometric quality
across an entire scene can be beneficial or detrimental to an
image processing effort. Therefore, an adeguate understanding
of the principle of digitally manipulating images is critical
to selecting effective merging methods for image enhancement.
Because of the importance of such a radiometric transformation
in merging images, an increasing amount of knowledge for the
spectral data characteristics of satellite images acguired by
various sensing systems will further enhance the utility of
remote sensing data.
Fourth, though the results observed here are based on the
linear combination (summation and subtraction) operations of
image data, the fundamental principle can be extended to
assessing the effectiveness of more elaborate merging
algorithms such as waveband ratioing method. A pre-merging

89
assessment will allow the feasibility of a particular image
processing effort to be effectively evaluated before vigorous
attempts are made to actually combine the image data. Because
the primary objective of this study is for multiresolution
merging, only a brief discussion of the ratioing method will
be presented later in this chapter to examine the technicality
of image data ratioing.
As illustrated in graphs (P) of Figures 5-2 and 5-3, the
preserving method was able to improve the radiometric variance
of all merged images in both case I and case II. In addition,
the merged images for each & value also had higher values than
the corresponding primary image as shown in graphs (P) of
Figures 5-4 and 5-5. The improvement in radiometric variance
and mean brightness indicates that those merged images would
be brighter and have more contrast than their primary data.
The radiometric enhancement will render a greater
differentiation of a satellite scene for land-use
classification applications using the merged data. When the
variance of the secondary image was larger than that of the
primary image (case II) , the relative improvement to a merged
image was more substantial. This signifies an importance of
improving the radiometric guality of the high spatial
resolution (panchromatic) image in a multiresolution dataset.
The primary cause for increasing the radiometric variance and
brightness in the merged data is the appendive effect created
by the preserving approach.

90
For the confining approach, the radiometric quality of a
merged image would depend on the relative radiometric variance
and brightness of the primary image due to the compromising
effect. For example, in case I when the primary image (LAC2)
had higher values and a larger variance than the secondary
image (LAC1), the resultant merged images each had a smaller
radiometric variance and lower values as shown in graphs (C)
of Figures 5-2 and 5-4. However, when the radiometric
variance and the data value of the primary image were smaller
than those of the secondary image data (case II), the merged
images were improved with slightly larger radiometric
variances and higher image values as indicated by graphs (C)
of Figures 5-3 and 5-5, respectively. The main impact of the
confining approach is its compromising effect which tends to
equalize both the contrast and brightness of the primary image
with those of the secondary data.
To find out whether the confining method will improve or
degrade the radiometric variance of a merged image, one
approach is to calculate the Bc value using equation [4-22].
By definition, the 6c value is the merging coefficient at
which a merged image by the confining method will have the
least radiometric variance (chapter 4) . If Rc < 0, the
radiometric variance of a merged image is on the ascending
side of a parabolic function for the whole (0-1) range of 6
values. When Bc«si.o, it will be certain that the merged image
will have a smaller radiometric variance (less contrast).

91
Using equation [4-22] with the values in Table 5-2 and a
correlation coefficient of r=0.577, the 6c values for case I
and case II were estimated at 1.04 and -0.03, respectively.
Hence, the confining approach would degrade a merged image in
case I (Bc=1.04), yet improve it in case II (Bc=-0.03).
The radiometric variances and mean values of merged LAC
image data by the differencing approach are shown in graphs
(D) of Figures 5-2 through 5-5. Similarly to the confining
approach, an enhancement or a detraction on the radiometric
variance of a merged image by the differencing method can be
assessed by a comparison between the 6 used and the critical
6d values from equation [4-30]. Using the values in Table 5-2
and a correlation coefficient r=0.577, the 6d value was 2.12
and 0.63 for case I and case II, respectively. As shown in
graph (D) of Figure 5-3 (case I), a merged image always had a
smaller radiometric variance than the primary image unless the
merging coefficient (6) would take a value greater than 2.12,
which would be very unlikely for the differencing method. In
case II, however, the radiometric variance of merged images
became slightly larger than that of the primary image (LAC2)
when B took values greater than 0.63 as shown in graph (D) of
Figure 5-2, though it was decreasing initially due to the
positive correlation between the two LAC images.
Comparison of Merged LAC Images
From the above discussions on the radiometric quality
(variance and means) of merged images, this section attempts

92
to further demonstrate those results using image displays.
The image contrast, brightness, and tonal gradations of the
merged LAC images were evaluated through visual comparisons
between the primary image and the merged data. To reduce the
subjectivity of evaluation and to avoid color preference,
black-and-white displays were used. In addition, all the
images to be evaluated have not been subjected to any digital
enhancement procedures (e.g. spatial filtering and contrast
stretching) which would alter the brightness and contrast.
The displays are strictly the results of unaltered merged
image data (gray shade data). Note that the evaluations were
based on the overall guality of image appearance and only
three merged images at 6 values of 0.2, 0.4, and 0.6 were
selected for each case.
The original LAC1 and LAC2 images are presented in Figure
5-6. Obviously, these two LAC images have very different
qualities in terms of contrast and brightness. Because of its
larger radiometric variance and greater mean data value (Table
5-2) , the LAC2 (NIR) image has more contrast as well as a
brighter appearance than the LAC1 (red).
For case I of the preserving method, the three selected
merged images at B=0.2, 0.4, and 0.6 are presented in Figure
5-7. One unambiguous indication in Figure 5-7 is that the
increase in radiometric quality in a merged image corresponds
to the increase in visual quality (contrast and brightness).
The increasing radiometric variances for 6=0.2, 0.4, and 0.6

LAC2 (NIR)
LAC1 (red)
Figure 5-6. Original clipped NOAA-11 LAC images of red and NIR wavebands.
VO
U>

(6=0.2)
(6=0.4)
(6=0.6)
Note: Primary image = LAC2 (NIR).
Secondary image = LAC1 (red).
Figure 5-7. Merged LAC images by the preserving method (case I)

95
resulted in more and more contrast in the merged image data.
The merged images also became increasingly brighter as R
increases. For case II, the corresponding merged images are
presented in Figure 5-8 where similar improvements on image
contrast and brightness were observed, even when the primary
image had a much smaller radiometric variance (Table 5-2). In
comparison with case I, the improvements in case II were more
substantial because its secondary image (LAC2) had a larger
variance. Though the enhancement was less apparent at small
R values (0.2), all merged images by the preserving method
have evidenced improvements in image contrast and brightness
when compared to the corresponding primary image. The reason
for such a consistent enhancement is that, given the positive
correlation (r=0.577), the preserving method was able to
preserve the primary image when the secondary image data were
merged, and as a result, the merged images each had increased
radiometric quality.
For both case I and case II of the confining method, the
merged images are presented in Figures 5-9 and 5-10. Recall
that the confining approach is in essence a compromising
method that attempts to equalize the contrast and brightness
between the primary and secondary images. Because of this
compromising effect, a merged image will have less contrast if
the primary image has a larger variance. In addition, a
brighter primary image will result in a relatively darker
merged image. For example, when the primary image in case I

(6=0.2)
(6=0.4)
(6=0.6)
Note: Primary image = LAC1 (red).
Secondary image = LAC2 (NIR).
Figure 5-8. Merged IAC images by the preserving method (case II).
vo
CT>

(6=0.2)
(6=0.4)
(6=0.6)
Note: Primary image = LAC2 (NIR).
Secondary image = LAC1 (red).
Figure 5-9. Merged LAC images by the confining method (case I).

(6=0.2)
(6=0.4)
(6=0.6)
Note: Primary image = LAC1 (red).
Secondary image = LAC2 (NIR).
Figure 5-10. Merged LAC images by the cinfining method (case II).
vo
oo

99
(LAC2) had a larger variance and greater brightness as
compared to the secondary image data (LAC1), the merged images
became increasingly darker and had less contrast (Figure 5-9)
as the merging coefficient 6 increased from 0.2 to 0.6.
However, a slightly improvement in both image contrast and
brightness is observed for the merged images in case II when
the primary image was relatively darker and had a smaller
variance (Figure 5-10). One method to evaluate the
effectiveness of the confining method is to examine the
critical 6c value, which was calculated as 1.04 and -0.03 for
case I and case II, respectively. Apparently, the confining
approach decreased the contrast of a merged LAC image in case
I (Figure 5-9), but slightly improved it in case II as shown
in Figure 5-10.
For the differencing method, the merged LAC images with
B values of 0.2, 0.4, and 0.6 for both case I and case II are
presented in Figures 5-11 and 5-12. Note that two completely
different sets of merged images were generated when the
differencing approach was utilized. Recall from Table 5-2 and
Figure 5-6 that the LAC1 image not only had a much smaller
variance, but also was much darker (a smaller mean value) in
comparison to the LAC2 image. In addition, the two LAC images
were also positively correlated (r=0.577).
Because of the positive correlation between the two LAC
images, the differencing method should not be utilized to
merge the LAC images in practical applications. However, the

(6=0.2)
(6=0.4)
(6=0.6)
Note: Primary image = LAC2 (NIR).
Secondary image = LAC1 (red).
Figure 5-11. Merged LAC images by the differencing method (case I).
o
o

(6=0.2)
(6=0.4)
(6=0.6)
Note: Primary image = LAC1 (red).
Secondary image = LAC2 (NIR).
Figure 5-12. Merged LAC images by the differencing method (case II).
101

102
purpose for the discussions here is to understand the merging
process as it affects the radiometric quality of merged
images. In case I when the LAC2 image was differenced by the
LAC1 data, the results (Figure 5-11) showed that the merged
image was not seriously impacted because the original LAC2
image had both a brighter appearance and a relative larger
variance. At a result, all the merged (differenced) images
(Figure 5-11) maintained a great deal of tonal similarity to
the primary image (LAC2). However, the results were
completely different when the primary image (LAC1) had both a
smaller mean and variance (case II). At fi=0.2, the merged
image appearance began to fade out and significant image
contrast was lost as a result of a smaller radiometric
variance in the merged data (Figure 5-12). When a slightly
larger R value (0.4) was used, a reverse tonal began to
surface in the merged image. For instance, the dark
appearance of water bodies (e.g. Lake Okeechobee and sea
water) became slightly bright or similar to those of land
areas. At R value of 0.6, the tonal gradations of the entire
image were completely reversed, making dark water bodies show
up as bright and bright areas (lands) appear as dark in the
merged image. While the positive correlation was responsible
for the decrease in merged image contrast, the reversed tonal
appearance was caused by the greater brightness of the
secondary image data (LAC2), which required the use of a
larger positive constant (Table 5-3) in the differencing
equation.

103
A mosaic of all the nine selected merged images for the
preserving, confining, and differencing methods is presented
in Figure 5-13 as a summary for the three selected R values of
0.2, 0.4, and 0.6. These images are shown in a way that the
changes of radiometric guality in the horizontal direction
indicate the effects of increasing R values for a given
method, while those in the vertical direction are related to
the effects of the different merging methods. Similarly, the
nine merged images for case II of the preserving, confining,
and differencing methods at R values of 0.2, 0.4, and 0.6 are
shown in Figure 5-14 with the same image arrangements as in
Figure 5-13.
From all the merged images in the two mosaics of Figures
5-13 and 5-14, three conclusions are as follows. First, the
preserving approach is a very effective method to generate
merged images with the greatest improvement in radiometric
quality. The radiometrically enhanced images will be more
useful for greater differentiations of land-use elements in
multispectral analyses using the merged image data. Second,
the confining approach is subordinate to the preserving method
in every aspect. The images merged by the confining approach
can have either an enhancement or a detraction in radiometric
quality, depending on the data characteristics of both the
primary and the secondary images. Even when a radiometric
enhancement is revealed, the extent of improvement will not be
comparable to that by the preserving approach. Third, the

104
(6=0.2)
(6=0.4)
(6=0.6)
Figure 5-13. Summary (mosaic) of merged LAC images for three
methods in case I.

Differencing Confining Preserving
105
(6=0.2) (6=0.4) (6=0.6)
Figure 5-14. Summary (mosaic) of merged LAC images for three
methods in case II.

106
differencing approach must be used with great caution because
of the possibility of inverting the merged image, particularly
when the primary image has relatively values. The efficacy of
the differencing method is limited to the circumstances when
the images to be combined have a strong negative correlation.
Ratioinq of Satellite Images
The ratioing of satellite images (often called waveband
ratioing) is a widely adopted approach for image enhancement
(Lillesand and Kiefer, 1979; Lo et al., 1986; Huete and
Jackson, 1988; Kidwell 1991). Because successful applications
of the ratioing technigue often depend on a trail-and-error
process with many failed efforts, this section attempts to
examine and understand the mechanics of waveband ratioing by
using the principle of random variable manipulations.
According to Mood et al. (1974), the ratio Yr of variables X1
and X2 (X2*0) can be expressed as
Yr = [5-1]
x2
for which the mean value () of ratioed variable Yr can be
estimated by
coy (X1, X2)
Mr ; + — *22 [5-2]
M2 M22 /x23
while the variance (ar2) can be approximated as

107
Mi O y 022 2 COV(X1fX2)
° 2 = ( )2 [ + : ] [5-3]
M2 Mi M2 Mt M2
where /i1 (*0) and /x2 (#0) are the means, and Oy and oz are the
variances for variables X1 and X2. In ratioing images, X1 and
X2 are the numerator and denominator images, respectively.
The covariance cqv(X.,,X2) term in both equations [5-2] and [5-
3] can be rewritten in the following form (Mood et al., 1974)
cov(X1,X2) = r a1 a2 [5-4]
where ct1 and a2 are the standard deviations and r is the
correlation coefficient for X1 and X2. Substituting equation
[5-4] into equations [5-2] and [5-3] yields
Mi r oy oz Hy
Mr I + — [5-5]
M2 m2 m2
for the mean (/xr) and
)2
2 r Oy o2
Hy M2
[5-6]
for the variance (ap2) of ratioed variable Yp. Note that the
a//* (n*0) terms in equations [5-5] and [5-6] are in fact the
coefficient of variation CV-a/u (where /x*0) . Thus, using the
CV values, both equations [5-5] and [5-6] can be rewritten as
(1 + CV22 - r CV, CV2)
M2
[5-7]

108
and
o
2
)2 (CV,2 + cv22 - 2 r CV1 CV2)
[5-8]
r
for the mean value and the variance of Yr, respectively. To
assist in the discussions for ratioing remote sensing image
data, let Fy be defined by the following
CV,2 + CV22 - 2 r CV, CV2
F,
[5-9]
V
as the variability factor, and Rb as the brightness ratio
Rb = m,/m2
[5-10]
where m2*0. Note that is a measure of the relative
magnitudes of brightness between the numerator (X,) and the
denominator (X2) images, while Fv provides a collective
assessment of the data variability and relation in X1 and X2.
As indicated by equations [5-1] and [5-9], Fy is a constant
when two images are given (a,, a2, and r are known). Its value
does not change when the numerator and denominator images are
alternated. However, Rb can be significantly different if the
numerator image is replaced by the denominator data.
Substituting both Rb and Fy into equations [5-7] and [5-8]
yields the followings
Mr = Rb (1 + CV22 - r CV, CV2)
[5-11]
[5-12]

109
for the mean and variance of ratioed image Yp. A clear
indication from equations [5-11] and [5-12] is that both the
variance and mean brightness of ratioed image Yr is a function
of Rjj. In fact, the radiometric variance (ur2) is related to
the square of 1^. This signifies that the selection of an
numerator image is critical for the effectiveness of waveband
ratioing.
One unique aspect in ratioing satellite images is to
scale the fractional ratioed results (Equation [5-1]) to a
range (typically 0-255) of integers. This makes it arbitrary
to compare both the radiometric variance (ar2) and mean
brightness (nr) to those of the two original images (X1 and
X2) . Since the scaling factor is applied to the entire scene,
the concepts of and Fy can be extended to the various land-
use elements when assessing the feasibility of waveband
ratioing.
In remote sensing applications when two images are to be
ratioed, the value of Fv for each and every land-use element
is determined regardless of the selection of the numerator (or
denominator) image. However, the values among the land-use
elements in a satellite scene can be significantly different
depending on which of the two ratioing images is used as the
numerator (X.,) for equation [5-1]. Note that a relative large
Rjj value provides an advantage in attaining a potential
radiometric enhancement, while a small value is the indication
of difficulty in achieving any enhancement. For instance, in

110
order to enhance vegetation lands, the ratioing image with
greater values for vegetation areas should be chosen as the
numerator image to achieve a relative large value for
increased radiometric variance and brightness. If the
ratioing image that possesses the larger mean value (brighter)
for vegetative areas is used as the denominator image, the
value will be small, making it difficult or even impossible
for vegetation land use to stand out in the resultant ratioed
image. This points out that one important consideration in a
ratioing approach is to select the numerator image with which
the land-use elements of interest can have relative large Ry
values.
The variability factor (Fy) is a function of both the
correlation coefficient (r) and the coefficients of variation.
If the correlation between images X1 and X2 approaches positive
unity (r=1.0), Fy can be expressed as
Fv = (CV, - CV2)2 [5-13]
which is the sguare of the difference between the coefficients
of variation CV1 and CV2. Consequently, the values of Fy will
be very small for those land-use elements with a strong
positive correlation between X, and X2. If r « -1.0, the value
of Fy can be written as
Fy = (CV, + CV2)2 [5-14]
which is the square of the sum of coefficients of variation

Ill
CV1 and CV2. When r = 0, equation [5-9] becomes
Fv = CV,2 + CV22 [5-15]
which is essentially the sum of the squares of the coefficient
of variation. From equations [5-13], [5-14], and [5-15], the
indication is that the correlation between the two ratioing
images plays a very important role in the feasibility of
waveband ratioing. If a strong positive correlation exists
for a land-use element such as urban structures, the Fy value
will be very small, implying a great difficulty in obtaining
an enhancement by the ratioing method. However, a strong
negative correlation (or even r=0) will allow a land-use
element in question to have a relative large Fy value,
creating the potential for that land-use element to have an
increased radiometric variance in the resultant ratioed image.
In addition, a negative or zero correlation (r<0) would also
make the land-use type in question appear brighter because the
(-r CV1 CV2) component in equation [5-11] is non-negative. It
becomes clear that it will not be feasible to use the ratioing
method in an effort to enhance the radiometric variances of
those land-use types that have a strong positive correlation
between the two ratioing images. To state alternatively, a
radiometric enhancement by the ratioing method can be achieved
only for those land-use types whose correlations are weak or
negative in the images to be ratioed.
It is worthwhile of pointing out that both the numerator
and denominator images (X1 and X2) can be manipulated by other

112
merging approaches (preserving, differencing, etc.) in a way
that the land-use elements of interest can attain relatively
large and Fv values. One example of this manipulation is
the normalized difference vegetation index (Huete and Jackson,
1988; Kidwell, 1991) for vegetation enhancement. Therefore,
given the understanding of the ratioing principle, an
increasing amount of knowledge about image spectral
characteristics for various land-use types in different
wavelength ranges as well as sensing systems will extend the
ratioing approach to greater applications of remote sensing
data. Since the primary objective of this study is in
multiresolution processing, further efforts will not be
undertaken for demonstrating the ratioing approach.
In summary of the waveband ratioing approach, two
comments are in order. First, the selection of the numerator
image is critical for the effectiveness of a ratioing method
for remote sensing applications. If the radiometric qualities
of a land-use element are to be enhanced, the ratioing image
which has relatively large digital (brighter) values for the
land-use element in question should be used as the numerator
image to attain a relative large Rb value. Otherwise, it
should be used as the denominator image to detract the
radiometric qualities of the land-use element. Second, the
feasibility of ratioing images for image enhancement depends
on the correlation between the ratioing images. Successful
applications of the ratioing method can be achieved only for

113
the land-use elements which have a negative or very weak
correlation (r<0) between the ratioing images.
Multiresolution Enhancement
Since merging actual multiresolution satellite datasets
was carried out in chapters 6 and 7, this section focuses on
the factors that are unigue to merging multiresolution images.
This arrangement was intended to address those unique aspects
before efforts were made to demonstrate the process of
multiresolution merging using a SPOT satellite dataset.
The spatial resolution difference in a multiresolution
dataset requires the resampling of all image data to the same
pixel size before being merged. One concern is the validity
of applying the merging principle discussed previously to the
resampled image data. In the statistical context, if the
elements of a random variable are each duplicated for a
certain number of times, the new variable will still attain
the characteristics of a random variable. Similarly, if the
pixels of a low spatial resolution image are each resampled
for a certain number of times, the resampled image will still
have the characteristics of a random variable. Hence, the
principle of merging images can be applied to multiresolution
image datasets after a resampling procedure.
Multiresolution merging can be considered as an unique
process in that there is no alternative in the selection of
the primary and secondary images from the multiresolution

114
data. Each of the multispectral images is used as the primary
image while the high spatial resolution panchromatic image
serves as the secondary image data. Stated another way, the
high spatial resolution image is merged to each of the low
spatial resolution multispectral images. Consequently, the
panchromatic information becomes a mutual component in the
resultant merged dataset. This will cause a concern with
elevating the between-waveband correlations in the merged
dataset. An increase in between-waveband correlation will
reduce the effectiveness of a merged dataset in multispectral
analyses to differentiate the land-use elements. Therefore,
the use of a larger value for the merging coefficient (6) must
be cautioned.
The difference in spatial resolution between the
panchromatic and multispectral images must also be considered.
For instance, if the spatial resolutions have a linear ratio
of two, one low spatial resolution pixel in the multispectral
images will encompass four sub-pixels in the panchromatic
image (Figure 1-1). If the four sub-pixels represent four
different land-use objects, the minimum difference in the
digital numbers of the four sub-pixels is 0, 1, 2, and 3 (or
any four contiguous integers within the 0-255 range). In
order for all of these four land-use objects to show up in a
merged image, a merging coefficient (6) of 1.0 is required
because of the truncation of integer image data. If a B value
of 0.5 is utilized, up to two of the four land-use objects

115
corresponding to a low resolution pixel will not show up in a
merged image. In other words, up to 50% of the panchromatic
spatial information could be lost in the merging process for
a B value of 0.5. If a 6 value is chosen to be greater than
0.5, more spatial details can be expected. However, this can
cause an increase in the between-waveband correlations as well
as the possibility of introducing a scaling factor to scale
back the radiometric variances in the merged dataset. On the
other hand, a smaller 6 value will lead to greater lost of
spatial information. Practically, it is difficult to expect
all panchromatic spatial information to be merged with the
multispectral image in a multiresolution processing,
particularly when the radiometric resolution of the
panchromatic image is low. If the spatial resolution ratio is
greater than two (one low resolution pixel has more than four
sub-pixels), more spatial objects could lose their presence in
a merged dataset. This constraint in spatial resolution
difference, which was also observed by Price (1984),
underlines a limitation to multiresolution processing as well
as a challenge to the development of future multiresolution
sensing systems.
A haze-correction procedure is recommended for the entire
multiresolution dataset. This correction eliminates the
radiance (a small fraction of digital count) caused by the
atmosphere rather than by scene reflectance. It is usually
performed by subtracting the value of each pixel with the

116
image-wide minimum digital number (typically of water areas).
This procedure can be applied to the panchromatic image in a
straight forward fashion. For the multispectral images, the
procedure must be done somewhat differently in order to
preserve the integrity of spectral information in the original
multispectral dataset. The correction factor has to be based
on the minimum of the minimum values for all the multispectral
images. For instance, if the minimum values of three
multispectral images are found to be 23, 35, and 48, the value
of 23 must be used for all three multispectral images.
Spatial filtering and contrast-stretching procedures are not
recommended for pre-merging processing because they alter the
original image data.
Summary: Appraisal of Merging Methods
Results from merging an actual NOAA LAC satellite dataset
conveys evidence that the principle of statistical variation
analyses for random variable manipulations can be applied in
the assessment of the radiometric quality (variance and
brightness) of pre-merged images. This understanding provides
the basis for both evaluating the effectiveness of existing
image processing efforts in digitally combining images and for
developing new merging approaches for more effective use of
satellite image datasets for remote sensing applications.
The preserving method is the preferred approach for
merging satellite images because of its effectiveness in

117
enhancing the radiometric quality of merged image data. The
confining approach is deemed as ineffective, while the
differencing method for radiometric improvement is limited to
circumstances when the images to be merged possess a strong
negative correlation. In a multiresolution dataset, the
panchromatic image usually has a broad waveband that extends
to parts or even the entire ranges of the multispectral
wavebands (e.g. SPOT datasets). This spectral waveband
characteristic, for which non-negative correlations are
usually observed between the panchromatic and multispectral
images, will make the use of the preserving approach
particularly suitable for merging multiresolution datasets.
For this same reason, however, the use of the differencing
approach will be detrimental to the radiometric quality of
multiresolution merged images.
When a merging method is chosen such as the preserving
approach, the value of merging coefficient (fi) will play a
vital role in affecting the overall quality (radiometric,
spatial, and spectral) of a multiresolution merged dataset.
In the context of both radiometric and spatial enhancement, a
large value of merging coefficient B will be beneficial.
However, the use of an excessively large B value could corrupt
the integrity of multispectral information because of the
possibility of increasing the between-waveband correlations
among the merged images. The corrupted spectral signatures
will diminish the usefulness of the merged dataset for remote

118
sensing applications involving multispectral analyses. On the
other hand, a too small R value will not be effective in
improving the spatial detail nor enhancing the radiometric
guality in the merged data. Therefore, when the radiometric,
spatial, and spectral considerations for a merged dataset are
put in perspective, the effective R values can be considered
as in the range of 0.5 to less than 1.0. In addition,
consideration must also be given to the ratio of linear
resolutions between the panchromatic and multispectral images.
If the linear spatial resolution ratio is greater than three,
any notable improvements in spatial detail will be difficult
in the merged dataset.
The feasibility of waveband ratioing for satellite image
enhancement depends on the correlation between the two images
to be ratioed. Successful applications can be achieved only
for the land-use elements which have a negative or very weak
correlation (r<0) between the two ratioing images. In
addition, selecting the numerator image is critical for the
effectiveness of a ratioing method. If the radiometric
qualities of a land-use element are to be enhanced, the image
which has relatively large digital (brighter) values for the
land-use element in question should be used as the numerator
image to attain a relative large brightness ratio (1^) .
Otherwise, it should be used as the denominator image to
detract the radiometric qualities of both variance and
brightness.

CHAPTER 6
MATERIALS AND METHODOLOGY FOR
MULTIRESOLUTION LAND-USE CLASSIFICATION
This chapter presents the materials and methodologies
which include sources of image dataset, and processing
equipment and systems, procedures for multiresolution data
merging, photogrammetric estimation of citrus canopy cover,
and land-use classification analyses. In addition, a special
attention was given to citrus land use, mainly because of the
economic importance of citrus crops to the State of Florida
(Jackson and Sauls, 1983, 1984; Shih et al., 1985).
Data Source and Equipment
The data sources and equipment utilized include a SPOT
HRV multiresolution dataset, an ACIR photography, two computer
image processing systems, an Arc/Info GIS (ESRI, 1993), and a
photogrammetric stereo plotter for making photogrammetric
measurements for the estimation of citrus canopy size.
SPOT Image Data and Study Area
A multiresolution scene acquired by the SPOT HRV sensor
was used. The SPOT scene (#622-295) has an area coverage of
the entire St. Lucie county, Florida (Figure 6-1), and
consists of four images that were acquired simultaneously on
October 3, 1987. Of the four SPOT images, one is panchromatic
119

120
while the others are multispectral with corresponding spatial
resolutions of 10 m and 20 m, respectively. The spectral
wavelength (¿un) ranges are 0.51-0.73 for the panchromatic
image, and 0.50-0.59 (green), 0.61-0.68 (red), and 0.79-0.89
(NIR) for the multispectral images. The panchromatic waveband
encompasses almost the entire bandwidth of the green and red
wavebands plus a small portion of the NIR wavelength range
(0.7-1.0 /¿m) . For ease of explanation, the SPOT green, red,
NIR, and panchromatic wavebands are denoted as wavebands HRV1,
HRV2, HRVj, and PAN, respectively.
The SPOT scene was clipped to an area of approximately 95
km2 (1000 by 950 pixels of 10-m size) located in the north-
central portion of St. Lucie county (Figure 6-1). This
clipped scene was designated as the study area in which
pasture lands and citrus groves were found to be predominant
together with some isolated urban lands and residential areas.
In the discussions that follow, a SPOT image is simply
referred to the clipped area (Figure 6-1). The main usage of
this SPOT scene was to study the effects of multiresolution
processing on land-use classification and the feasibility of
differentiating citrus groves based on canopy size difference.
Since the differentiation of citrus canopy cover is the most
difficult on satellite images acquired in summer seasons, the
use of this SPOT satellite scene will render additional
insights into the feasibility of classifying citrus groves
using remote sensing datasets.

10 km
Figure 6-1. Location of clipped SPOT multiresolution dataset and study area.
121

122
ACIR Photography
ACIR photography covering the same area as the clipped
SPOT scene was taken on February 5, 1987. The Kodak
Aerochrome 2443 color infrared film was used along with a
15.24 cm (6 inch) focal length camera (with a minus-blue
filter) flown at a height of 3657 m (12,000 ft). The film was
developed into a set of 228.6 x 228.6 mm (9 inch x 9 inch)
transparencies with a 1:24,000 scale at which the resolution
limit is about 0.25-0.75 m according to the film granularity
information provided by the Kodak Company. The main usage of
this ACIR photography was to obtain photogrammetric
measurements for citrus canopy cover estimations and to
provide data for ground-truthing land-use classification
results. The estimates of percentage canopy cover were used
to assess the feasibility of separating citrus groves based on
canopy size difference. Note that there is an eight-month
time lapse between taking this ACIR photography and the
acquisition of the SPOT scene. However, due to the slow
growth of citrus trees, the changes of canopy size were
considered as negligible during this eight-month period,
particularly the relative changes among the selected fields.
Image Processing Systems
The primary image processing system utilized in this
study was the earth resources data analysis system (ERDAS)
located in the Remote Sensing Application Laboratory (RSAL) of

123
the Department of Agricultural Engineering at the University
of Florida. This image processing package contains extensive
image processing capabilities for image enhancement, image
registration/rectification, land-use classification, GIS
analyses, etc. (ERDAS, 1991) . The ERDAS system used is the PC
version (7.4) for micro computers with a VGA display. In
addition to the ERDAS system, the Earth Resources Laboratory
Application Software (ELAS) image processing system (PC
version) was also used (Graham et al., 1986). The primary
usage of ELAS was for land-use classification comparisons as
well as for various interactive image display purposes in
ground-truthing classified datasets. For more information
regarding the two entire image processing systems, the
appropriate documentation (Graham et al., 1986; ERDAS, 1991)
of the aforementioned software systems should be consulted.
The Arc/Info GIS (ESRI, 1993) system located at the same RSAL
lab was also utilized for digitizing operations of graphical
map data entry, and miscellaneous processing and conversions
of image grid data.
Photogrammetric Stereo Plotter
A photogrammetric stereo plotter (FMA Model 503290-2
Multi-Format Photo Interpretation Station) was utilized to
make photogrammetric measurements from the ACIR photography
for citrus canopy cover estimation. The plotter consists of
two viewing plates, one adjustable magnifying viewing lens

124
assembly with a maximum 15 magnification power, a body frame,
and two vernier measuring devices (for x and y directions)
each with a designed precision of 0.001 mm. For this 1:24,000
ACIR photography, the plotter precision (0.001 mm) can be
translated (0.001x24,000 mm) into a 24-mm (or 2.4 cm)
horizontal distance on the ground. Photogrammetric
measurements were used to obtain field planting geometry (row
and tree spacings) and tree crown diameter for the estimation
of citrus canopy size.
Procedures for Merging SPOT Dataset
Before the SPOT multiresolution images were digitally
merged, some pre-merging processing was necessary which
included image co-registration and haze corrections. A
merging method must be chosen according to the SPOT image data
characteristics (a, n, and r) to generate merged image data
from the co-registered multiresolution images for the
assessments of radiometric enhancement, spatial improvement,
and land-use classification.
Pre-merging Processing
The multispectral images with a 20-m spatial resolution
were each resampled to a 10-m pixel size through a duplication
approach. As a result of this resampling, each of the pixels
in an original multispectral image became four identical ones
in the resampled dataset. Then, the panchromatic image, which

125
had a 10-m spatial resolution, was co-registered to the
resampled multispectral images. Because of accuracy concerns
for topographical maps (Thorpe, 1990; ASPRS, 1990) and map
data entry operations (Bolstad et al., 1990; Tan and Shih,
1991b), the image co-registration was done without using an
actual geographical reference system (e.g. UTM). A total of
25 mutual points were selected as tie points between the
multispectral and panchromatic images. The root-mean-square
(RMS) error for these selected points was 6.26 m. The
multispectral images were treated as a master to which the
panchromatic image was rectified as a slave. Since the
between-waveband registrability of the SPOT sensor is 6.0 m
(SPOT, 1989), the co-registration of the SPOT images was
considered very accurate with a RMS error of 6.26 m.
Haze correction was also applied to the clipped SPOT
scene before being merged. From the raw image data of the
clipped area, the minimum values for the panchromatic, red,
green, and NIR wavebands were 13, 25, 14, and 9, respectively.
Therefore, the haze-correction coefficients were chosen as 13
for the panchromatic waveband and 9 (the minimum of 9, 14, and
25) for the three multispectral images. The pixel values each
were subtracted by 13 for the panchromatic image and by 9 for
all the multispectral images. This specific haze-correction
procedure was done to preserve the integrity of spectral
information in the original multispectral data. The standard
deviations for the green, red, NIR, and panchromatic wavebands

126
of the haze-corrected SPOT dataset are presented in Table 6-1.
Also shown in Table 6-1 are the correlation coefficients (r)
of the panchromatic waveband to the multispectral images.
Note that a haze-correction procedure will not affect the
correlation coefficients as well as the radiometric variances
of the original image data.
Generating Merged Dataset
When merging multiresolution images, a merging approach
must be determined based on the image data characteristics of
the original multiresolution dataset. According to the
information presented in Table 6-1, each of the multispectral
images is positively correlated to the panchromatic waveband
with respective correlation coefficients (r) of 0.826, 0.852,
and 0.085 for the green, red, and NIR wavebands. Therefore,
the preserving approach is chosen in order to generate
radiometrically enhanced merged image data for improving the
differentiation of land-use elements.
The value of merging coefficient (6) for the selected
merging method must be determined with due considerations to
the radiometric quality and potential spatial improvement as
well as the spectral integrity of the final merged dataset.
From chapter 5, it was noted that the magnitude of merging
coefficient R can have a strong impact on the quality of a
multiresolution merged dataset. A large value of 6 is
beneficial to both the radiometric and spatial enhancements.

127
Table 6-1. Standard deviation (a), mean (n), maximum and
minimum values, and correlation coefficients (r)
of SPOT multiresolution dataset.
Waveband#
(M>
(<7)
(r)
Max.
Min.
1 (green)
29.8
6.73
0.826
148
11
2 (red)
18.1
7.41
0.852
157
1
3 (NIR)
65.2
11.51
0.085
141
0
P (pan.)
27.3
9.22
—
238
0
Note: Correlation coefficients (r) are to the panchromatic
image which was used as secondary image data.

128
However, the use of excessively large R values will raise the
possibility of altered or even corrupted spectral information
for a merged dataset. In multiresolution merging, there is no
alternative in the selection of the primary and secondary
images from the multiresolution dataset. The multispectral
images are each utilized as the primary images and the
panchromatic waveband as the secondary image data for every
multispectral image. In other words, the panchromatic image
was merged to each of the multispectral images. Therefore, a
large merging coefficient (R) will increase the extent of
panchromatic information in each of the merged multispectral
images, creating the potential for corrupting the integrity of
multispectral information in the original data. When the
spatial, radiometric, and spectral considerations are put in
perspective, a R value of 0.5 was chosen for the preserving
method to generate a multiresolution merged dataset from the
co-registered SPOT image data. In addition, a normalized
difference vegetation index (NDVI) image was also generated
using the 20-m NIR (HRV3) and 10-m panchromatic (PAN)
wavebands to develop a new approach in using SPOT image data
for vegetation study. This NDVI image is named as NDVIp in
order to distinguish it from the customary NDVI image
(Kidwell, 1991) usually created from the HRV3 (NIR) and HRV2
(red) wavebands. The NDVIp for a SPOT dataset is defined as
NIR - PAN
NDVIp =
[6-1]
NIR + PAN

129
The purpose of generating the NDVIp image was to assess its
effectiveness in differentiating vegetation such as citrus
canopy covers. There were three datasets (Table 6-2) used for
further analyses including land-use classification assessment.
These datasets are denoted as (1) OMD—original multispectral
dataset of the 20-m multispectral images of the green, red,
and NIR wavebands; (2) MMD—multiresolution merged dataset by
the preserving approach with 6=0.5 for each image; and (3)
MMND—multiresolution merged and NDVIp dataset which is
similar to MMD except that the merged NIR image was replaced
by the NDVIp data.
Evaluation of Merged Data
The evaluation of merged image data includes the
assessment of radiometric and spatial improvements, the
integrity of spectral information, and more importantly the
feasibility for improving land-use classification. However,
the procedures for assessing the effectiveness of merged
datasets in improving land-use classification will be
discussed in the final section of this chapter.
To evaluate the radiometric quality of merged images, the
standard deviations (a) of image data in OMD, MMD, and MMND
were obtained through the ERDAS image processing system and
then compared with those of the original data. In addition,
the estimates of standard deviation were also calculated based
on the corresponding equations in chapter 4, and then compared

130
Table 6-2. Multiresolution datasets and corresponding
merging equations.
Dataset
Waveband
Merging equation
OMD
1 (green)
2 (red)
3 (NIR)
HRV1 (original)
HRV2 (original)
HRVj (original)
MMD
1 (green)
2 (red)
3 (NIR)
HRV1 + 0.5PAN
HRV2 + 0.5PAN
HRV3 + 0.5PAN
MMND
1 (green)
2 (red)
3 (NDVIp)
HRV1 + 0.5PAN
HRV2 + 0.5PAN
(HRV3 - PAN) / (HRV3+PAN)
Note: 1. OMD = original multispectral dataset which includes
the original three 20-m multispectral images.
2. MMD = multiresolution merged dataset generated by
the preserving approach with B=0.5 for each image.
3. MMND = multiresolution merged and NDVIp dataset
which is similar to MMD except that the merged NIR
image is replaced by the NDVI data.
4. HRVj and PAN are multispectral and panchromatic
images, respectively.

131
to the actual values computed from the merged data digital
counts. The assessment of spatial improvement on a merged
dataset was based on color composite comparisons to examine
the spatial details present in the merged data. For each
merged dataset, its color composite was visually compared to
that from the original multispectral images, and the image
interpretability enhancement through multiresolution merging
was evaluated.
Because of its simplicity as well as availability in most
image processing systems, the direct RGB display system was
used to generate color composites. The green, red, and NIR
wavebands in each dataset (Table 6-2) were assigned to the
blue, green, and red color primaries, respectively. This
color assignment was done to make the appearance of the
generated color composites similar to that of an ACIR
photography which is the most widely used in photographic
remote sensing applications. The IHS transform was not used
because of its universal adaptability or insensitivity to a
wide range of data quality (Pellemans et al., 1992; Chavez et
al., 1991; Carper et al., 1990; Harris et al., 1990; Welch and
Ehlers, 1987; Cliche et al., 1985; Daily, 1983; and Hydan et
al., 1982) , which could introduce ambiguity to the evaluation.
The evaluation of spectral integrity of a merged dataset
was based on comparisons of color composite and correlation
analyses. If the color composite of a merged dataset shows a

132
great resemblance to that of original dataset OMD, the
spectral information in the original image data is well
preserved after the panchromatic image was merged. In
addition, a high correlation between a merged image and its
original multispectral counterpart can provide the indication
of well maintained spectral disposition of original
multispectral data. The weakening in the spectral integrity
can also be reflected by an increase in between-waveband
correlations within a merged dataset.
Image Response and Citrus Canopy Cover
The feasibility to separate citrus groves based on canopy
cover difference was investigated using the SPOT data. The
effect of multiresolution merging on such a differentiation
was also evaluated. The percentage canopy covers of citrus
groves were estimated photogrammetrically using both the ACIR
photography and the stereo plotter.
Photoqrammetric Measurement
Photogrammetric measurements from the ACIR photography
were converted to ground distance by the following equation
(Lillesand and Kiefer, 1979)
L = D x h/f [6-2]
where L is the actual ground distance (m) , h is the flying
height (m), f is the focal length of camera lens (mm), and D

133
is the distance (nun) on the photo which is obtained by
D = y(x2-Xl)2 + (y2-Yl)2 [6-3]
where x and y are photo coordinates (mm) for points 1 and 2,
which were read directly from the ACIR photography through the
stereo plotter. The photogrammetric accuracy of the ACIR
photography was tested using highway pavement (Interstate
Highway 95, Florida Turnpike, and local roads). The photo
measurements of highway pavement width at 22 locations were
obtained from the stereo plotter and then converted to ground
distance using equations [6-2] and [6-3]. A comparison of the
photogrammetric results with the data obtained from the local
highway maintenance offices indicated a RMS error of 0.251 m
(0.823 ft) which suggested a very accurate estimation for this
photogrammetry.
Eighteen citrus groves within the study area (Figure 6-1)
were selected through a visual inspection of the ACIR
photographs. These 18 groves were uniform in that the number
of missing or dead trees was few or zero. Photogrammetric
measurements were made only in the central portion of each
photograph. This was done to minimize the potential scale
distortions resulting from camera lens and flight operations
(Lillesand and Kiefer, 1979; Curran, 1985). The radius of the
central portion was about 63.5 mm (2.5 inches) centered at the
photo principal point. Because of the flat terrain in south
Florida, corrections were not needed for the effect of
topographic variations on the photogrammetric measurements.

134
For each selected grove, two to five rows were randomly
chosen for taking photogrammetric measurements which included
row length for the selected rows, field width at several
locations (at least three), and the crown diameter of
individual trees in all selected rows. The measurements were
used for calculating field planting geometry (row and tree
spacings) and the diameter of tree crown.
Tree spacing (a) within a row was obtained by dividing
the row length by the number of trees in a row and averaged
over the selected rows in a field, excluding three trees from
each of the row ends. Similarly, row spacing (b) was obtained
by dividing the field width by the number of rows in the grove
and averaged over the number of measured locations (at least
three locations) along the row length, excluding two rows from
each side of the field. The diameter of tree crown (d) was
based on the average of all measured trees in a selected
grove. In addition, the photogrammetric measurements of tree
and row spacings were ground-truthed for accessible selected
groves.
Canopy Cover Estimation
Two cases were encountered in the estimation of citrus
canopy covers using the ACIR photogrammetric measurements.
The first case was that tree crowns were within the area
bounded by tree spacing (a) and row spacing (b) . In this
case, percentage citrus canopy cover (0) for each selected

135
grove was estimated by the following equation
7T(d/2) 2
0 = x 100%. [6-4]
a x b
For mature groves with trees slightly overlapped or tree crown
larger than tree spacing, the overlapping areas (Ao) on both
sides must be excluded. For this case, percentage canopy
cover 9 was estimated by
7r(d/2)2-A0
0 = x 100% [6-5]
a x b
and the overlapping areas Ao (m2) were calculated by the
following equations
A0 = 0.5[7rd2 (0/360)-a7(d2-a2 ) ] [6-6]
0 = 2 tan'1 [7(d2 -a2 )/a] (0 <

where a is tree spacing (m) , b is row spacing (m) , and d is
diameter of tree crown (m).
Locations of the selected citrus groves in the SPOT scene
were identified by scan lines and pixels in each of the three
datasets including the original one with a 20-m spatial
resolution. For each waveband of a dataset, the mean and
standard deviation of grove-wide pixel values were obtained,
excluding those pixels along field boundaries. The relations

136
between estimated canopy cover and image spectral response
were investigated.
To assess the feasibility of differentiating citrus
groves based on differences of canopy cover, the variations of
image spectral responses (or pixel values) were analyzed for
all selected groves through coincident plots of field-wide
image data (n±a). Within a spectral waveband, a data overlap
between two groves is the implication that these two groves
can not be separated satisfactorily in that waveband because
they possess image data of the same magnitude. An increase in
the overlapping of image data is the indication of greater
difficulty in separating the groves in a land-use
classification analysis. In fact, it will be impossible to
differentiate two groves if they have severe image data
overlaps between all wavebands in a dataset (Lillesand and
Kiefer, 1979).
Land-use Classification
Land-use classification analyses were performed on the
three datasets listed in Table 6-2. The analyses were based
on the capability of each dataset to differentiate the scene
environment through spectral signature extraction. In
addition, a GIS-based discrete land-use classification
technigue was introduced and applied to the canopy-size
classification of citrus groves.

137
Précls and Concept
Computerized land-use classification from remote sensing
datasets is a two-step pattern recognition procedure which
involves a training process and a sorting technigue or
classification decision rule. In order to classify a scene or
dataset, the spectral signature patterns that are related to
various land-use types within the scene must be extracted and
defined using statistical criterion (e.g. means, variances,
and covariances) implemented in an image processing system.
This step of defining signature patterns is called the
training process whose purpose is to "teach" the computer
system to recognize the signature patterns inherent in the
multi-waveband data. It is usually done through either a
supervised or an unsupervised approach (Lillesand and Kiefer,
1979; ERDAS, 1991). In a supervised training, the analyst
directs or supervises the computer in defining the signature
patterns with the help of his prior knowledge or existing
information about the ground. The process takes place in an
interactive fashion between the computer and the analyst. One
apparent advantage of a supervised training is that accurate
signature patterns can be generated for the land-use types for
which there is abundant existing information. However, for
those land-use types for which there is not sufficient
information, they are usually ignored or treated as background

138
elements. The emphasis is given mainly to the land-use types
with available information. In addition, the analyst is often
incapable of identifying the subpatterns within a broad land-
use type even though those signature patterns are
statistically separable and might possess some significance.
Consequently, there is a great possibility that the whole set
of signature patterns inherent to a dataset will either be
incomplete or subjective in a supervised training.
In contrast to the supervised approach, the unsupervised
training is very automated. Based on some input criterion
specified by the analyst, the computer system searches through
the dataset to unveil all the unique statistical patterns that
are inherent in the image data. This training approach will
allow the derivation of a complete set of signature patterns
while alienating the likely subjectivity of a supervised
training. To choose or select the proper criterion (or input
parameters), some image processing experience is needed.
However, the implementation of modern image processing systems
has made such a task much easier by minimizing the number of
input parameters. After the spectral signature patterns are
defined, a classification decision rule is invoked to sort
through or to classify all pixels in an entire dataset. The
result of classification is a thematic image that contains the
numberings of spectral patterns or classes which are later
related to various land-use types through a ground-truthing

139
procedure. A summary of the commonly used classification
decision rules is presented in Appendix D, which includes the
parallelepiped classifier, the minimum distance classifier,
the mahalanobis distance classifier, and the most widely used
maximum likelihood classifier (Lillesand and Kiefer, 1979;
ERDAS, 1991).
Extracting Signature Patterns
One method to assess the effects of multiresolution
processing was to evaluate the capability of a merged dataset
to unveil the signature patterns for the given scene
environment. If a dataset indicates a greater prospect to
derive more signature patterns under the same given criterion,
it will be advantageous to use the dataset for improving land-
use classification results. On the other hand, a dataset
would be considered as inferior if its ability to unveil
spectral signature patterns is limited. In order to have an
objective evaluation, the signature patterns for each dataset
have to be complete while the statistical criterion used for
a clustering procedure should be identical. In addition, the
subjectivity associated with the supervised training method
must be avoided to ensure that none of the potential signature
patterns inherent in a dataset will be overlooked.
To derive the signature patterns for each dataset, the
ERDAS STATCL (statistical clustering) module was used. In an

140
unsupervised statistical clustering procedure, the most
important parameter is the scaled (spectral) distance (ERDAS,
1991; Graham et al. , 1986) which defines the separability
criteria for all signature patterns of a dataset within a
multidimensional space bound by the wavebands. Two signature
patterns are considered not separable if their scaled distance
is less than the specified value (automatically merged). When
the scaled distance is set at a large value, the number of
separable signature patterns will become smaller. On the
other hand, a small scaled distance will allow a "tight"
clustering, making closely related signature patterns become
separable (ERDAS, 1991).
The ERDAS STATCL module was used with a large number (80)
of conceivable spectral patterns to ensure that none of the
potentially separable signature patterns will be forced to
merge to the others before the clustering process is
completed. Also, several values of scaled distance were used
in order to examine the consistency as well as the
dependability of a merged dataset. In order for a signature
pattern to be statistically reliable, the adequate sample size
for each signature pattern must contain at least (10-100) x
(n+1) pixels where n is the number of spectral wavebands used
(Swain, 1978). For instance, the desired sample size for a
three-waveband dataset is about 40-400 pixels. At the
completion of the STATCL module, a spectral pattern with a

141
scaled distance less than the specified value is automatically
merged to its closest neighbor. After such a merging based on
the specified scaled distance, those patterns with a sample
size less than 99 pixels (10 fields in an ERDAS term) were
discarded. The input parameters for the STATCL module are
summarized in Table 6-3. Similar clustering procedures and
parameters were also used in the ELAS image processing system
(TMTR module) to derive signature patterns for each dataset
for comparisons between the two systems. Since an identical
methodology that included clustering module and input
parameters was utilized to generate spectral signature
patterns for each of the datasets, a larger number of spectral
patterns is a clear indication that the dataset will have a
greater differentiations among the various land-use elements.
When sufficient ground-truth information is available, a
larger number of spectral classes will be advantageous to
land-use classification efforts for obtaining land-use data
with greater detail.
GIS-based Discrete Classification
A GIS-based discrete land-use classification technique
was introduced in an effort to classify the citrus groves
based on differences of canopy cover. The basic concept of a
discrete approach is to utilize GIS techniques to guide the
entire process of both clustering and classifying to only the

142
Table 6-3. Parameters used in ERDAS STATCL and
modules for signature extraction.
ELAS TMTR
Presumed number of patterns:
80
Lower bound standard deviation:
0.1
Upper bound standard deviation:
1.2
Coefficient of variation (%):
5
Scaled distance (used):
3, 2, 1
Minimum field threshold:
10
Perform final merge:
Yes

143
land-use types of interest. This will eliminate the pixels of
unrelated land-use types in the classification results. In
remote sensing land-use classification, confusion often exists
that one spectral class entails several different land-use
types. For instance, pasture lands can be mixed with brushes
while citrus groves mingle with forests, pasture lands, and
brushes. This inter-class mingling creates a great difficulty
in improving classification results. Though the extent of
inter-class confusions depends on many factors such as low
radiometric quality of image data, the method to cluster and
classify the image data is very critical. If a traditional
clustering procedure is applied, the derived signature
patterns often consist of pixels related to other land-use
categories. When using GIS techniques, both the clustering
and classifying processes can be confined within each
respective land-use category to extract the potential
subclasses. There are several advantages for this discrete
classification technique.
First, efforts and resources can be concentrated on the
land-use type(s) of greater interest by confining the
processes of clustering and classifying to only the land-use
category (e.g. citrus land use) being studied. This
significantly reduces the time and resources devoured to the
less important land-use types.
Second, spectral signature patterns will consist of
pixels only from the land-use category that is being

144
investigated. This eliminates the problems of inter-class
confusion and as a result, increases the accuracy of
classification results.
Third, the subclasses within each category of land use
can be classified and evaluated individually, allowing the
problems associated with a given land-use category to be
isolated and identified with greater accuracy.
Fourth, as the capability of remote sensing systems
continues to improve, information in image datasets becomes
less and less generalized while more detailed land-use
information is increasingly demanded. The use of this GIS-
based discrete approach will make more efforts for improving
land-use classification successful.
The discrete classification procedure can be achieved
through a collaborate use of GIS techniques and traditional
land-use classification procedures. The approach utilizes a
supplementary data layer to guide the processes of both
signature extraction and classification for all subclasses
within their respective category of land use. For instance,
when a GIS database containing general citrus land use is
used, both the derivation of spectral signatures and the
classification of subclasses can be confined within the citrus
land use. This will avoid the impurity of spectral signature
patterns because the pixels used are only from citrus land
use. As a result, the inter-class confusions between citrus

145
and non-citrus land uses are eliminated, allowing a further
classification of citrus land use. This discrete approach
will allow the problems related to the land use type of
interest to be isolated for further investigation.
The discrete classification technique was demonstrated in
the classification of citrus land use. Since a GIS dataset
containing the general land use of citrus was not available,
it had to be constructed from map data together with the ACIR
photography. The field boundaries of all groves in the study
area were transferred from the ACIR photography to the USGS
7.5 minute series quadrangle maps and then digitized as a data
layer of polygons using the Arc/Info GIS software. The
polygon data layer was projected to the UTM coordinate system
before being converted (by use of Arc/Info POLYGRID command)
to a grid of 10-m cells compatible with the SPOT satellite
data. This grid is named as CITRUS data layer.
Through the use of ERDAS NRECTIFY (non-linear rectify)
module along with the nearest neighbor resampling method, the
three datasets (Table 6-2) were also georeferenced to the UTM
coordinate system in order to be geographically compatible
with the CITRUS grid data layer. Because an integrated module
for the discrete clustering and classification is not
available in either the ERDAS or ELAS image processing systems
nor does it exist in the Arc/Info GIS system, some additional
efforts were required which included clipping the citrus areas

146
using the CITRUS grid layer and setting all the non-citrus
pixels to zero. The resultant datasets each (OMD, MMD, and
MMND) allowed the clustering and classifying processes to be
directed to only citrus pixels (non-zero pixels) while non¬
citrus pixels were ignored. If an integrated module for
discrete classification was available, these efforts to clip
and manipulate the image data could have been avoided. All
the areas outside the citrus land use could also have been
classified in just one unified procedure.
For its high clustering accuracy, the ERDAS ISODATA
module (ERDAS, 1991), which is based on the iterative self¬
organizing data analysis technique (Tou and Gonzalez, 1974 in
ERDAS, 1991), was utilized to derive the spectral signature
patterns from all the groves. The STATCL module was not used
because of concerns about its clustering process that relies
on blocks of pixels (3x3 pixel arrays) which could introduce
problems to the boundary areas between citrus and non-citrus
land-use types. For each of the three datasets, the ISODATA
module was instructed to derive seven signature patterns which
were later used by the ERDAS MAXCLAS (maximum likelihood)
classification module to classify all the citrus pixels in
each entire dataset into seven spectral classes. For both the
ISODATA and MAXCLAS modules, the non-citrus pixels were
ignored and treated as a background class (class zero). The
ELAS system was not used because its implementation does not

147
render the alternative of ignoring pixels with certain values
(e.g. zero).
The discrete classification technique is not a supervised
classification procedure, though a supplemental GIS dataset is
used in the clustering and classifying processes. Within each
category of land use, all potential subclasses are clustered
and classified using the unsupervised classification method.
Therefore, the seven spectral classes for each dataset (OMD,
MMD, and MMND) were ground-truthed using canopy cover
estimates from the ACIR photography as well as data collected
during field visits.

CHAPTER 7
DISCUSSIONS AND ANALYSES OF
MULTIRESOLUTION LAND-USE CLASSIFICATION
The results from merging the SPOT multiresolution data
are discussed in this chapter, which include the radiometric
quality of merged datasets, the feasibility for a canopy-size
differentiation of citrus groves, and the effect of
multiresolution processing on land-use classification.
Evaluation of Merged Image
To evaluate the quality of merged images, image standard
deviations (or radiometric variances) and color composites of
merged image data are examined. Since the primary emphasis of
multiresolution processing is to enhance the multispectral
data, evaluations and comparisons of merged image/datasets
will be made based on the same quality factors of the
corresponding original multispectral image.
Radiometric Quality
The standard deviations (a) and mean brightness values
(M) for the merged SPOT images are summarized in Table 7-1.
A substantial increase in image standard deviation was
observed for all merged images (Table 7-1). Even for the NIR
waveband which had a near-zero correlation (r=0.085) to the
panchromatic data (Table 6-1), the image standard deviation
148

149
Table 7-1. Standard deviations (a) and mean brightness values
(H) for multiresolution merged SPOT images.
Wave¬
band#
Merging-
method &
coeff.
Mean (n)
Standard
deviation (a)
pan.
raw data
27.3
9.22
green
raw data
29.8
6.73
red
raw data
18.1
7.41
NIR
raw data
65.2
11.51
green
Pa (0.5)
43.7
10.86
red
P (0.5)
32.0
11.59
NIR
P (0.5)
73.5
12.06
NDVIpb
-
179.8
18.52
Note: a — Preserving method with B=0.5.
b — NDVIp is normalized difference vegetation index
using panchromatic waveband.

150
(radiometric variance) was also increased in the merging
process. Note that the radiometric enhancement in all these
merged images was not the contemplations of a contrast¬
stretching or PCA procedure, even though those technigues can
be applied for further image enhancement. They are the
results of increased image gray shades in the merged data,
which are essential to improve the visual qualities for image
interpretation and to achieve a greater differentiation of the
scene environment for improving land-use classification. In
addition, the enhanced radiometric quality also demonstrates
the effectiveness of the preserving approach to merge the
panchromatic data to the multispectral images for
multiresolution processing, which was already observed in the
results from the NOAA-11 LAC data discussed in chapter 5.
For the NDVIp image, the use of a scaling factor hampers
an objective comparison of its radiometric quality with that
of the multispectral NIR waveband. The scaling factor used
for the fractional ratioed results was functionally equivalent
to a linear stretching procedure. In addition, the NDVIp
method had a special purpose of image enhancement for
vegetation. For the three images of MMD, the standard
deviations (a) computed from the merged image data were found
virtually identical to the estimates from equation [4-25].
These results not only extend the applications of the
principle of statistical variation analyses of combining
random variables to satellite images with different spatial

151
resolutions, but also provide a feasible means to assess and
evaluate the radiometric quality of pre-merged multiresolution
datasets.
Spatial Improvement and Spectral Integrity
The evaluation of spatial enhancement is based on an
visual comparison of the color composites between datasets OMD
and MMD (Table 6-2). After the panchromatic data is merged,
the composite of merged dataset MMD indicated a substantial
improvements in spatial detail. As noted in the study by
Ehlers (1989), the most obvious enhancement was revealed in
linear features which included interstate highway 95, the
Florida turnpike, local roads, and field boundaries. The
spatial enhancement is attributed to the preserving approach
with a B=0.5 merging coefficient, which effectively merged the
panchromatic spatial information to the multispectral images
while increasing the radiometric quality in the merged data.
The spectral integrity in a multispectral dataset is the
disposition of image data in the respective multispectral
wavebands. Its assessment includes three analyses: (1) a
comparison of the color composite of a merged dataset with
that of the original multispectral data; (2) a correlation
analysis between a merged image and its multispectral
counterpart; and (3) a comparison of between-waveband
correlations among the images within a dataset. While the
color appearance of a composite renders an effective

152
comparison of the overall spectral quality of a dataset, the
correlation analyses provides a further assessment of the
spectral disposition of the merged image data.
The color composites of datasets OMD and MMD indicated an
outstanding conformity based on a visual assessment. This
correlation in visual quality suggests that the multispectral
information in merged dataset MMD is comparable to that of
original dataset OMD. In addition, the color composite of
merged dataset MMD also exhibited a great resemblance to an
ACIR photography of good quality, suggesting its usefulness
and effectiveness for image interpretation applications. All
vegetative areas (e.g. citrus groves, pasture lands, and
forest stands) showed up in bright red colors of varying
intensities for different vegetation conditions, while roads
and urban structures were indicated with white colors as they
are usually observed in a typical ACIR photography.
The high correlation between each merged image and its
original multispectral counterpart (Table 7-2) suggests that
there is no significant alterations of image spectral data
between datasets OMD and MMD. In other words, the disposition
of spectral information in merged dataset MMD is similar to
that of dataset OMD. Though a slight increase in the between-
waveband correlations was noted for dataset MMD (Table 7-3),
these changes are neither substantial nor deleterious to the
original multispectral integrity of dataset OMD. When the
factors of radiometric improvement, spatial enhancement, and
spectral integrity are put in perspective, the conclusion is

153
Table 7-2. Summary of correlations between a merged image
and its original multispectral counterpart.
Waveband
Green (HRV1)
Red (HRV2)
NIR (HRV3)
NDVIa
0.971
0.978
0.921
0.935a
a — for NDVI and
NDVI images.

154
Table 7-3. Between-waveband correlations (r) within
multiresolution merged datasets.
Spectral waveband
Data¬
set#
Merging-
method
Wave¬
band
green
red
NIR
-
raw data
Pan
0.826
0.852
0.085
OMDa
raw data
raw data
raw data
green
red
NIR
0.963
0.155
0.022
MMDa
Pb (0.5)
P (0.5)
P (0.5)
green
red
NIR
—
0.986
0.451
0.384
(NDVIp)
MMNDa
P (0.5)
P (0.5)
NDVI
green
red
NDVIp
0.986
-0.610c
-0.685c
a — Refer to Table 6-2 for dataset definition.
b — Preserving method.
c — NDVIp image was used instead of NIR waveband for the
correlation analysis.

155
that the preserving approach (with 6=0.5) is an effective
method for multiresolution processing of SPOT multiresolution
datasets for remote sensing applications.
From a black-and-white display (Figure 7-1), the NDVIp
image indicated a great resemblance to the customary NDVI
image generated from the original 20-m multispectral NIR and
red wavebands [Note: NDVI=(NIR-Red)/(NIR+Red)]. These two
vegetation index images had a (r=0.935) high correlation
(Table 7-2), implying that the information of one image is
very similar to the other. In both the NDVIp and NDVI images,
vegetative areas appeared as bright (large NDVI values) and
had a greater image contrast, while urban lands/structures and
water bodies including marshes showed a black appearance with
little contrast. This demonstrates not only the capable
enhancement of vegetative lands by the NDVIp method, but also
the comparable NDVIp effectiveness to that of the original
NDVI method. The benefit of substituting the red waveband by
the panchromatic data was the added spatial enhancement while
maintaining the effectiveness of the original NDVI image. The
enhanced spatial details makes the NDVIp approach more
appealing for vegetation studies.
In summary for the radiometric assessment of the SPOT
multiresolution merged dataset, three observations were made.
First, the preserving approach with 6=0.5 is a very effective
method to generate multiresolution merged SPOT datasets with
improved radiometric guality and to produce spatially enhanced

NDVI=(NIR-Red)/(NIR+Red) NDVIp=(NIR-PAN)/(NIR+PAN)
Figure 7-1. Comparison of SPOT 20-m NDVI and 10-m NDVIp images.
156

157
color composites for image interpretation applications. The
well preserved spectral information in the merged data will
allow the merged datasets for further applications such as
land-use classification. Second, the effectiveness of the
NDVIp method for vegetation enhancement is comparable to that
of the customary NDVI method using the original 20-m NIR and
red wavebands. The added improvement in spatial detail by
replacing the red waveband with the panchromatic image makes
the NDVIp method more appealing for vegetation studies.
Third, the radiometric guality of pre-merged multiresolution
SPOT datasets can be accurately assessed by using the
principle of statistical variation analyses for random
variable manipulations discussed in chapter 4.
Image Response and Citrus Canopy Cover
The focus of this section is to discuss the effect of
citrus canopy cover on image spectral response as well as the
feasibility of a canopy-size differentiation for citrus
groves. The specific points included the photogrammetric
estimation of citrus canopy cover, the relations between SPOT
image response and citrus canopy cover, the differentiation of
citrus groves based on canopy cover differences, and the
effect of multiresolution processing.
Estimation of Citrus Canopy Cover
For the 18 selected citrus groves, the percentage canopy
covers ranged from about 20% to 75% based on photogrammetric

158
estimations. Groves with canopy cover less than 20% have
trees too small to measure on the ACIR photography with a
1:24,000 scale and were not selected. Canopy cover estimation
for young groves (small canopy cover) requires photographs of
a larger scale (e.g., 1:2,400). However, the irregular tree
shape in young groves can create further problems for making
reliable measurements. On the other hand, citrus trees in
mature groves are over-growing into each other's canopies.
When a grove is over-grown, it becomes impossible to identify
the separation between trees for making measurements of tree
spacing and tree crown size (diameter). As a result, canopy
covers outside the 20 to 75% range are considered to be
difficult to estimate photogrammetrically. However, since the
ground-based estimation of citrus canopy cover is extremely
difficult, the photogrammetric approach might be the only
practical solution to the problem of citrus canopy cover
estimation. In addition, the ground-truthing in four
accessible groves indicated very accurate measurements for
tree and row spacings with a RMS error of 0.35 m which is
within the spatial resolution limits of the ACIR photography.
It should be noted that the scale of the photography will
have a direct effect on the accuracy of photogrammetric
measurements. A large scale (e.g., 1:2,400) is desirable for
better accuracy, but aerial photography at large scales is
expensive, particularly when a large coverage area is needed.
Also, it is important to recognize that the benefit of photo

159
enlargement or magnification is limited by the spatial
resolution constraints of the original photographs/films.
Therefore, the selection of a photo scale for citrus canopy
cover estimation must be based on consideration of the actual
tree crown (object) diameter (size) and the equipment
capability (precision). Generally, ACIR photographs with a
scale from 1:24,000 to 1:2,400 can be considered as
appropriate for citrus canopy cover estimation.
Relation of Image Response to Canopy Cover
The relations between citrus canopy cover and image
response for the green and red wavebands of the original 20-m
multispectral dataset OMD are shown in Figures 7-2 and 7-3.
The difference of citrus canopy cover does have an effect on
the SPOT spectral responses of the green and red wavebands
(Figures 7-2 and 7-3). However, the effect was not profound
enough to result in well defined relationships. In other
words, citrus canopy size does not have a solitary correlation
with the SPOT spectral responses of the green and red
wavebands. Also observed in Figures 7-2 and 7-3 is an inverse
relationship between canopy size and spectral response for the
green and red wavebands. The primary cause for such inverse
relationships, which were also observed for wheat crops by
Idso et al. (1977), was due to the relatively higher spectral
reflectance of underlying soils. In partial canopy groves,
the spectral response of a pixel depends on the collective

34 -
22 i i i 1 1 1 1 1 1 1 1 1 r~
15 25 35 45 55 65 75
Percentile citrus canopy cover (CC)
Figure 7-2.
Effect of citrus canopy cover on SPOT green waveband response.
160

Figure 7-3
Effect of citrus canopy cover on SPOT red waveband response
161

162
effect of both exposed soils and canopy covers. As compared
to vegetation, exposed soils (especially sandy soils in south
Florida orchards) tend to have significantly strong
reflectance in the visible (e.g. green and red) wavelength
ranges, particularly when soil moisture content is low
(Lillesand and Kiefer, 1979; Shih, 1988; and Rees, 1990). An
increase in canopy cover would shut out more high-reflectance
exposed soils from the sensor's instantaneous viewing area.
This will reduce the overall reflected radiance from the
target (pixel). As a result of increased canopy cover, a
smaller value of spectral response (digital count) was
recorded in the image. In citrus groves in south Florida,
bare soils between trees as well as in traffic tracks are
examples that have relatively higher spectral reflectance than
trees in the green (0.50-0.60 /xm) and red (0.60-0.70 jum)
wavelength ranges. For the SPOT panchromatic waveband, which
encompasses both the green and red wavebands while extending
to a small portion of the NIR wavelength range (generally
regarded as 0.7-1.0 ¿xm) , its spectral response to citrus
canopy cover maintained the general characteristics of both
the green and red wavebands (Figure 7-4).
Unlike those of the green and red wavebands, the spectral
response of the NIR waveband did not indicate to correlate to
citrus canopy cover (Figure 7-5). For the NIR waveband, the
lack of a perceivable relationship of spectral response to
citrus canopy size can be caused by many factors including

Figure 7-4. Effect of citrus canopy cover on SPOT panchromatic waveband
response.
163

88
"I i i i i 1 1 1 1 1 r~
15 25 35 45 55 65
Percentile citrus canopy cover (CC)
T"
75
Figure 7-5. Effect of citrus canopy cover on SPOT NIR waveband response.
164

165
canopy itself and underlying soils. In a study of cotton
crops spectra, Huete and Jackson (1988) found that there is a
strong interaction between canopy cover and underlying soils
for partial canopy fields. For instance, the NIR spectral
reflectance of exposed soils is generally lower than that of
vegetation (Lillesand and Kiefer, 1979; Rees, 1990). In a
land-use classification study, Shih (1988) found that barren
soils had a lower NIR response than agricultural lands
including citrus groves in south Florida. Therefore, an
increase in citrus canopy cover would increase the reflected
radiance from the sensor's viewing area, resulting in a larger
image value. However, the spectral response of the NIR
waveband is not influenced by canopy cover alone. In the NIR
wavelength range, the reflectance of citrus trees (vegetation)
is predominately related to tree health/growth conditions.
While a healthy citrus tree exhibits very high reflectance, a
stressed one will not (Shih et al., 1985). In addition, the
stage of growth, cultural practices (e.g. hedging, topping,
weeding, etc.), and diversity of soil substrates (e.g. dry,
wet, dark, or bright) could also contribute individually or
collaborately to the variations of the NIR image response for
groves with partial canopy cover. Therefore, these factors
together will make it extremely difficult for the NIR waveband
to have a defined relation to the differences of citrus canopy
size.
In summary, the SPOT image response does indicate
tangible inverse relations to citrus canopy size for the

166
green, red, and panchromatic wavebands. However, these
relationships are neither strong nor solidary. On the other
hand, the SPOT NIR response did not indicate a perceivable
relation to citrus canopy cover. In general, the lack of well
defined relations between canopy cover and image spectral
response is the implication of great variations of both soil
and tree conditions over the study area. Recall that the SPOT
scene was acguired in early October when the season is
generally wet with miscellaneous vegetation still thriving in
the fields. In order for a satellite sensor to effectively
differentiate the differences of citrus canopy cover, soil
conditions must be as less variable (e.g. dry winter months of
January and February) as possible over the entire area of
study. This will minimize the strong influence of soil
substrate variations.
Differentiation of Canopy Cover
The feasibility for a canopy-size differentiation of
citrus groves based on percentage canopy covers was evaluated
using coincident plots of the field-wide image response of the
selected groves. In land-use classification analyses, the
variations of grove-wide image data will have a direct impact
on the separability of groves with different canopy covers.
To examine the feasibility of a canopy-size differentiation of
citrus groves, the grove-wide image response (a±/x) for each

167
selected field in dataset OMD is illustrated in Figures 7-6,
7-7, and 7-8 for the green, red, and NIR wavebands,
respectively.
From the results presented in Figures 7-6, 7-7, and 7-8,
three comments are in order. First, the number of image gray
shades were very limited for the entire 20-75% range of canopy
cover. This strong containment of image gray shades, which
were respectively about 13, 14, and 26 for the green, red, and
NIR wavebands, not only revealed a very limited resolving
capability of the SPOT image data for the entire 20-75% canopy
cover range, but also implied a great difficulty for a canopy-
size differentiation of citrus groves. The limited gray
shades together with the lack of well defined relations
between canopy cover and image response did not suggest likely
separations within the 20-75% canopy cover range.
Significant grove-wide variations of image response
created severe data overlaps among the groves with different
canopy sizes, and as a result, these data overlaps further
complicated the separability problem. If two groves have a
data overlap in a waveband, the two groves may not be
separated in that waveband because they posses image data of
the same magnitude. The more severe the overlapping is, the
more likely two groves are inseparable. As shown in Figures
7-6, 7-7, and 7-8, none of the selected groves are free from
data overlaps in any of the three SPOT wavebands. In order to
achieve a canopy-size differentiation of citrus groves, the

Green waveband response (DC)
36-
22H 1 1 1 1 1 1 1 1 1 1 1 r—
15 25 35 45 55 65 75
Percentile citrus canopy cover (CC)
Note: DC—digital count.
Figure 7-6. Coincident plot of SPOT green waveband response
for selected citrus groves.
168

Red waveband response (DC)
Note: DC—digital count.
Figure 7-7. Coincident plot of SPOT red waveband response
for selected citrus groves.
169

NIR waveband response (DC)
Note: DC—digital count.
Figure 7-8. Coincident plot of SPOT NIR waveband response
for selected citrus groves.
170

171
image response in some ranges of canopy cover must be unique
as well as free from data overlaps in at least one waveband.
In a citrus field with partial canopy cover, the response
value (digital count) of a pixel is determined by the
collective effect from the areas of canopy cover and exposed
soils. The variability in both tree crown diameter and
underlying soil substrates is a very important factor
responsible for the variations of image response of a partial
canopy cover grove.
The uniformity of image response of a grove is affected
by the overall field conditions including the variations of
tree crown diameter and soil "brightness". In general, a
larger variation in tree crown diameter would result in more
variable image response. However, such a relation was not
observed for the green, red, and NIR wavebands (Figures 7-9,
7-10, and 7-11), suggesting that there existed significant
variations of soil condition among the groves. According to
Huete and Jackson (1988), the soil "brightness" had a strong
influence on the spectra of partial canopy cotton fields.
Also, it was noted from an early discussion that citrus canopy
cover was inversely related to image spectral response.
Apparently, the effect of soil brightness was so strong that
canopy cover was acting only like a dampening factor to the
overall spectral response of a partial canopy pixel. Hence,
limiting the variability of soil conditions is very critical
to the feasibility in remote sensing applications for canopy
cover studies.

Standard dev. of green response (DC)
Note: DC—digital count.
Figure 7-9. Effect of tree crown variations on SPOT green
waveband response variability for partial
canopy groves.
172

Standard dev. of red response (DC)
Note: DC—digital count.
Figure 7-10. Effect of tree crown variations on SPOT red
waveband response variability for partial
canopy groves.
173

Standard dev. of NIR response (DC)
4-
â–¡
3-
â–¡
â–¡
0.5-
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Std. dev. of tree crown diameter (m)
Note: DC—digital count.
Figure 7-11. Effect of tree crown variations on SPOT NIR
waveband response variability for partial
canopy groves.
174

175
Citrus trees tended to be more uniform in groves with
large canopy covers (Figure 7-12). This is probably due to
some increased cultural attention such as hedging and topping
practices. Also, the variation of grove-wide image response
was not the same across the entire 20-75% canopy cover range
(Figures 7-6, 7-7, and 7-8). The image response was slightly
less variable for groves with canopy sizes greater than 40%,
especially for the green and red wavebands (Figures 7-6 and 7-
7). When canopy cover increased, the area of exposed soils
decreased. This reduced the strong effect of soil substrates.
In addition, an increase in canopy cover will have less
variable tree crown diameter as indicated in Figure 7-12.
Conseguently, groves of young citrus trees are spectrally more
variable due to the greater variability in both tree crown
diameter and exposed area.
Recall again that the SPOT satellite scene was acquired
in late summer (October 3, 1987) when the season is generally
wet and ponderous weeds/grasses are still actively growing.
However, field conditions in south Florida are generally less
variable in winter months than in the summer because of the
dry season as well as relatively inactive growing of
weeds/grasses in the field environment. Therefore, satellite
scenes acquired in dry winter months (e.g. January and
February) would render a greater possibility for citrus canopy
cover to stand out spectrally in the area to be imaged when
the influence of soil conditions is minimized.

Coef. of var. (CV) of tree crown size
25
20-
15-
10-
5-
0 —
15
Figure
CVt = 20.49 - 0.202 CC
-i 1 1 1 1 1 1 1 1 1 r-
25 35 45 55 65 75
Percentile citrus canopy cover (CC)
7-12. Relation of tree crown variation to
canopy cover difference.
176

177
Effect of Multiresolution Merging
For the SPOT multiresolution merged data, the correlation
coefficients (r2) for the relations between citrus canopy
cover and image response are summarized in Table 7-4. These
relations did not reveal improvements after the panchromatic
image was merged, and this lack of improvement is attributed
to the variability of field environments. Note that, in each
multispectral waveband (green, red and NIR) of the original
multiresolution dataset, there existed significant variations
of correlation between the panchromatic and multispectral
images among the 18 selected groves (Table 7-5), even though
these groves were considered relatively uniform. Because of
these variations of correlation, the changes of image data
among the 18 groves were not consistent within each waveband
(Table 7-6) when the panchromatic waveband is merged. While
the standard deviation of image data increased for some
groves, it decreased for others in a merged image (Table 7-6).
Consequently, the grove-wide image responses of some groves
became more uniform, while those of others were more variable.
Unfortunately, additional ground-truth information was not
available to allow a further assessment of these image data
transformations. In land-use classification analyses, the
groves with more uniform image data can be easily separated as
unified individual fields. However, those with more dispersed
response each would split into small areas, making an entire
field mingling between different classes in the classification
results.

178
Table 7-4. Summary of correlations between citrus canopy
cover and image response for multiresolution
merged images.
Waveband#
Explanation
Corr. coef. (r2)
Pan.
Original
(-)1
0.61
Green
Original
(-)
0.58
Merged
(-)
0.60
Red
Original
(-)
0.57
Merged
(-)
0.59
NIR
Original
( + )
0. OO2
Merged
(-)
0.05
NDVI
NIR and red waveband
( + )
0.37
NDVIp
NIR and pan. waveband
(+)
0.40
1
Note:
2
The (-) and (+) signs are to indicate positive and
negative correlations, respectively.
Actual value is 0.003.

'ie
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
179
Variations of image data correlation (r) between
panchromatic and original multispectral wavebands
among select groves.
Correlation coefficient (r) to pan. image
Green Red NIR
0.476
0.552
-0.387
0.675
0.757
-0.118
0.376
0.476
-0.082
0.543
0.712
-0.598
0.525
0.606
0.080
0.690
0.733
0.356
0.325
0.662
-0.089
0.666
0.696
0.413
0.754
0.692
-0.444
0.507
0.691
0.071
0.371
0.323
-0.032
0.690
0.766
-0.331
0.412
0.503
-0.326
0.677
0.698
0.207
0.266
0.353
0.226
0.313
0.200
-0.117
0.151
0.195
-0.189
0.822
0.720
0.744

180
Table 7-6. Standard deviations (a) of merged image data for
selected citrus groves.
Field#
Original data
Merged image data
standard dev. (a)
(green waveband)
(r)
( °greeri)
(CTpan)
1
0.476
0.808
1.080
1.167
2
0.675
1.399
2.183
2.312
3
0.376
0.607
1.052
1.002
4
0.543
0.832
1.407
1.401
5
0.525
1.394
2.280
2.239
6
0.690
1.990
2.843
3.205
7
0.325
0.609
1.139
1.022
8
0.666
0.956
1.347
1.542
9
0.754
0.859
1.492
1.428
10
0.507
0.913
1.380
1.462
11
0.371
0.758
0.913
1.065
12
0.690
1.197
1.877
1.963
13
0.412
0.862
1.351
1.312
14
0.677
0.949
1.537
1.596
15
0.266
0.438
0.824
0.713
16
0.313
0.484
0.751
0.783
17
0.151
1.387
1.173
1.638
18
0.822
1.337
1.650
2.087

181
Table 7-6 — continued.
Original data Merged image data
Field# standard dev. (a)
(r) (ared) (CT^) (red waveband)
1
0.552
0.875
1.080
1.299
2
0.757
1.436
2.183
2.402
3
0.476
0.600
1.052
1.037
4
0.712
1.379
1.407
1.997
5
0.606
1.585
2.280
2.469
6
0.733
2.327
2.843
3.569
7
0.662
0.869
1.139
1.351
8
0.696
0.861
1.347
1.473
9
0.692
1.101
1.492
1.631
10
0.691
1.283
1.380
1.902
11
0.323
0.710
0.913
1.017
12
0.766
1.436
1.877
2.215
13
0.503
1.015
1.351
1.489
14
0.698
0.802
1.537
1.488
15
0.353
0.964
0.824
1.184
16
0.200
0.484
0.751
0.750
17
0.195
1.209
1.173
1.506
18
0.720
0.944
1.650
1.663

182
Table 7-6 — continued.
Field#
Original data
Merged image data
standard dev. (a)
(NIR waveband)
(r)
Kir)
(apan)
1
-0.387
2.470
1.080
2.260
2
-0.118
2.573
2.183
2.708
3
-0.082
1.760
1.052
1.832
4
-0.598
1.619
1.407
1.332
5
0.080
2.355
2.280
2.736
6
0.356
2.827
2.843
3.638
7
-0.089
1.070
1.139
1.216
8
0.413
2.227
1.347
2.599
9
-0.444
1.200
1.492
1.133
10
0.071
2.189
1.380
2.400
11
-0.032
3.694
0.913
3.722
12
-0.331
1.239
1.877
1.287
13
-0.326
1.143
1.351
1.145
14
0.207
0.970
1.537
1.389
15
0.226
2.097
0.824
2.179
16
-0.117
1.352
0.751
1.377
17
-0.189
1.922
1.173
1.943
18
0.744
5.941
1.650
6.595
Note: r — correlation coefficient.
a — standard deviation with subscripts for waveband
index.

183
In summary for the differentiation of citrus canopy cover
on SPOT multiresolution images, four conclusions are reached.
First, the photogrammetric estimation of citrus canopy cover
is feasible and accurate using 1:24,000 ACIR photography. The
measurable canopy cover is considered to be within the 20-75%
range, provided that the photo scale is properly chosen (from
1:24,000 to 1:2,400). Second, the image response of the SPOT
green, red, and panchromatic wavebands indicated an inverse
relation to the difference of citrus canopy size. However, a
definable relation to citrus canopy size was not observed for
the SPOT NIR response. Third, the grove-wide spectral
response of 20-75% partial canopy fields varied significantly,
and the variation is attributed mainly to the soil substrate
variability in the summer field environment. For this reason,
it is anticipated that alternative satellite scenes acquired
in dry winter months (January and February) would allow an
improved differentiation of citrus canopy cover when the
influence of soil conditions is minimized. Fourth, due to the
influence of variable summer field environment, the
variability of image response for each individual grove can be
significantly affected by merging the panchromatic waveband
because of the large variations of correlation between the
panchromatic and multispectral images among the groves.
Land-use Classification
This section is focused on the effects of multiresolution
processing and the use of GIS techniques for improving land-

184
use classification. The analyses involved all three datasets
(OMD, MMD, and MMND) as shown in Table 6-2 and some special
attention was given to the classification of citrus land use.
To acquire land-use information from satellite datasets,
three factors must be considered. First, the image dataset to
be used must have the spatial, radiometric, and spectral
qualities to resolve and record the land-use elements in the
scene. Second, the conceivable spectral signatures inherent
in the scene environment can be extracted from the dataset
through image processing procedures. This is a very important
consideration in remote sensing land-use classification.
Third, adequate ground-truth information is available for
determining the ground actuality of generated spectral
classes.
Potential for Signature Extraction
For the three datasets (OMD, MMD, and MMND) in Table 6-2,
a summary of the statistically separable spectral signatures
unveiled by the ERDAS STATCL module is presented in Table 7-7.
These result conveys a useful assessment of the effectiveness
with which each dataset can differentiate the scene. When
used in a land-use classification process, each of these
signatures will result in one spectral class that can be
related to a land-use type/condition through a ground-truthing
process.
From the results in Table 7-7, two comments are in order.
First, a SPOT satellite scene can be differentiated to a

185
Table 7-7. Summary of spectral signatures unveiled by ERDAS
STATCL module.
Scaled-
distance
Dataset
OMD
MMD
MMND
1.0
37
63
63
tv>
•
o
26
51
17
3.0
10
21
10
Note: 1. OMD = original multispectral dataset which includes
the original three 20-m multispectral images.
2. MMD = multiresolution merged dataset generated by
the preserving approach with B=0.5 for each image.
3. MMND = multiresolution merged and NDVIp dataset
which is similar to MMD except that the merged NIR
image is replaced by the NDVIp data.

186
significantly greater extent when a multiresolution merged
dataset is used. At the scaled distance of 3.0, for example,
the original dataset (OMD) could only differentiate the SPOT
scene into 10 spectral classes, while merged dataset MMD was
able to separate it into 21 classes. This effectiveness of
dataset MMD was consistent for all three cases (Table 7-7).
The increased differentiation by dataset MMD is an irrefutable
advantage of using multiresolution merged data for land-use
classification efforts. As a result, the acguisition of
improved land-use information becomes increasingly feasible
through a multiresolution processing approach.
Second, there is a limitation in using the NDVIp image
(dataset MMND) for land-use classification applications (Table
7-7). In order to understand this limitation, three factors
must be considered. First, the NDVIp method is primarily for
vegetation enhancement and its effectiveness is limited to
vegetative areas (Chavez and MacKinnon, 1994). This will make
non-vegetative lands such as barren soils, urban lands, and
water bodies inseparable in the NDVIp image. Second, the use
of a scaling factor in the NDVIp equation to stretch the
fractional results to the possibly largest range (0-255) could
have exaggerated the radiometric information of the merged
NDVIp image. Therefore, the NDVIp standard deviation is not
a factual indication for the radiometric information present
in the original scene. Third, the study area is covered
primarily with vegetation (e.g. citrus groves, pasture lands)
while non-vegetation areas were very limited.

187
According to ERDAS (1991), using the STATCL module with
a small scaled distance will allow a tight separation to
discriminate closely related classes. For the study area
dominated by vegetative lands, this tight clustering will make
all closely related vegetation signatures distinguishable,
resulting in a large number of spectral signatures (Table 7-
7) . However, when the scaled distance was set at a larger
value, the differentiation by dataset MMND became a problem
because many originally separable signatures in a tight
classification became assimilated. In addition, the spectral
signatures for non-vegetative land-use elements are very
limited in the NDVIp image. Conseguently, only a small number
of signatures were unveiled for a scale distance of 3.0 (Table
7-7). This points out that the NDVIp image is feasible only
in a tight classification of vegetative land use types.
The results from the ELAS TMTR clustering module are
consistent with those from the ERDAS STATCL module (Table 7-
8) , though these two image processing systems have a different
implementation of the clustering technique. For example,
merged dataset MMD had either the largest number of spectral
classes for a given scaled distance or for a given number of
classes it would have the largest scaled distance between the
derived classes. These are important factors for improving
land-use classifications from satellite datasets.

188
Table 7-8. Summary of spectral signatures unveiled by ELAS
TMTR module.
Scaled-
distance
Dataset
OMD
MMD
MMND
3.00
39
58
49
3.25
36
55
37
3.50
28
48
32
3.75
27
40
27
4.00
22
35
23
4.25
21
32
19
4.50
20
30
18
4.75
18
27
17
5.00
17
24
-
5.25
15
23
16
5.50
13
21
15
Note: 1. OMD = original multispectral dataset which includes
the original three 20-m multispectral images.
2. MMD = multiresolution merged dataset generated by
the preserving approach with 6=0.5 for each image.
3. MMND = multiresolution merged and NDVIp dataset
which is similar to MMD except that the merged NIR
image is replaced by the NDVI data.

189
GIS Discrete Classification
The spectral classes generated by the GIS-based discrete
classification approach were each ground-truthed using the
estimates of canopy cover, the ACIR photography, and field
visits. For each of the three datasets of OMD, MMD, and MMND
(Table 6-2) , a summary of the ground-truth for the seven
spectral classes is provided in Table 7-9.
As indicated in Table 7-9, a spectral class of the
original dataset OMD can encompass citrus groves for a large
range of canopy size. For example, class four virtually
included every measured grove within the 20-75% canopy cover
range. This points out that a canopy-size classification of
citrus groves is very difficult using the original 20-m
multispectral dataset. When multiresolution merged datasets
MMD and MMND were used, an improvement was noted. The citrus
groves at the upper range of canopy size tended to be less
mixed with those at the lower range as indicated by the
results of merged datasets MMD and MMND (Table 7-9). When a
correlation was performed between the canopy covers and the
spectral classes in Table 7-9, the coefficient of correlation
(r2) was 0.01, 0.40, and 0.29 for datasets OMD, MMD, and MMND,
respectively. Though this improvement was not enough to
substantiate the practicality of classifying citrus groves
based on some discrete ranges of canopy size, the advantage of
using multiresolution processing is clear. The primary
difficulty is the summer field environment, which resulted in
a large variability of image data for each grove. However,

190
Table 7-9. Canopy cover for spectral classes by GIS-based
discrete classification technique.
Dataset OMDa
Spectral class
No.
Field-ID
Canopy (%)
1
2
3
4
5
6
7
1
6
19.52
X
X
2
16
26.97
X
X
3
10
28.01
X
X
4
14-1
35.25
X
X
5
15-2
36.15
X
X
X
6
15-1
40.26
X
X
7
14-2
40.88
X
X
10
8
41.27
X
X
X
8
A4
42.73
X
X
X
9
A1
44.14
X
X
11
7
52.07
X
X
12
2
52.79
X
X
13
1
56.41
X
X
X
14
A5
59.46
X
X
15
12
61.69
X
X
16
#3
64.87
X
17
9
69.15
X
X
X
18
A2
73.31
X
X
X

2
3
4
5
6
7
10
8
9
11
12
13
14
15
16
17
18
191
7-9 — continued.
Dataset MMDa
Spectral class
Field-ID
Canopy%
a
b
c
d
e
f
g
6
19.52
X
X
16
26.97
X
X
X
10
28.01
X
X
14-1
35.25
X
X
X
15-2
36.15
X
X
15-1
40.26
X
X
14-2
40.88
X
8
41.27
X
A4
42.73
X
X
X
A1
44.14
X
X
7
52.07
X
X
X
2
52.79
X
1
56.41
X
X
A5
59.46
X
X
12
61.69
X
X
#3
64.87
X
9
69.15
X
X
A2
73.31
X
X

192
Table 7-9 — continued.
Dataset MMNDa
Spectral class
No.
Field-ID
Canopy%
A
B
c
D
E
F
G
1
6
19.52
X
X
2
16
26.97
X
X
3
10
28.01
X
X
4
14-1
35.25
X
X
X
5
15-2
36.15
X
X
6
15-1
40.26
X
X
7
14-2
40.88
X
X
10
8
41.27
X
X
8
A4
42.73
X
X
X
9
A1
44.14
X
X
11
7
52.07
X
X
12
2
52.79
X
X
13
1
56.41
X
X
14
A5
59.46
X
X
15
12
61.69
X
16
#3
64.87
X
X
17
9
69.15
X
X
18
A2
73.31
X
— Refer to Table 6-2 for dataset definition.

193
further improvements are expected through the use of satellite
scenes acquired in dry winter months (January and February) to
minimize field variability.
Also indicated in Table 7-9 is that the canopy-size
differentiation by merged dataset MMND was not as effective as
one would expect. In a late summer month (October) in south
Florida orchards, miscellaneous vegetation (e.g. weeds and
grasses between rows as well as between trees) still remains
active growing in the field environment, creating the primary
source for these between-class confusions among the groves of
different canopy covers. In a canopy-size differentiation,
the miscellaneous vegetation acted as a mask for the entire
citrus land-use areas, making it difficult for the citrus
groves with different canopy covers to stand out spectrally in
the image dataset.
In summary, two comments are in order. First, there is
a clear advantage of using multiresolution processing for
land-use classification applications. For a given satellite
scene, a multiresolution merged SPOT dataset will allow the
land-use elements to be discriminated to a significantly
greater extent. This enhanced differentiation provides a
greater amount of land-use information for improving land-use
classifications. Second, though multiresolution merging has
indicated some improvement on a canopy-size classification of
citrus groves, such an effort is still difficult in practical
applications. The lack of such a differentiation for citrus

194
groves suggests that there exist other factors such as the
differences in soil substrate, tree health/growth conditions,
tree varieties, and cultural practices, which could have
played a vital role individually and/or collaborately in
affecting the canopy-size differentiation of citrus groves.
In addition, the seasonal differences in the field environment
also play a role in affecting the classification results.
Without sufficient information of ground-truth, it is
impossible to assess the impacts of these factors. Therefore,
research efforts are needed in this regard in order to gain
more understanding and to evaluate the impacts of these
factors on using satellite imagery data for regional citrus
land-use classification and monitoring.

CHAPTER 8
CONCLUSIONS AND RECOMMENDATIONS
Through the efforts undertaken in this research, several
conclusions have been reached regarding merging satellite
imagery data for image enhancement and multispectral analyses.
Some recommendations are also discussed for future research
efforts to extend the results of this research to broader
applications of satellite remote sensing.
Research Conclusions
In the context of digitally merging satellite images, the
principle of statistical variation analyses can be used as the
fundamental basis to evaluate an image merging method and to
assess the radiometric guality (variance and brightness) of
pre-merged images including those from multiresolution
datasets. The introduction of this merging principle for
combining satellite images will lead to more effective use of
remote sensing data.
Merging satellite images is not simply a mathematical
procedure. It is a transformation of radiometric information
from the combining images to the merged image data. This
radiometric transformation, which has long been overlooked,
can be utilized to benefit image processing efforts as well as
to develop new merging methods for improving remote sensing
195

196
applications. Because a satellite image is unique in that it
contains many subvariables representing the various land-use
elements throughout the entire scene and because these
subvariables will undergo a radiometric transformation in a
merging process, an increasing amount of knowledge about the
image data characteristics of various land-use types in
different spectral wavelength ranges will extend this
radiometric transformation to a broader scope of applications.
The radiometric quality of a resultant merged image depends on
(1) the data characteristics (r, a2, and /x) of the images to
be combined and (2) the method used to digitally merge the
image data. These same criteria can also be applied to
assessing the radiometric qualities of the land-use types of
interest in a merged image.
Of the three merging approaches (confining, preserving,
and differencing), the preserving method is the most effective
approach for digitally combining image data including those
with different spatial resolutions. The selection of a
merging method to achieve an image enhancement objective must
be made with consideration of the correlation and the
radiometric variance difference between the images to be
combined. To enhance the radiometric quality of merged data,
the preserving method should be used for non-negatively
correlated (r>0) images while the differencing method can only
be applied in the case where the images to be merged have a
strong negative correlation and the primary image is brighter

197
and has a greater radiometric variance. In every aspect, the
confining method is ineffective and inferior to the preserving
method. Hence, the customary use of the confining approach
for multiresolution merging should not be continued. The
preserving method with a merging coefficient (fl) of 0.5 was
found to be a very effective approach for merging SPOT
multiresolution datasets for both radiometric and spatial
enhancements.
The photogrammetric approach for citrus canopy cover
estimation is feasible and accurate using ACIR photography
with a scale no smaller than 1:24,000. The spectral response
in SPOT images was found to be inversely related to
differences in citrus canopy cover, except for the NIR
waveband. These inverse relations suggest a strong influence
of soil substrates on the spectra of partial canopy groves.
For this SPOT scene taken in the late summer (early October),
large variations of image response were observed for each
grove, suggesting that satellite scenes acquired in dry winter
months of January and February will be more feasible for
citrus canopy studies in south Florida. In general, the SPOT
image response is less variable for canopy cover greater than
40%, while citrus trees are more uniform in groves with higher
percentage of canopy cover.
Multiresolution processing of SPOT satellite images will
generate both radiometrically and spatially enhanced merged
datasets which increase the differentiation of a satellite

198
scene to a significantly greater extent. This indicates the
advantage of using multiresolution processing for improving
land-use classification. The enhanced differentiation
provides a greater amount of land-use information for remote
sensing applications. For the canopy-size classification of
citrus groves, an improvement was indicated through the
combined use of multiresolution merged SPOT dataset and GIS-
based discrete classification techniques. However, the
improvement was not enough to substantiate the practical
application of a canopy-size classification of citrus groves
without additional refinement. Nonetheless, further
improvements are anticipated from using satellite scenes
acquired in dry winter months (e.g. January and February) in
south Florida when the variability of summer field environment
is minimized. The GIS-based discrete classification technique
was very useful for eliminating the inter-class confusions
between citrus and non-citrus land-use types.
In ratioing satellite images, there are two important
considerations. First, the effectiveness of a ratioing method
relies on the selection of the numerator image. If a land-use
type is to be enhanced, the image with larger values for the
land-use type in question should be used as the numerator
image. Otherwise, it should be used as the denominator data.
Second, the feasibility of waveband ratioing depends on the
state and strength of correlation of the ratioing image data.
If a land-use element has a high positive correlation between

199
the two ratioing images, it will be extremely difficult to
enhance its radiometric quality through a ratioing approach.
In other words, successful applications of waveband ratioing
can be achieved only for those land-use types which have weak
or negative correlations between the images to be ratioed.
Recommendations
The understanding of the principle and the radiometric
transformations of merging images including waveband ratioing
provides new opportunities for using satellite image data to
improve remote sensing applications. Nonetheless, continuing
research is needed to further the efforts undertaken in this
study.
The customary approach of using the confining method for
digitally merging satellite images including those of
multiresolution datasets should be avoided because of its
ineffectiveness for radiometric and spatial enhancement. The
confining approach is currently the most commonly used merging
method for multiresolution processing and unfortunately can
only generate radiometrically inferior merged image data while
creating a great possibility of corrupting the spectral
information in a multispectral dataset.
The merging methods (preserving, differencing, and
ratioing) demonstrated in this study should be extended to
other datasets to increase the utility of current and future
remote sensing data. Through an effective data merging and

200
radiometric transformations, the collaborate utilizations of
satellite datasets including those of Landsat MSS, Landsat TM,
SPOT HRV, SPOT panchromatic, and other satellite sensors will
provide new approaches and opportunities in remote sensing
monitoring and land-use assessment applications.
Research efforts aimed at gaining an increasing amount of
knowledge about the spectral data characteristics of different
land-use types/conditions in various wavelength ranges are
crucial to the effective use of satellite image data for
broader remote sensing applications including land-use data
acguisition. These image data characteristics provides the
basis for developing more productive merging approaches while
avoiding ineffective efforts in using the remote sensing data
of current as well as future sensors.
The image data characteristics in the form of variation
and correlation for different wavebands might be of great
significance in providing additional information of the land
surface such as the soil/tree/crop/water conditions/relations
needed for many agricultural, environmental, and water
resource management applications. Therefore, research efforts
in that regard will increase both the scope and effectiveness
of collaborating remote sensing data for broader applications
while enriching our understanding of land-sensor relations,
which are vital to the continuing success of remote sensing
efforts now and in the future.

201
Because canopy cover is an important factor used in many
environmental and vegetation-related investigations, the
photogrammetric approach for canopy cover estimation needs to
be extended to other agricultural crops and forest plantations
through further research efforts. In addition, satellite
scenes acquired in the dry winter months of January and
February in south Florida should be used for citrus canopy
cover studies because the influence of soil conditions will be
minimized.

APPENDIX A
RGB COLOR DISPLAY
The RGB color system is based on the color additive
theory for the three primary colors (red, green, and blue) to
create color display. Because the color associated with a
particular object depends on the amounts of red, green, and
blue lights reflected by the object, by mixing different
proportions of the three color primaries, therefore, all the
colors can be created (Lillesand and Kiefer, 1979).
To create a color display for remote sensing data, three
images are needed and each of them represents one of the three
primary colors. When the three images are mixed together by
the display device, the result is colorful renditions for the
image data. Because human eyes can discriminate many more
colors than gray shades (Lillesand and Kiefer, 1979; Gonzalez
and Wintz, 1987) , it is an advantage for photo interpreters to
use color products.
202

APPENDIX B
IHS TRANSFORM FOR IMAGE DISPLAY
The intensity-hue-saturation (IHS) color transform is a
simulation of the process of human color perception. Unlike
the well-known RGB (red, green, and blue) color display
method, the IHS transform uses the attributes called
brightness or intensity (I) , hue (H) , and saturation (S) to
distinguish one color from another. Brightness refers to
intensity of light (Haydn et al., 1982) or illumination
(Boynton, 1980) and is associated with spatial information
(Carper et al., 1990) . A low intensity will have a relatively
dark display. Hue is an attribute associated with the
dominant wavelength in a mixture of light waves. Thus, hue
represents the dominant color as perceived by an observer.
When an object is called red, orange, or yellow, its hue is
being specified (Gonzalez and Wintz, 1987). Saturation refers
to the relative purity of hue mixed with white light. The
degree of saturation is inversely proportional to the amount
of added white light (Gonzalez and Wintz, 1987).
The IHS transform takes a two-step transformation which
includes a forward transformation from raw RGB image data to
the I, H, and S components and a reverse transformation from
the IHS components to RGB color values. In practical
implementation of the IHS transform for remote sensing data,
203

204
the forward transformation is accomplished by the following
equations (Haydn et al., 1982):
R + G + B
[ B-l ]
(G - B)/(I - 3B)
[B-l]
(I - 3B)/I
[B-3]
where R, G, B represent the image data of three spectral bands
(red, green, and blue). Then, another set of equations is
used for the reverse transformation from the I, H, and S
components to the three color values for an electronic color
display device (Haydn et al., 1982):
r = 1/3
I
(1 + 2S - 3SH)
[B-4]
g = 1/3
I
(1 - S + 3SH)
[B-5]
b = 1/3
I
(1 - S)
[B-6]
where r, g, and b respectively represent the primary colors
for red, green, and blue for a electronic color display
device. The three primary colors are used to define the
visible colors when mixed together with varying magnitude
(Haydn et al., 1982).
Several points need to be noted when using this color
model for remote sensing data display purposes. First, a
maximum of only three images can be displayed in one time.
This is a drawback for multispectral datasets with more than
three spectral wavebands. Second, the resultant (r, g, and b)
values do not have any relations to the physical importance of

205
spectral information. Therefore, the merged data can only be
used for display purpose and any multispectral analyses
related to the transformed image data will be irrelevant.
Third, the image display does not render any quantitative
information for different land-use types in the image. Such
information is totally left up to the user or photo¬
interpreter to determine. Finally, the IHS transform is only
an attempt to make display colors pleasant to the human eyes
rather than an image processing procedure which sharpens image
data (Pellemans et al., 1993).
The IHS transform method has been successfully used in
many studies (e.g. Haydn et al., 1982; Carper et al., 1990;
Grasso, 1993) that aimed at improving image interpretation
through color enhancement. However, the physiopsychological
process of human color perception is not yet fully understood
(Gonzalez and Wintz, 1987).

APPENDIX C
PROGRAM CODES TO UNPACK AVHRR LAC DATA
A Turbo-C compiler is needed to compile the following
program codes. For detailed information regarding how the LAC
data is packed, consult the TIROS manual (Kidwell, 1991). The
the 32-bit arrangement for three 10-bit pixels is as:
32 bits â– 
->l
00111111 11112222 22222233 33333333 00111111 11112222 22222233 33333333 00111111 11112222 22222233 33333333 ...
| pi 1 p2 1 p3 1 | pi 1 p2 1 p3 1 | pi 1 p2 1 p3 1...
bl b2 b3 b4 b5 bl b2 b3 b4...
Note: bl...b5 = bands 1 through 5.
pl...p3 = pixels 1 through 3.
/**** cut here, actual program codes begin next line *******/
#include
#include
#include
main() {
long Skip?
unsigned int i,Read,Line,Pixel,Count,PI,P2,P3,II,12;
unsigned int OUT[5][2050];
unsigned char IN[4],Name[25],dumy;
FILE *fin, *fout;
Name[0]=20;
printf("\n Enter input (LAC) file name : ");
fin=fopen(cgets(Name),"rb");
if(fin==NULL) return;
printf("\n Skip (7400-byte) records of input file : ");
scanf("%ld", &Skip);
Skip=Skip*7400;
if(Skip<0) return;
Name[0]=20;
printf("\n Enter output file name : ");
fout=fopen(cgets(Name),"wb");
if(fout==NULL) return;
206

207
printf("\n Begin unpacking input file .... ");
Line=Read=Pixel=Count=0;
rewind(fl);
if(Skip>0) fseek(fl,Skip,SEEK_SET);
fseek(fin,448,SEEK_CUR); /* Skip first 448 bytes */
while(!feof(fin)) {
fread(IN,1,4,fin); /* read 4-byte = 3 pixels */
Read=Read+l;
Count=Count+l;
dumy=IN[0];
Il=dumy;
11=11 « 4;
dumy=IN[l];
dumy=dumy >> 4;
I2=dumy;
Pl=(11+12)/4;
dumy=IN[1];
dumy=dumy << 4;
Il=dumy;
11=11 « 2;
dumy=IN[2];
dumy=dumy » 2;
I2=dumy;
P2=(11+12)/4;
dumy=IN[2];
dumy=dumy « 6;
Il=dumy;
11=11 « 2;
I2=IN[3];
P3=(11+12)/4;
switch(Read) {
case 1 : /* if first 4-byte */
OUT[0][Pixel]=P1;
OUT[1][Pixel]=P2;
OUT[2][Pixel]=P3;
break;
case 2 : /* if second 4-byte */
OUT[3][Pixel]=P1;
OUT[4][Pixel]=P2;
Pixel=Pixel+l;
OUT[0][Pixel]=P3;
break;

208
case 3 : /* if third 4-byte */
OUT[1][Pixel]=P1;
OUT[2][Pixel]=P2;
OUT[3][Pixel]=P3;
break;
case 4 : /* if fourth 4-byte */
OUT[4][Pixel]=P1;
Pixel=Pixel+l;
OUT[0][Pixel]=P2;
OUT[1][Pixel]=P3;
break;
case 5 : /* if fifth 4-byte */
OUT[2][Pixel]=P1;
OUT[3][Pixel]=P2;
OUT[4][Pixel]=P3;
Pixel=Pixel+l;
Read=0;
break; }
if(Count==3415) {/* if 3415 4-byte reads or one scan */
for(i=0;i<=4;i++) fwrite(OUT[i],2,2048,fout);
fseek(fin,692+488,SEEK_CUR);
Pixel=Read=Count=0; /* begin a new line */
Line=Line+l;
if(Line%100==0) printf("\n Finish line %d”,Line); }
}
clrscr();
printf("\n\n Output file is written in a band interleave by") ;
printf("\n line or BIL 8-bit data format. The entire scene");
printf("\n has %d scan lines and 5 bands.", Line);
printf("\n There are 2048 pixels per scan.\n");
fcloseall();
exit(0); )

APPENDIX D
CLASSIFICATION DECISION RULES
The classification decision rules implemented in land-use
classification procedures for satellite remote sensing
datasets have been well established and documented. These
decision rules namely include the parallelepiped classifier,
the minimum distance classifier, the mahalanobis distance
classifier, and the maximum likelihood classifier (Lillesand
and Kiefer, 1979; Thomas et al., 1987; ERDAS, 1991). A brief
discussion for each of these four classifiers is presented.
The Parallelepiped Classifier
The simplest classification decision rule is the
parallelepiped classifier. The criterion used to assign a
candidate pixel to a spectral class are based on both the
upper and lower limits of the image data values in each
waveband for the spectral class in question. If the image
data values of a candidate pixel fall between the upper and
lower limits of a spectral class in every waveband in a
multispectral dataset, the pixel is assigned to that spectral
class.
The parallelepiped classifier is the simplest as well as
the fastest among the four classifiers. But, if the image
data of a spectral class indicates some correlations between
209

210
the spectral wavebands in a dataset, the parallelepiped
boundaries defined by the upper and lower data limits (e.g. a
rectangular in a two-waveband space) is unable to adequately
describe the slanted or elongated clustering tendency of image
data of that spectral class (Lillesand and Kiefer, 1979) . In
this regard, the parallelepiped classifier is not sensitive to
the correlations of image data between spectral wavebands
within a spectral class. Because of its fast implementation,
the parallelepiped classifier is often used as a first-pass
process in a more involved classification procedure (ERDAS,
1991) such as the maximum likelihood classifier to be
discussed later.
The Minimum Distance Classifier
The minimum distance decision rule calculates, in a
multi-dimensional space bound by the spectral wavebands in a
dataset, the Euclidean distance between the vector of a
candidate pixel and the mean vector of each spectral class.
The candidate pixel is then assigned to the class to which its
Euclidean distance is the smallest. The minimum distance
decision rule takes no account for the data distributions of
different spectral classes (Lillesand and Kiefer, 1979).
Therefore, it is insensitive to the image data variations
among different spectral classes. As a result, a pixel is
more likely to be assigned to the classes which have smaller
data variations or are more closely clustered.

211
The Mahalanobis Distance Classifier
The mahalanobis distance classifier is similar to the
minimum distance classifier except that an attempt is made to
account for the image data variability by modifying the
Euclidean distances. The approach is that the calculated
Euclidean distances of a pixel in question to all spectral
classes are each divided by the image data variance of the
corresponding spectral class being evaluated. Then, the
candidate pixel is assigned to the spectral class to which it
has the smallest (modified) Euclidean distance. By this
modification, a pixel is as likely to be assigned to the
classes with a large data variability as to those with small
image data variances.
The Maximum Likelihood Classifier
The maximum likelihood classifier operates under the
assumption that the image data of each spectral waveband are
normally distributed (Gaussian distribution), which is
generally acceptable for most remote sensing datasets
(Lillesand and Kiefer, 1979). Using the image data of
training samples, a parametric statistical approach is
undertaken to prepare a multivariate probability density
function for each spectral class in a multispectral dataset
(Thamos et al., 1987). Then, the likelihood values or
probabilities for a candidate pixel to each of the spectral
classes are calculated and the candidate pixel is assigned to

212
the class to which it has the highest probability. The
determination of a candidate pixel to a spectral class is
based on the likelihood probability of that pixel rather than
on the Euclidean distance (minimum distance or Mahalanobis
distance) or the lower and upper data limits (Parallelepiped
classifier). The maximum likelihood classifier is the
slowest, but the most accurate decision rule among the
classifiers.

REFERENCES
Albertz, J.A. and K. Zelianeos. 1990. Enhancement of
satellite image data by data cumulation. ISPRS Journal
of Photogrammetry and Remote Sensing, 45:161-174.
American Society of Photogrammetry and Remote Sensing. 1990.
ASPRS accuracy standards for large-scale maps. Photog-
rammetric Engineering and Remote Sensing, 56:1068-1070.
Badhwar, G.D., J.G. Carnes, and W.W. Austin. 1982. Use of
Landsat-derived temprol profiles for corn-soybean feature
extraction and classification. Remote Sensing of
Environment, 12:57-79.
Bolstad, P.V., P. Gessler, and T.M. Lillesand. 1990.
Positional uncertainty in manually digitized map data.
Inti. J. of Geographic Information Systems, 4(4):399-412.
Boynton, R.M. 1979. Human color vision. Holt, Rinehart and
Winston, New York, NY.
Carper, W.J., T.M. Lillesand, and R.W. Kiefer. 1990. The use
of intensity-hue-saturation transformation for merging
SPOT panchromatic and multispectral image data.
Photogrammetric Engineering and Remote Sensing,
56(4):459-467.
Chavez, P.S., G.L. Berlin, and M. A. Tarabzouni. 1983.
Discriminating lithologies and surficial deposits in the
A1 Hisma plateau of Saudi Arabia with digitally combined
Landsat MSS and SIR-A images. Proc. of National
Conference on Resource Management Applications, Vol. IV-
Remotely Sensed/Geographic Information Systems in
Geologic Applications. San Francisco, CA. August 22-26.
Chavez, P.S. Jr., S.C. Sides, and J.A. Anderson. 1991.
Comparison of three different methods to merge
multiresolution and multispectral data: Landsat TM and
SPOT panchromatic. Photogrammetric Engineering and
Remote Sensing, 57(3):295-303.
Chavez, P.S. Jr. and D.J. MacKinnon. 1994. Automatic
detection of vegetation changes in the southwestern
United States using remotely sensed images.
Photogrammetric Engineering and Remote Sensing,
60(5):571-583.
213

214
Cliche, G., E. Bonn, and P. Tellet. 1985. Intergration of
the SPOT panchromatic channel into its multispectral mode
for image sharpness enhancement. Photogrammetric
Engineering and Remote Sensing, 51(3):311-316.
Coleman, T.L., L. Gudapati, and J. Derrington. 1990.
Monitoring forest plantations using Landsat thematic
mapper data. Remote Sensing of Environment, 33:211-221.
Colwell, R.N. and C.E. Poulton. 1985. SPOT simulation
imagery for urban monitoring: A comparison with Landsat
TM and MSS imagery and with high altitude color infrared
photography. Photogrammetric Engineering and Remote
Sensing, 51(8):1093-1101.
Curran, P.J. 1985. Principles of remote sensing. Longman
Inc., New York, NY.
Daily, M. 1983. Hue-saturation-intensity split-spectrum
processing of Seatsat radar imagery. Photogrammetric
Engineering and Remote Sensing, 49(3):349-355.
Daily, M.I., T. Farr, C. Elachi, and G. Schaber. 1979.
Geologic interpretation from composited radar and Landsat
imagery. Photogrammetric Engineering and Remote Sensing,
45(8):1109-1116.
Degloria, S.D., R. Bernstain, and S. DiZenzo. 1986.
Discrimination of natural and cultivated vegetation using
Thematic Mapper spectral data, in P.N. Slater, editor,
Earth Remote Sensing Using the Landsat Thematic Mapper
and SPOT Sensor Systems, Proc. SPIE 660, pp 144-150.
Dye, R. and L. Wood. 1989. Resolution improvement by multi¬
temporal data merging. ISPRS Journal of Photogrammetry
and Remote Sensing, 44:14-20.
Ehlers, M. 1989. The potential of multisensor satellite
remote sensing for geographic information systems.
Technical Papers of ASPRS/ACSM Annual Convention, 4:40-
45.
Engel, J. 1986. Land satellite (Landsat) systems: Earth
observation satellite company (EOSAT's) plans for
Landsat-6 and beyond. Earth Remote Sensing Using the
Landsat Thematic Mapper and SPOT Sensor Systems, in P.N.
Slater, editor, Earth Remote Sensing Using the Landsat
Thematic Mapper and SPOT Sensor Systems, Proc. SPIE 660,
pp 169-174.
Earth Observational Satellite (EOSAT). 1992a. Special
Landsat-6 issue, Landsat data users notes. 4300 Forbes
Blvd., Lanham, MD. 7(2):3-5.

215
1992b. Landsat technical notes, September, 1992.
4300 Forbes Blvd., Lanham, MD.
Earth Resource Data Analysis System (ERDAS). 1991. Field
guide (manual for pc version 7.5). ERDAS Inc., 2801
Buford Highway, Suite 300, Atlanta, GA 30329.
Environmental System Research Institute (ESRI). 1993.
Arc/Info manuals. Environmental and Scientific Research
Institute. Redlands, CA.
Fukushima, T. and K. Muraoka. 1988. Simple model to predict
water quality in 90 Japanese lakes. Proc. of the Inti.
Assoc, for Theorectical and Applied Limnology, 23(8):812-
827.
Gillespie, A.R., A.B. Kahle, and R.E. Walker. 1986. Color
enhancement of highly correlated images. I. Decorrelation
and HSI contrast stretches. Remote Sensing of
Environment, 20:209-235.
Gonzalez, R.C. and P. Wintz. 1987. Digital image processing,
2nd ed. Addison-Wesley Pub. Company, Reading, MA.
Graham, M.H., B.G. Junkin, M.T. Kalcic, R.W. Pearson, and B.R.
Seyfarth. 1986. Earth resources laboratory applications
software uer reference, vol. I & II., Report No. 183.
Earth Resources Laboratory, National Space Technology
Laboratories, National Aeronautics and Space
Administration.
Grasso, D.N. 1993. Applications of the IHS color
transformation for 1:24,000-scale geologic mapping: A low
cost SPOT alternative. Photogrammetric Engineering and
Remote Sensing, 59(1):73-80.
Harris, J.R., R. Murray, and T. Hirose. 1990. IHS transform
for the integration of radar imagery with other remotely
sensed data. Photogrammetric Engineering and Remote
Sensing, 56(12):1631-1641.
Haydn, R. , G.W. Dakle, J. Henkel, and J.E. Bare. 1982.
Application of the IHS color transform to the processing
of multisensor data and image enhancement. Proceedings
of the Inti. Symp. on Remote Sensing of Arid and Semi-
Arid Lands, Cairo, Egypt. January 19-25.
Huete, A.R. and Jackson. 1988. Soil and atmosphere
influenses on the spectra of partial canopies. Remote
Sensing of Environment, 25:89-105

216
Idso, S.B., R.J. Reginato, and R.D. Jackson. 1977. Albedo
measurement for remote sensing of crop yields. Nature,
266(4):625-628.
Jackson, L.K. and J. Sauls. 1983. Fruit crops fact sheet:
The sweet orange. FC-25, Inst, of Food and Agrie. Sci.,
Univ. of Florida, Gainesville, FL.
1984. Fruit crops fact sheet: Grapefruit. FC-35,
Inst, of Food and Agrie. Sci., Univ. of Florida,
Gainesville, FL.
Judd, D.B. and G. Wyszechi. 1975. Color in business, science
and industry, 3rd edition. John Wiley & Sons, Inc., New
York, NY.
Kidwell, K.B. 1991. NOAA polar obitor data (TIROS-n, NOAA-6,
NOAA-7, NOAA-8, NOAA-9, NOAA-IO, NOAA-11 & NOAA-12) users
guide. National Oceanic and Atmospheric Adaministration,
National Environmental Satellite, Data, and Information
Service, National Climatic Data Center, Satellite Data
Devision, Princeton Executive Square, Rm 100, Washington
D.C., 20233.
Lillesand, T.M. and R.W. Kiefer. 1979. Remote sensing and
image interpretation. John Wiley & Sons, Inc., New York,
NY.
Lo, T.H.C., F.L. Scarpace, and T.M. Lillesand. 1986. Use of
multitemporal spectral profiles in agricultural land-
cover classification. Photogrammetric Engineering and
Remote Sensing, 52(4):535-544.
Mendenhall, W., R.L. Scheaffer., and D.D. Wackerly. 1986.
Mathematical statistics with applications, 3rd edition.
Prindie, Weber & Schmit, Duxbury Press, PWS Engineering,
Breton Publishers, Salter Office Bldg., 20 Park Plaza,
Boston, MA.
Mood, A.M., F.A. Graybill, and D.C. Boes. 1974. Introduction
to the theory of statistics. McGray-Hill, Inc., New
York, NY.
Moore, H. 1989. SPOT vs. Landsat TM for the maintenance of
topographical databases. ISPRS J. of Photogrammetry and
Remote Sensing, 44:72-84.
Munechika, C.K., J.S. Warnick, C. Salvaggio, and J.R. Schott.
1993. Resolution enhancement of multispectral image data
to improve classification accuracy. Photogrammetric
Engineering and Remote Sensing, 59(l):67-72.

217
Novotny, V. and G. Chesters. 1981. Handbook of nonpoint
pollution sources and management. Van Nostrand Reinhold
Company, New York, NY.
Pellemans, A.H.J.M., R.W.L. Jordans, and R. Allewijn. 1993.
Merging multispectral and panchromatic SPOT images with
respect to the radiometric properties of the sensor.
Photogrammetric Engineering and Remote Sensing, 59(1) :81-
87.
Pionke, H.B. and J.B. Urban. 1985. Effect of agricultural
land use on ground-water quality in a small Pennsylvania
watershed. Ground Water, 23(l):68-80.
Piwowar, J.M., E.F. LeDrew, and D.J. Dudycha. 1990.
Integration of spatial data in vector and raster formats
in a geographic information system environment. Inti. J.
Geographical Information Systems, 4(4):429-444.
Price, J.C. 1984. Comparison of information content of data
from the Landsat-4 thematic Mapper and the Multispectral
Scanner. IEEE Trans. Geosci. Remote Sensing, GE-22:272-
281.
1987. Combining panchromatic and multispectral
imagery from dual resolution satellite instruments.
Remote Sensing of Environment, 21:119-128.
Rees, W.G. 1990. Topics in remote sensing 1: Physical
principles of remote sensing. Cambridge University
Press, New Tork, NY.
Schowengerdt, R.A. 1980. Reconstruction of multispatial
multispectral image data using frequency content.
Photogrammetric Engineering and Remote Sensing,
46(10):1325-1334.
Shih, S.F. 1984. Landsat data availability. Proc. Fla. Soil
and Crop Science Society, 43:21-25.
1988. Satellite data and geographic information
system for land use classification. J. of Irrig. and
Drainage Engineering, 114(3):505-519.
Shih, S.F., D.L. Myhre, G.J. Edwards, C.H. Blazquez, and J.M.
Gardner. 1985. Wavelength intensity indices in relation
to tree condition and leaf-nutrient content. 11th Inti.
Symp. on Machine Processing of Remotely Sensed Data, June
25-27, 1985. Purdue Univ., West Lafaytte, IN. pp.350-
356.

218
Spotlight. 1991. SPOT Image Corporation Newsletter. SPOT
Image Corporation, Reston, VA. March, 1991.
Swain, P.H. 1978. Fundamentals of pattern recognition in
remote sensing, in P.H. Swain and S.M. Davis, editors,
Remote sensing: The quantitative approach. McGraw-Hill,
Inc., New York, NY.
Systeme Probatoire de 1 'Observation de la Terre (SPOT). 1989. SPOT
user's handbook, Vols. I and II, 1st ed. SPOT Image
Corporation, Reston, VA.
Tan, Y.R. and S.F. Shih. 1991a. GIS in monitoring
agricultural land use changes and well assessment.
Trans. ASAE, 33(4):1147-1152.
1991b. Geographic errors involved in data entry of
geographic information systems. Proc. Inti. Conference
on Computer Applications in Water Resources, Taipei,
Taiwan, R.O.C., July 3-6. pp 627-634.
Thomas, I.L., V.M. Benning, and N.P. Ching. 1987.
Classification of remotely sensed images. IOP Publishing
Limitted Techno House, Redcliffe Way, Bristol BS1 6nX,
England.
Thorpe, J. 1990. The need for photogrammetry in building an
urban GIS. Photogrammetric Engineering and Remote
Sensing Florida Section, Civil Engineering Department,
University of Florida, 14(4):1-5.
Tou, J.T. and R.C. Gonzalez. 1974. Pattern recognition
principles. Addison-Wesley Pub. Company, Reading, MA.
United States Environmental Protection Agency (USEPA). 1973.
Methods for identifying and evaluating the nature and
extent of nonpoint sources on pollutants. Office of Air
and Water Programs, Washington D.C.
. 1984. Report to Congress: Nonpoint sources pollution
in the U.S. Water Planning Division, Washington D.C.
Walsh, S.J., J.W. Cooper, I.E.V. Essen, and K.R. Gallager.
1990. Image enhancement of Landsat thematic mapper data
and GIS data integration for evaluation of resources
characteristics. Photogrammetric Engineering and Remote
Sensing, 56(8):1135-1141.
Welch, R. and M. Ehlers. 1987. Merging multiresolution SPOT
HRV and Landsat TM data. Photogrammetric Engineering and
Remote Sensing, 53(3):301-303.

219
Wong, F.H. and R. Orth. 1980. Registration of Seasat/Landsat
composite images to UTM coordinates. Proc. of the 6th
Canadian Symp. on Remote Sensing, Halifax, Nova Scotia,
May 21-23.
Zobrist, A.L., R.J. Blackwell, and W.D. Stromberg. 1979.
Integration of Landsat, Seasat, and other geo-data
sources. Proceedings of the 13th Annual Symp. on Remote
Sensing of Environment, Environmental Research Institute
of Michigan, Ann Arbor, pp 271-279.

GLOSSARY
a merging coefficient for primary image.
6 merging coefficient for secondary image.
Rc merging coefficient for minimum variance in merged
image by confining method.
6d merging coefficient for equal variance in merged image
by differencing method.
/x1 mean for image one or variable one.
H2 mean for image two or variable two.
Mc mean for merged image by confining method.
/¿d mean for merged image by differencing method.
/xp mean for merged image by preserving method.
Mr mean for merged image by ratioing method.
My mean for merged image or merged variable (Y).
ay variance for image one or variable one.
a2 variance for image two or variable two.
am2 minimum variance at 6C by confining method.
ur2 variance of merged image (Yr) by ratioing method.
a.,2 normalized variance for image one or variable one.
a22 normalized variance for image two or variable two.
a 2 normalized variance for merged image or merged
variable (Y).
g_^ normalized variance for merged image (Yc) by confining
method.
o_£ normalized variance for merged image (Yd) by
differencing method.
220

normalized variance for merged image (Yp) by preserving
method.
normalized variance for merged image or variable (Y).
canopy cover (%).
canopy overlapping area.
tree spacing.
row spacing.
coefficient of variation,
tree crown diameter,
distance on photo,
focal length,
variability factor,
flying height,
hue (component).
intensity (component).
ground distance (measured from photo).
correlation coefficient,
brightness ratio,
saturation (component).
variable one or image one.
variable two or image two.
photo coordinate x for point one.
photo coordinate x for point two.
photo coordinate y for point one.
photo coordinate y for point two.
merged image or merged variable,
merged image by confining method.

222
Yd merged image by differencing method.
Yp merged image by preserving method.
Yr merged image by ratioing method.
ACIR aerial color infrared (photography).
AVHRR advanced very high resolution radiometer.
DC digital count (image gray shade).
DEM digital elevation model.
ELAS earth resource laboratory application software.
ERDAS earth resource data analysis system.
GIS geographic information systems.
GPS global positioning system.
HPF high pass filter.
HRV high resolution visible (sensor).
IHS intensity-hue-saturation (transform).
LAC local area coverage.
MI merged image.
MMD multiresolution merged dataset by the preserving
method with B=0.5.
MMND multiresolution merged and NDVIp dataset (similar to
MMD with merged NIR waveband replaced by NDVIp) .
MSS multispectral scanner.
NDVI normalized difference vegetation index.
NDVIp normalized difference vegetation index by panchromatic
waveband.
NIR near-infrared.
NOAA National Oceanographic and Atmospheric Administration.
OMD original multispectral dataset.

OMD
original multispectral dataset.
PAN panchromatic (image or aveband).
RBV return beam vidicon.
RGB red, green, and blue.
RMS root-mean-square (error).
RSAL Remote Sensing Applications Laboratory.
SAR synthetic aperture radar.
SPC state plane coordinate (system).
SPOT (French) Systeme Probatoire de 1 'Observation de la Terre.
TIR thermal infrared.
TM thematic mapper.
UTM universal transverse mercator (coordinate system)
USGS United States Geological Survey.

BIOGRAPHICAL SKETCH
The author was born and raised in a countryside in
Guangdong Province, The People's Republic of China. He
received his Bachelor of Science in Agriculture degree from
South China Agricultural University in 1982. Then he was
assigned to work as a lecturer in Nanjing Agricultural
University until 1985 when he was awarded a one-year
scholarship from the Ministry of Education of China for
studying abroad. In 1986, he was admitted to a graduate
program in the Department of Agricultural Engineering at the
University of Florida, and in 1988 he received his Master of
Engineering degree.
He continued his graduate study at the University of
Florida in 1988 and is completing all the requirements for a
Ph.D. degree in agricultural engineering.
224

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosc
Sun Fu SlYih,Chairman
Professor of Agricultural
Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Ud'uJ
Brian J. Boman
Associate Professor of
Agricultural Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Edward P.Lincoln ^
Associate Professor of
Agricultural Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Allen R. Overman
Professor of Agricultural
Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Byron E. Ruth
Professor of Civil Engineering

This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
December, 1994
Winfred M.^KiilVips
Dean, College of Engineering
Karen A. Holbrook
Dean, Graduate School