Fractal analyses of satellite data with geographic information systems in land use classification

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Fractal analyses of satellite data with geographic information systems in land use classification
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Myhre, Bruce Ernest, 1957-
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FRACTAL ANALYSES OF SATELLITE DATA WITH
GEOGRAPHIC INFORMATION SYSTEMS IN LAND USE CLASSIFICATION









By

BRUCE ERNEST MYHRE


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


1996














ACKNOWLEDGMENTS


The author wishes to acknowledge and recognize the

people involved with this project. As with any task of this

scope, there are many people without whose help this work

could not have been accomplished.

Gratitude is extended to the author's committee

members, Dr. Kenneth L. Campbell, Dr. Allen R. Overman, Dr.

Donald J. Pitts, Dr. Byron E. Ruth, Dr. Fedro S. Zazueta,

and especially to Dr. Sun Fu "Tony" Shih for support,

advice, and, when needed, prodding to continue this arduous

journey.

Also, many thanks go to Orlando Lanni, Jack Jordan,

Yurong Tan, and Chi-Hung Tan of the Remote Sensing Lab in

the Agricultural and Biological Engineering Department.

Their comments, suggestions, and general discussions on this

research are greatly appreciated.

Special thanks go to my father, Dr. Donald L. Myhre,

for his assistance, not only in this project, but throughout

my life; he gave me the inspiration and confidence to set

high goals.

Additional special thanks go to my mother, Donna Myhre,

for her assistance and guidance throughout my life.








Lastly, and most important of all, gratitude goes to my

wife, Cynthia Silvestre, for all her support, love,

patience, and friendship.














TABLE OF CONTENTS


ACKNOWLEDGMENTS ............................................... ii

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

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

ABSTRACT ...................................... .......... xvi

CHAPTERS

1 INTRODUCTION................................... ...... 1

Importance of Land Use Determination ............... .1
Classification of Satellite Images...... ............ 2
Combining Geographic Information System
Applications with Satellite Images...... ......... 5
Applications of Fractal Research................... 7
Waveband Combinations ............................... 8

2 OBJECTIVES............................................. .... 9

3 REVIEW OF LITERATURE ................................ 10
Conventional Land Use Classification Methods....... 10
Satellite-based, Land Use Classification
Methods............ .... .... ........ .... .... 10
Traditional Satellite Image Classification
Methods ....................................... 10
Land Use Classification Systems................. 11
Integration of Remote Sensing and Geographic
Information Systems ............ ................ .12
Use of Fractals in Remote Sensing and Satellite
Imagery ................. ....................... -20
Waveband Combinations.............................. .24

4 MATERIALS AND METHODS..................... ..... ...... ..... 26
SPOT Images ................................... ..... 26
Study Areas........................................ .............. 29
Image Processing System............................ 34
Geographic Information System...................... 34
Maximum Likelihood Classification Method........... 35
Fractal Dimension Calculation....... .............. 36
Variograms ...................................... 38
Fourier Power Spectrum......................... 40
Walking-Divider............. ............. ............ 41
Triangular Prism Surface........................ 41








Robust Fractal Estimator.................... ...42
Fractal Shape Calculation..................... ..46
Statistical Analyses.................... ......... 48
Use of Different Pixel Groupings................... 49
Unique Area-Perimeter Combinations .............. 49
Using Different Cell Sizes...................... 50
Spectral Reflectance and Waveband Combinations.....50
Normalized Difference Vegetation Index.......... 50
Proposed Fractal Analyses............................ 53
Historical Fractal Analyses.................... 53
New Fractal Analyses ........................... 54

5 RESULTS AND DISCUSSION ................................ 55

Conventional Classification of SPOT Images......... 55
Spatial Distribution of Land Uses............... 62
Fractal Dimension by Class and Land Use............ 66
Class Analysis .................................. 66
Land Use Analysis............................... 70
Fractal Shape by Class and Land Use................ 82
Class Analysis.................................. 82
Land Use Analysis ............................... 83
Unique Area-Perimeter Combinations................. 90
Fractal Dimension Analysis...................... 90
Fractal Shape Analysis.......................... 99
Using Different Cell Sizes........................ 107
Fractal Dimension Analysis..................... 107
Fractal Shape Analysis......................... 114
Mean Spectral Reflectance versus Fractal
Parameters ..................................... 118
Waveband Combinations versus Fractal Parameters...128
Normalized Difference Vegetation Index......... 128
Other Band Combinations........................ 137

6 CONCLUSIONS, RECOMMENDATIONS, AND FUTURE WORK....... 146
Conclusions......................................................... 146
Recommendations....................................... 150
Future Work................................. ....... 151

GLOSSARY.................................................. 153

REFERENCES ................................. 999. ....... 155


APPENDICES

A ELAS SPECTRAL CLASSIFICATION CALCULATIONS........... 163

B ELAS RESAMPLING METHODOLOGY......................... 168

C FRACTAL DIMENSION VERSUS FRACTAL SHAPE FOR THE
HASTINGS, PALATKA, AND SEVILLE STUDY AREAS..... 171








D FIGURES SHOWING THE EFFECT OF CELL SIZE ON
FRACTAL PARAMETERS FOR PALATKA AND SEVILLE
STUDY AREAS............................................... ... 178

E FIGURES OF SPECTRAL REFLECTANCE VERSUS FRACTAL
PARAMETERS FOR PALATKA AND SEVILLE STUDY AREAS...... 191

F FIGURES OF WAVEBAND COMBINATIONS VERSUS FRACTAL
PARAMETERS FOR PALATKA AND SEVILLE STUDY AREAS...... 204

BIOGRAPHICAL SKETCH....................................................229














LIST OF TABLES


Tables Page

1-1 A comparison of Landsat, SPOT, NOAA, GOES, and TIROS
satellite characteristics............................ 3

3-1 Florida land use, cover, and landform classification
scheme for remote sensing data....................... 13

4-1 Universal Transverse Mercator (UTM zone 19) boundary
coordinates for Hastings, Palatka, and Seville
study areas .......................................... 33

4-2 Fractal dimension by Landsat band for three land
uses ................................................. 45

4-3 Waveband combinations and ratios ..................... 52

5-1 Land use descriptions for SPOT images................ 56

5-2 Land use spectral classes for SPOT image 619-290.....58

5-3 Land use spectral classes for SPOT image 619-291.....59

5-4 Spatial distribution of land use areas for SPOT
image 619-290....... .................................. 63

5-5 Spatial distribution of land use areas for SPOT
image 619-291............................................ 64

5-6 Spatial distribution of land use areas for combined
SPOT images 619-290 and 619-291......................65

5-7 Fractal dimension and fractal shape for 59 spectral
classes for Hastings, Palatka, and Seville study
areas ........................................... .... 68

5-8a Fractal dimension and fractal shape for eight land
uses for the Hastings study area.....................71

5-8b Fractal dimension and fractal shape for eight land
uses for the Palatka study area ...................... 72

5-8c Fractal dimension and fractal shape for eight land
uses for the Seville study area......................73








5-9 Area and perimeter statistics for Hastings,
Palatka, and Seville study areas.................... 77

5-10a Fractal dimensions for eight land use categories
using area-perimeter combinations which include
either all data, unique data, or data of areas
greater than three pixels for the Hastings
study area......................... ................. 91

5-10Ob Fractal dimensions for eight land use categories
using area-perimeter combinations which include
either all data, unique data, or data of areas
greater than three pixels for the Palatka
study area .......................................... 92

5-0lOc Fractal dimensions for eight land use categories
using area-perimeter combinations which include
either all data, unique data, or data of areas
greater than three pixels for the Seville
study area.......................................... 93

5-11a Fractal shape for eight land use categories
using area-perimeter combinations which include
either all data, unique data, or data of areas
greater than three pixels for the Hastings
study area....................... ..................... 100

5-lib Fractal shape for eight land use categories
using area-perimeter combinations which include
either all data, unique data, or data of areas
greater than three pixels for the Palatka
study area................................................. 101

5-lic Fractal shape for eight land use categories
using area-perimeter combinations which include
either all data, unique data, or data of areas
greater than three pixels for the Seville
study area.............................................. 102

5-12 Mean reflectance of channel 1 (green), channel 2
(red), and channel 3 (infrared) for eight land
uses in the Hastings area ..........................119

5-13 Normalized difference vegetation index (standard,
revised, and modified revised) for eight land
uses in the Hastings area.......................... 129

5-14 Comparison of three waveband combinations for
enhancement of the spectral image of land
use in the Hastings study area..................... 138


viii













LIST OF FIGURES


Figure Page

4-1 Location of SPOT images............................. 27

4-2 Hastings, Palatka, and Seville quadrangle locations.28

4-3 Photograph of Hastings quadrangle map
(reduced scale) ............................................... .30

4-4 Photograph of Palatka quadrangle map
(reduced scale) ..............................................31

4-5 Phtograph of Seville quadrangle map
(reduced scale) ........................................ 32

5-1 SPOT Image 619-290 land use classes.................60

5-2 SPOT Image 619-291 land use classes .................61

5-3 Fractal dimension versus land use for the Hastings
study area ......................................... 74

5-4 Fractal dimension versus land use for the Palatka
study area .....................................................75

5-5 Fractal dimension versus land use for the Seville
study area..................................... ......76

5-6 Fractal shape versus land use for the Hastings
study area ........................................ 84

5-7 Fractal shape versus land use for the Palatka
study area............................................. 85

5-8 Fractal shape versus land use for the Seville
study area......................................... 86

5-9 Fractal dimension for unique area-perimeter
combinations for the Hastings study area............95

5-10 Fractal dimension for unique area-perimeter
combinations for the Palatka study area.............96

5-11 Fractal dimension for unique area-perimeter
combinations for the Seville study area.............97








5-12 Fractal shape for unique area-perimeter
combinations for the Hastings study area...........103

5-13 Fractal shape for unique area-perimeter
combinations for the Palatka study area............ 104

5-14 Fractal shape for unique area-perimeter
combinations for the Seville study area............ 105

5-15a Fractal dimension versus minimum number of pixels
for the Hastings study area for pine and hardwoods
land use ........................................... 110

5-15b Fractal dimension versus minimum number of pixels
for the Hastings study area for pasture, clearings,
and row crop land use.............................. 111

5-15c Fractal dimension versus minimum number of pixels
for the Hastings study area for urban, water, and
marsh/shadehouse land use .......................... 112

5-16a Fractal shape versus minimum number of pixels for
the Hastings study area for pine and hardwoods
land use.......................................... 115

5-16b Fractal shape versus minimum number of pixels for
the Hastings study area for pasture, clearings,
and row crop land use.............................. 116

5-16c Fractal shape versus minimum number of pixels for
the Hastings study area for urban, water, and
marsh/shadehouse land use .......................... 117

5-17 Fractal dimension versus mean reflectance of band 1
(green) for the Hastings study area................. 120

5-18 Fractal dimension versus mean reflectance of band 2
(red) for the Hastings study area................... 121

5-19 Fractal dimension versus mean reflectance of band 3
(infrared) for the Hastings study area.............. 122

5-20 Fractal shape versus mean reflectance of band 1
(green) for the Hastings study area ................. 125

5-21 Fractal shape versus mean reflectance of band 2
(red) for the Hastings study area ...................126

5-22 Fractal shape versus mean reflectance of band 3
(infrared) for the Hastings study area.............. 127

5-23 Fractal dimension versus normalized difference
vegetative index (NDVI) for the Hastings study area.130









5-24 Fractal dimension versus revised normalized
difference vegetative index (NDVI) for the
Hastings study area ................................... 131

5-25 Fractal dimension versus modified revised normalized
difference vegetative index (NDVI) for the Hastings
study area ....................................... .... 132

5-26 Fractal shape versus normalized difference
vegetative index (NDVI) for the Hastings
study area .......................................... 134

5-27 Fractal shape versus revised normalized difference
vegetative index (NDVI) for the Hastings
study area .......................................... 135

5-28 Fractal shape versus modified revised normalized
difference vegetative index (NDVI) for the Hastings
study area ............................................ 136

5-29 Fractal dimension versus infrared/red (IR/R) for
the Hastings study area ............................. 139

5-30 Fractal shape versus infrared/red (IR/R) for the
Hastings study area................................. 140

5-31 Fractal dimension versus infrared red (IR-R) for
the Hastings study area ............................. 141

5-32 Fractal shape versus infrared red (IR-R) for
the Hastings study area ............................. 142

5-33 Fractal dimension versus red/green for the
Hastings study area..................................... 143

5-34 Fractal shape versus red/green for the
Hastings study area......................... .......... 144

C-i Fractal dimension versus fractal shape for the
Hastings study area using 59 class image............ 172

C-2 Fractal dimension versus fractal shape for the
Palatka study area using 59 class image.............173

C-3 Fractal dimension versus fractal shape for the
Seville study area using 59 class image............. 174

C-4 Fractal dimension versus fractal shape for the
Hastings study area using 8 land use image.......... 175

C-5 Fractal dimension versus fractal shape for the
Palatka study area using 8 land use image........... 176










C-6 Fractal dimension versus fractal shape for the
Seville study area using 8 land use image........... 177

D-1 Fractal dimension versus minimum number of pixels
for the Palatka study area for pine and hardwoods
land use........................................... 179

D-2 Fractal dimension versus minimum number of pixels
for the Seville study area for pine and hardwoods
land use....................... .. ........................ 180

D-3 Fractal dimension versus minimum number of pixels
for the Palatka study area for pasture, clearings,
and row crop land use..................... .............. 181

D-4 Fractal dimension versus minimum number of pixels
for the Seville study area for pasture, clearings,
and row crop land use....................................... .. 182

D-5 Fractal dimension versus minimum number of pixels
for the Palatka study area for urban, water, and
marsh/shadehouse land use ........................... 183

D-6 Fractal dimension versus minimum number of pixels
for the Seville study area for urban, water, and
marsh/shadehouse land use.......................... 184

D-7 Fractal shape versus minimum number of pixels for
the Palatka study area for pine and hardwoods
land use............................................ 185

D-8 Fractal shape versus minimum number of pixels for
the Seville study area for pine and hardwoods
land use ..................................... .......... 186

D-9 Fractal shape versus minimum number of pixels for
the Palatka study area for pasture, clearings, and
row crop land use................................... 187

D-10 Fractal shape versus minimum number of pixels for
the Seville study area for pasture, clearings,
and row crop land use........................ ....... ..... 188

D-11 Fractal shape versus minimum number of pixels for
the Palatka study area for urban, water, and
marsh/shadehouse land use ........................... 189

D-12 Fractal shape versus minimum number of pixels for
the Seville study area for urban, water, and
marsh/shadehouse land use........................... 190
E-1 Fractal dimension versus mean reflectance of band 1
(green) for the Palatka study area..................192

xii










E-2 Fractal dimension versus mean reflectance of band 1
(green) for the Seville study area.................. 193

E-3 Fractal dimension versus mean reflectance of band 2
(red) for the Palatka study area.................... 194

E-4 Fractal dimension versus mean reflectance of band 2
(red) for the Seville study area................... 195

E-5 Fractal dimension versus mean reflectance of band 3
(infrared) for the Palatka study area .............. 196

E-6 Fractal dimension versus mean reflectance of band 3
(infrared) for the Seville study area............... 197

E-7 Fractal shape versus mean reflectance of band 1
(green) for the Palatka study area.................. 198

E-8 Fractal shape versus mean reflectance of band 1
(green) for the Seville study area.................. 199

E-9 Fractal shape versus mean reflectance of band 2 (red)
for the Palatka study area..........................200

E-10 Fractal shape versus mean reflectance of band 2 (red)
for the Seville study area......................... 201

E-11 Fractal shape versus mean reflectance of band 3
(infrared) for the Palatka study area............... 202

E-12 Fractal shape versus mean reflectance of band 3
(infrared) for the Seville study area...............203

F-i Fractal dimension versus normalized difference
vegetative index (NDVI) for the Palatka study area..205

F-2 Fractal dimension versus normalized difference
vegetative index (NDVI) for the Seville study area..206

F-3 Fractal dimension versus revised normalized
difference vegetative index (NDVI) for the Palatka
study area .......................................... 207

F-4 Fractal dimension versus revised normalized
difference vegetative index (NDVI) for the Seville
study area .......................................... 208

F-5 Fractal dimension versus modified revised normalized
difference vegetative index (NDVI) for the Palatka
study area .......................................... 209


xiii









F-6 Fractal dimension versus modified revised normalized
difference vegetative index (NDVI) for the Seville
study area .......................................... 210

F-7 Fractal dimension versus infrared/red (IR/R) for
the Palatka study area..................... ............. .. 211

F-8 Fractal dimension versus infrared/red (IR/R) for
the Seville study area......... ................... .. 212

F-9 Fractal dimension versus infrared red (IR-R) for
the Palatka study area............................. 213

F-10 Fractal dimension versus infrared red (IR-R) for
the Seville study area .............................. 214

F-li Fractal dimension versus red/green for the
Palatka study area.......... ....................... 215

F-12 Fractal dimension versus red/green for the
Seville study area................................ .216

F-13 Fractal shape versus normalized difference vegetative
index (NDVI) for the Palatka study area.............217

F-14 Fractal shape versus normalized difference vegetative
index (NDVI) for the Seville study area............. 218

F-15 Fractal shape versus revised normalized
difference vegetative index (NDVI) for the Palatka
study area .......................................... 219

F-16 Fractal shape versus revised normalized
difference vegetative index (NDVI) for the Seville
study area.............. ............ ......... ....... 220

F-17 Fractal shape versus modified revised normalized
difference vegetative index (NDVI) for the Palatka
study area .......................................... 221

F-18 Fractal shape versus modified revised normalized
difference vegetative index (NDVI) for the Seville
study area....................... .................. 222

F-19 Fractal shape versus infrared/red (IR/R) for
the Palatka study area..................................... 223

F-20 Fractal shape versus infrared/red (IR/R) for
the Seville study area........... *............. .... 224

F-21 Fractal shape versus infrared red (IR-R) for
the Palatka study area.................... .......... 225


xiv










F-22 Fractal shape versus infrared red (IR-R) for the
Seville study area................................... 226

F-23 Fractal shape versus red/green for the Palatka
study area......................................... 227

F-24 Fractal shape versus red/green for the Seville
study area .......................................... 228














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

FRACTAL ANALYSES OF SATELLITE DATA WITH
GEOGRAPHIC INFORMATION SYSTEMS IN LAND USE CLASSIFICATION

by

Bruce Ernest Myhre

December 1996

Chairman: Sun-Fu Shih
Major: Agricultural and Biological Engineering

The major objective of this research was to apply the

conventional fractal dimension technique and new fractal

shape technique using old and new pixel groupings for

improvement of land use classification of satellite images.

Relationships were developed for mean reflectance and

waveband combinations/ratios with fractal parameters. Two

SPOT scenes from May 1988 were selected for analysis. Three

subsets were selected for study areas to show the range of

different land uses for the three quadrangle areas of

Hastings, Palatka, and Seville, Florida. The SPOT images

were classified by use of ELAS software. The fractal

dimension and fractal shape were used to distinguish 59

different spectrally separate classes and eight land uses

which resulted from the maximum likelihood classification.

The fractal dimension and fractal shape for a set of areas

were statistically calculated. The mean, standard deviation


xvi









(SD), and coefficient of variation (CV) were used to compare

the fractal dimension and fractal shape of the spectral

classes and land uses.

First, differentiating among land uses was improved by

using eight land uses instead of 59 classes. Second, an

inverse relationship existed between the fractal dimension

and the fractal shape. Third, when using all the area-

perimeter data combinations, the fractal dimension technique

was successful in differentiating among most land uses.

Fourth, the fractal dimension technique was improved by

using either an area-perimeter combination only once (unique

data) for a given land use, or by using areas greater than

three pixels. Fifth, the newly developed fractal shape

technique maximized differentiation among land uses, and was

further improved by using unique data as compared with the

fractal dimension. Sixth, the relative rank among land uses

is identical for green and red wavebands, with reflectance

highest for urban and lowest for water. Seventh, the red

channel may be the superior channel for differentiating

among land uses. Eighth, the new revised normalized

difference vegetation index (NDVI) methods are slightly better

than the standard NDVI method for land use classification.

Ninth, the new revised NDVI and the infrared band minus red

band with fractal shape are superior for maximizing

differentiation among land uses.


xvii














CHAPTER 1
INTRODUCTION


Importance of Land Use Determination


The need for land use determination is wide and varied.

Land use is an important parameter in environmental studies.

These studies include water quantity and quality management

research which has gone into the modeling and quantifying of

non-point source pollution (Beasley, 1977; Haan et al., 1982;

Marani and Delluer, 1986; and Zhang et al., 1990). In general,

land use and land use activities can be partially correlated

to non-point source pollution (Novotny and Chesters, 1981).

Therefore, a strong need exists to identify the amount and

spatial extent of different land uses for hydrologic analysis.

Many existing hydrologic/water quality models (CREAMS,

AGNPS, and others) use the Soil Conservation Service runoff

equations (SCS, 1972). Additionally, the Universal Soil Loss

Equation (USLE) is very popular for erosion modeling. Both of

these equations are dependent on land use; therefore, to

successfully predict water quantity or quality land use must

be determined.

Other environmental studies requiring land use

information include wetland assessment (Still and Shih, 1991),

ecotone analysis (Johnson and Bonde, 1989), and temporal

shifting of agriculture (Williams and Shih, 1989; and Tan and








2

Shih, 1990). Soil moisture estimates using Landsat data have

been in part based on land use (Shih and Jordan, 1992 and

1993).

Land use information is also very important in forestry

applications. Locations of clear cut areas, forest

inventories, deforestation of developing countries and the

spatial extent of forest fires have been studied with land use

playing a very important role. These studies include Lachowski

et al., 1979; Strahler, 1981; Johnston, 1987; and Hudson,

1991.

Land use classification systems include the United

States Geological Survey system (Anderson et al., 1976);

Florida Department of Transportation system (Kuyper et al.,

1981); and Florida Land Use/Cover Classification system

(FLUCCS). The latter two are designed for applications in

Florida.


Classification of Satellite Images


The beginning of using satellites for remote sensing

devices began in 1972 with the launch of what was to become

the United States Landsat series. Since then other satellites

have been used for different types of remote sensing systems

(see Table 1-1). The Landsat and French Systeme Probatoire










Table 1-1.


A comparison of Landsat, SPOT, NOAA, GOES, and
TIROS satellite characteristics.


Band Spectral Spatial
Satellite Sensor designation Range Resolu-
tion
2
ym m
Landsat Return Beam Band 1 0.475-0.575 76
1,2 Vidicom (RBV)
Band 2 0.580-0.680 76
Band 3 0.690-0.830 76
Multispectral Band 4 0.5-0.6 76
Scanner (MSS)
Band 5 0.6-0.7 76
Band 6 0.7-0.8 76
Band 7 0.8-1.1 76


Landsat 3 RBV
MSS


Landsat Thematic
4,5 Mapper (TM)


Two Cameras 0.505-0.750
Band 4 0.5-0.6
Band 5 0.6-0.7
Band 6 0.7-0.8
Band 7 0.8-1.1
Band 8 10.4-12.6
Band 1 0.45-0.52


Band 2
Band 3
Band 4
Band 5
Band 6
Band 7


0.53-0.61
0.62-0.69
0.78-0.91
1.57-1.78
10.42-11.66
2.08-2.35


40
76
76
76
76
234
30

30
30
30
30
120
30










-- continued.


Satellite Sensor Band Spectral Spatial
designation Range Resolu-
tion
Lam mn
MSS Band 1 0.5-0.6 76
Band 2 0.6-0.7 76
Band 3 0.7-0.8 76
Band 4 0.8-1.1 76
SPOT Panchromatic 0.51-0.73 10
Band 1(green) 0.50-0.59 20
Band 2(red) 0.61-0.68 20
Band 3 0.79-0.89 20
(infrared)
GOES E/W Visible 0.66-0.7 7000
Thermal 10.5-12.6 7000
IR
TIROS 9- APT AVHRR 1 0.55-0.90 4000
14
AVHRR 2 0.725-1.10 4000
AVHRR 4 10.50-11.50 4000


Table 1-1.








5

pour l'Oberservation de la Terre (SPOT) satellites are most

frequently used in land use classification.

Traditional methods of satellite classification include

supervised and unsupervised classification schemes. The

methods usually involve statistically manipulating raw and/or

processed satellite digital numbers. The most popular of

these methods encompass minimum distance to means,

parallelepiped, and maximum likelihood classifiers.

These classification systems provide the link between

the satellite reflectance data and land use classification.

The importance of satellite classification is its ability to

spatially determine land use (and/or other important

environmental factors such as soil moisture or geologic

substratum).


Combining Geographic Information System Applications
with Satellite Images


The ability to integrate different types of data from

many sources can be a very powerful tool. One area of

importance for water resources studies is the link between

remotely sensed data and geographical information systems

(GIS). Currently the interface between remote sensing systems

and GIS is still weak, and many problems must be solved before

the combination becomes widely available.








6

The term GIS is relatively new. However, the concepts

GIS employs are both old and new. The concept of GIS is to

relate spatial data to informational databases. The modern

component of the GIS is the computer system.

A complete GIS should have computer hardware,

application software, and a proper organizational context

(Burrough, 1986; and Shih, 1988). The hardware components

include a digitizer (for input), a CPU, disk and/or tape

drives, a monitor, and a plotter (for output). The software

should be capable of manipulating the various hardware

components. An efficient organization will have a management

system that effectively communicates with the rest of the GIS.

The data structure of a GIS can be based on either a

raster or vector format. A raster format is a simple matrix of
"x" and "y" coordinates with an appropriate relational

database for each pixel. A vector format consists of lines (or

arcs), points, and areas (or polygons).

Lines are often used to represent roads, canals, etc.,

while areas are used to represent regions that are homogeneous

for a single attribute. Points can be used to represent wells,

sewer holes, etc.

Database files are used to relate the geographic and

attribute data. The attributes are artificial descriptors

assigned by the user or others (i.e., soil type, land use,

elevation, tax status, etc.).










Applications of Fractal Research


The concept of fractals is relatively new, being defined

by Mandelbrot in 1967. Simply stated, the fractal dimension

of a phenomena is a measure of randomness or variability.

This dimension is different from the traditional dimension of

Euclidian geometry.

Application of fractals range from stream networks

(Tarboton et al., 1988) to economics (Mandelbrot, 1970; and

1977) to satellite images (Lovejoy, 1982; and Lam, 1990).

From this one can see the variety of applications possible

with fractals.

Another property of fractals is self-similarity. This

means that the fractal dimension does not vary with scale,

thus the fractal dimension will be the same regardless of the

unit of measure. In the area of hydrology this concept was

applied to a drainage basin area and main river length (Hack,

1957). This study showed the ratio of (length/area)06 to be

consistent over a large range of scales.

The use of fractals in satellite classification of land

use has been sparse to date (Ramstien and Raffy, 1989; De

Cola, 1989; and Lam, 1990). These studies and others

represent a beginning upon which this research will start.

Thus, a need exists to further develop fractal applications.









Waveband Combinations


The use of waveband combinations and/or ratios (CR) is

done for spectral and spatial enhancement and separability

of remote sensing images. Many different combinations have

been devised (Lillisand and Keifer, 1987; Lo, 1986; Huete

and Jackson, 1988; and Kidwell, 1991). These combinations

are often trial and error procedures with some combinations

being used more widely, most notably the normalized

difference vegetation index (NDVI). The NDVI is used for

enhancement of different types of vegetation (Lillisand and

Keifer, 1987; and Shih, 1994). The relationship between

waveband CR and fractal parameters has not been explored to

this point. This research will examine this area.













CHAPTER 2
OBJECTIVES


The main objective of this research is to apply fractal

techniques for land use classification of a SPOT satellite

image. The specific objectives are as follows:

1. To classify a SPOT image using conventional methods for

land use classification;

2. To determine the conventional fractal parameter (i.e.,

the fractal dimension) for different land uses;

3. To define a new fractal parameter (i.e., the fractal

shape) for different land uses and to compare it with

the fractal dimension;

4. To evaluate the impact of using different pixel

groupings on the fractal dimension and fractal shape;

5. To develop a relationship between mean reflectance and

fractal parameters for improving land use

classification;

6. To develop a relationship between existing and new

waveband combinations and/or ratios (CR), and fractal

parameters for further improving land use

classification;

7. To evaluate the performance of methods in objectives 5

and 6.













CHAPTER 3
REVIEW OF LITERATURE


Conventional Land Use Classification Methods


Traditionally land use is classified by aerial

photographs, ground surveys or a combination of both. This

involves creating a mosaic of the aerial photographs (often

color infrared photographs are used) and relating this to

known land uses (Baker et al., 1979; and Campbell, 1983).

This is done through use on ancillary information such as

field checks, soils maps, tax documents, and similar

literature.

The resultant land use areas are then transferred to a

base map through the use of a zoom transfer scope or

digitizer. Areas for each land use can then be determined by

a planimeter or computer programs.


Satellite-based, Land Use Classification Methods


Traditional Satellite Image Classification Methods


Image processing methods have been available since the

development of environmental satellites such as Landsat, and

have included many applications in land use classification.

The advantages of satellites over aerial photography are the







11

availability of repetitive coverage, wide coverage area, and

cost effectiveness (Lo, 1986).

The classification process involves geometric

correction, radiometric manipulations, and statistical

classification. Geometric corrections are needed to adjust

for the spacecraft movement and tilt and the earth's movement.

Radiometric manipulations are done to enhance certain features

or bands within the images. The statistical classifications

are minimum distance to means, parallelepiped, and maximum

likelihood classifier.

These different methods group the image pixels together

into different classes. A-priori information is assigned to

the data through training sets. The classes are then combined

by a supervised or unsupervised (or a combination of both)

methods. This allows the classes to be based solely on

spectral separability.


Land Use Classification Systems


Classification of remote sensing data by land use is

commonly through the use of the Anderson classification system

(Anderson et al., 1976). This system, devised for the United

States Geological Survey, divides land use into different

levels of increasingly specific land use. While this system

is used on many remote sensing applications, many projects use

modifications of the Anderson system.








12

The Anderson system was developed to meet the following

criteria: (1) 85% classification accuracy; (2) equal accuracy

for each class; (3) repeatability; (4) applicable over

extensive areas; (5) categorization permitting land cover to

be used as a surrogate for activity; (6) usable with satellite

data from different times; (7) integration with ground survey

data or large scale remote sensor data possible through use of

sub-categories; (8) aggregation of categories; (9) comparison

with future data; and (10) multiple uses of land recognizable.

The Anderson system is the most widely used classification

scheme and its adaptation to Florida by Kuyper, et al. (1981)

is shown for Levels I and II in Table 3-1.


Integration of Remote Sensing and
Geographic Information Systems


The merging of photogrammetry, remote sensing, GIS, and

related technologies was addressed by the International

Society for Photogrammetry and Remote Sensing (ISPRS) (Welch,

1988; and Shih, 1990). The working group for the ISPRS was

formed in 1985 and held its first symposium in conjunction

with the American Society of Photogrammetists and Remote

Sensors/American Congress on Surveying and Mapping

(ASPRS/ACSM) convention in April 1987.









Table 3-1. Florida land use, cover, and landform
classification scheme for remote sensing data
(Kuyper et al., 1981).


Major Land Use Land Use Land Use Description
Number

Urban And Built-Up 110 Residential, Low Density
120 Residential, Medium Density
130 Residential, High Density
140 Commercial and Services
150 Industrial
160 Extractive
170 Institutional
180 Recreational
190 Open Land
Agricultural 210 Cropland and Pastureland
220 Tree Crops
230 Feeding Operations
240 Nurseries and Vineyards
250 Specialty Farms
260 Other Open Lands
Rangeland 310 Herbaceous
320 Shrub and Brushland
330 Mixed Rangeland
Forestland 410 Coniferous Forest
420 Hardwood Forest
430 Hardwood Forest (continued)
440 Tree Plantation
Water 510 Streams
520 Lakes
530 Reservoirs
540 Bays and Estuaries
550 Major Springs
560 Slough Waters
Wetlands 610 Hardwood Forest
620 Coniferous Forest
630 Forested-Mixed
640 Vegetated Non-Forested
650 Non-Vegetated
Barren Lands 710 Beaches other than Swimming
Beaches
720 Sand other than Beaches
730 Exposed Rock
740 Disturbed Lands
Transportation, 810 Transportation
Communication, and 820 Communication
Utilities 830 Utilities








14

The merging of remotely sensed data into GIS can be

accomplished by three different methods (Curran, 1985). The

first method converts all data (remotely sensed and otherwise)

into polygon layers. These layers are then overlaid for

importation into the GIS.

The second method keeps the remotely sensed data in a

raster format. The data are converted into geo-referenced

thematic maps and inserted with other necessary data into the

geographically registered GIS database.

The third method omits the conversion of remotely sensed

data into thematic maps and inserts input data directly into

the registered GIS. Systems that at present attempt to use one

of these three methods to merge remotely sensed data and GIS

include ODYSSEY, GIRAS, IBIS, and ARC/INFO-ERDAS (Lo, 1986).

Several problems exist when integrating remotely sensed

data and GIS. One problem involves regions of high topographic

relief. In this case, displacement of polygons from the

remotely sensed data will occur and thus a digital terrain

model (DTM) must be employed (Goodenough, 1988).

Another possible problem is distortion/displacement due

to the conversion of raster satellite data to GIS vector data.

Also, attributes associated with the GIS vector database

present a problem. Thus, should one simply let the GIS

determine the appropriate attribute assignments, or should the

user manually determine these assignments through a given







15

procedure? Another solution is to let the spatial attribute

values at the center of the raster cell determine the

characteristics. Barker (1988) illustrates this raster-to-

vector and vector-to-raster problem.

The overlaying of data sets with different scales

presents a problem somewhat similar to that caused by raster-

to-vector conversion. The similarity comes from the fact that

distortions can occur, but the solution to this problem

involves the choice of automatic or manual rectification.

Finally, the classification accuracy and positional

accuracy of the remote sensing data are often not comparable

with those of other data in the GIS (Marble and Peuquet, 1983;

Ehlers et al., 1989; and Ehlers, 1989). Thus, for any

calculations made within the GIS, the largest errors will be

attributable to the remote sensing data. However, the larger

the study area, the less influence these errors will have on

GIS calculations.

The calculation of SCS runoff curve numbers was the

focus of a study by Berich and Smith (1985). Two Landsat

scenes taken 10 years apart were used as the basis for land

cover analysis. ERDAS software was used to resample the

landcover data (originally 60 m x 80 m) to 61 m x 61 m. This

was done in order to match the soil-type and zoning data which

were also used. The GIS in that study was IRIS, which is a








16

raster format system. Thus, each cell in GIS was set to

correspond with the resolution of the soils/zoning data.

Williams and Shih (1989) studied the land use change

within the Florida Everglades Agricultural Area (EAA) using

Landsat images captured 13 years apart. They achieved a Level

I classification of the data and used the Earth Resources

Laboratory Applications Software (ELAS) GIS to analyze the

data. They discerned that agricultural development was moving

southeast toward the water conservation area of the EAA.

In another study, Shih (1989) was able to achieve a

Level I classification of land use from Landsat data using the

ELAS GIS. A 100 m2 cell size was used in that analysis.

The classification of SPOT imagery in conjunction with a

GIS was used by Jadkowski and Ehlers (1989) to study the

growth of an urban/suburban area. They used a raster-based GIS

to overlay SPOT land use/land cover with zoning maps.

Vegetation change detection using Landsat data was

performed by Jakubauskas (1989). He used images from 1973 and

1982 to analyze the impact of a forest fire on the spatial

extent of different tree species. The raster based GIS used

matrix manipulations to analyze the classified digital data

for changes that occurred over time.

Jampoler and Haack (1989) used aerial photography,

Landsat and SPOT imagery within a GIS framework to analyze

land use change, deforestation, slope failures, and soil








17

suitability. Their use of the remotely sensed data was

particularly important due to a lack of other data sources.

The study was conducted for the Kathmandu, Nepal, area which

does not have the historical databases that are available in

more developed countries. The ERDAS raster-based GIS used a 70

m grid cell size. One problem they encountered was in

comparing historical land use (from 1972 and 1979) from aerial

photography with recent land use (March and October, 1987)

from SPOT digital data.

Walsh et al.(1990) stressed the importance of using a

digital elevation model (DEM) with Landsat TM within the GIS.

This was performed to enhance the satellite data where

topography is an important factor. They also used the GIS for

spatial rectification of the Landsat data during image

processing.

Wilkening (1987) used a Landsat/GIS merger for regional

water resource management. The software packages were ELAS and

ARC/INFO. Hydrologic sub-basins were manually determined and

input into the GIS in vector format and then converted to

raster format (60 m2 cell size). This enabled the overlaying

of the sub-basins with Landsat landcover data. Other data

(soils, hydrologic, etc.) were also entered into the system

and were used in water resource management.

One study (Johnston and Bonde, 1989) analyzed the

boundaries between adjacent ecosystems using Landsat TM data








18

(bands 2, 3, and 4). A normalized difference vegetation index

(NDVI) was calculated within the GIS using brightness values

from bands 2 and 4. A 3 pixel x 3 pixel scan was used to

enhance the difference among the vegetation classes. They

concluded that the GIS helped in determining subtle

differences between ecosystems.

A study by Tan and Shih (1990) was conducted by

overlaying digitized aerial photographs and a classified

Landsat image at the Remote Sensing Application Laboratory

(RSAL) in the Department of Agricultural and Biological

Engineering, University of Florida. This study (performed on

St. Lucie County, Florida) was done to compare historical

agricultural land use. Aerial photographs from 1958 were

digitized and input as polygon data into the ELAS GIS. These

data were then overlain on a 1973 classified Landsat MSS

image. This study showed a slight decrease in agricultural

land use between 1958 and 1973.

The merging of remotely sensed data with GIS has many

applications. As mentioned earlier, there are many possible

uses for their combination in water resource studies. Land use

and land cover analysis are obtainable from classified Landsat

and SPOT digital data and can serve as input to a GIS. Most

researchers have used a raster GIS with cell sizes ranging
from 60 m2 to 00 2. This eliminates the need for conversion
from 60 m to 100 M This eliminates the need for conversion








19

to a vector-based GIS. However, to overlay this data with

vector data, a transformation must be performed.

Lam et al. (1987) analyzed the errors involved with

vector-raster-vector transformations. They concluded that for

their set of test areas, the maximum error increases as the

raster grid cell size increases. However, this could be due to

the fact the starting and ending vector area values were kept

equal. One area that needs to be studied further is raster-

vector conversion error. One would suspect that the more

irregular the perimeter the greater the error.

Problems with raster-vector conversions include the

"stair-step" look of the resulting polygon layer and small

polygons which produce a "salt-and-pepper" appearance in the

image (Bury, 1989). The resulting polygons do not have a

"realistic" appearance. The processing required user

interaction with the program to decide if any errors had

occurred. The results of Bury (1989) were within National Map

Accuracy Standards for 1:24,000 scale maps.

Another concept that should encourage the merging of

remote sensing with GIS is the use of multi-temporal data

(Xiao et al., 1989). Thus, satellite (or other remotely

sensing) data from different dates would be used to increase

the effectiveness of the GIS. For example, the GIS manager

would then be able to overlay different "snapshots" of







20

landcover with static data (such as soils information) and

dynamic data (such as zoning and ownership).


Use of Fractals in Remote Sensing
and Satellite Imagery


The use of fractals to study natural phenomena has only

recently begun. The concept of fractals was first introduced

by Mandelbrot, who based his work on Hausdorf and Besicovitch

(Mandelbrot, 1977). Fractals can be defined as an entity for

which the Hausdorf-Besicovitch dimension exceeds the

topological dimension.

The use of fractals in satellite classification of land

use has been sparse to date (Krummel, 1987; Ramstien and

Raffy, 1989; De Cola, 1989; Lam, 1990; and La Gro, 1991).

These will be examined in greater detail later.

Fractals have been applied to terrain surfaces (real and

digital elevation models, DEM) by Shelburg et al. (1983);

Burrough (1983); Mark and Aronson (1984); Roy et al. (1987);

and Clarke (1988). Other studies include coastline analysis

(Mandelbrot, 1967), particle shape analysis (Clark, 1986),

coral reefs (Mark, 1984), and stream networks (Tarboton et

al., 1988; and La Barbera and Rosso, 1989). Presently, the

applications to satellite data include 1) determination if

rain and cloud areas are scale-independent (Lovejoy, 1982;

Lovejoy and Schertzer, 1990; and Cahalan, 1990); 2) using








21

fractals and a chaos model as a forecasting tool (Brammer,

1989); 3) describing different satellite bands in terms of

texture (Ramstein and Raffy, 1989); and 4) classifying land

use (De Cola, 1989; and Lam, 1990). These studies will be

briefly reviewed and their relationship to the present study

will be shown.

Lovejoy (1982) first examined the fractal dimension of

rain areas (determined from radar images) and cloud areas

(determined from geostationary operational satellite [GOES]

images). The resolution of the radar images was 1 km x 1 km,

while the GOES resolution was 4.8 km x 4.8 km. The fractal

dimension of the rain and cloud areas were determined using

the area-perimeter method. The fractal dimension (D) was 1.35

for both areas. The correlation coefficient from the

regression analysis was 0.99. To take into account these

different resolutions the GOES perimeter data were "corrected"

by the ratio of the two resolutions taken to the power of one

minus the fractal dimension of the radar data. Thus the GOES

perimeters were multiplied by (1/4.8) 1.35 = 1.73. Even more

interesting was that this analysis was done over a range from

1 km2 to 106km2.

The work of Brammer (1989) concentrated on using

fractals and a chaos model to simulate GOES satellite images.

The simulations were short range (6 to 48 hours) and required







22

the use of temperature, pressure, humidity, and wind fields

(speed and direction).

Ramstein and Raffy (1989) used fractals and variograms

to analyze Landsat TM and NOAA-7 images. This study was able

to distinguish urban, field, and forested areas from texture

analysis alone. However, no spectral analysis was included.

De Cola (1989) used the area-perimeter method described

earlier to determine fractal dimensions of a classified

Landsat TM image. The image was classified into eight classes

with ranges of D from 1.35 to 1.82. De Cola concluded that it

was possible to associate land cover patterns with fractal

measurement.

The remote sensing data were considered a form of a

spatial surface by Lam (1990). The objective of the study was

to determine land use/land cover for a Landsat TM image. Lam

calculated the fractal dimension for surfaces using an

algorithm developed by Shelburg et al. (1983), but calculated

the surface fractal dimension as D = 2 B (the slope of the

regression line). The study only calculated fractal dimensions

for each band and neglected the band combinations which are

very important in land use classification. Thus, one

objective of the present study is to calculate the fractal

dimension for the condition of band combinations.

Olsen et al. (1993) used a modified fractal dimension to

measure landscape diversity. The research evaluated the







23

diversity of landscapes at various scales (e.g., with various

changes of extent and/or grain size) and how to evaluate the

distribution of diversity over a landscape (i.e., what areas

within a given landscape are more diverse than others).

The modified fractal dimension combined the number of

landscape patches, their distribution, and shape into an

overall measure of landscape diversity. Olsen et al. (1993)

concluded that the modified fractal index can provide a simple

measure of diversity which can be related to land management

practices, wildlife/habitat interactions, and biodiversity;

however, the index can not be used as a tool for land use

classification.

Vasil'yev and Tyuflin (1992) analyzed ecosystems spatial

structure and its fractal characteristics. They indicated

that the spatial structure of geosystems is reflected

primarily by the nature of land uses. This was examined by

determination of whether fractal properties of spatial

structures exist and, if so, interpretation of the fractal in

a geometric sense. They concluded that agroengineering

geosystems have a fractal character, the dimension of which

should be used in the spatial differentiation of the land use

system. The main limitation of their research is that only

variations between different agricultural systems were

analyzed. Thus, no comparison was made between urban,

forested (hardwood or conifer), marsh, etc. land uses.








24

De Jong and Burrough (1995) used variograms and

coefficients of variation of satellite image pixels, and a

triangular prism surface area method to estimate the fractal

dimension. This work is similar to that of Clarke (1986) and

Lam (1990), but was applied to Mediterranean vegetation types.

They classified a given rectangular area by land use and then

calculated the fractal dimension versus the percentage of

pixels in the study area of that particular land use. They

did not conclusively relate the fractal dimension to land use,

but indicated that the fractal dimension could be used as

ancillary information to the classification process.


Waveband Combinations


The use of waveband combinations (mainly waveband

ratios) began almost as soon as digital imagery was

available. However, the integration of waveband combinations

with fractal analysis for processing images in land use

classification is a totally new field, which the present

study will research. A brief background for the range of

NDVI values is given below.

Shih (1994) studied the vegetation distribution in the

Everglades Agricultural Area using the High Resolution

Picture Transmission (HRPT) data from the NOAA weather

satellite. The NDVI values varied from -0.05 to 0.341 with

an average of 0.183 and a standard deviation of 0.054. In








25

the current study the revised NDVI was used to eliminate the

negative values.

Lillesand and Kiefer (1987) reported that in highly

vegetated areas the NDVI typically ranges from 0.1 to 0.6 in

proportion to the density and greenness of the plant canopy.













CHAPTER 4
MATERIALS AND METHODS


SPOT Imaces


Two SPOT satellite scenes were selected from northeast

Florida which cover the Lower St. Johns River Basin (LSJRB)

and the Lake George Basin (LGB). Figure 4-1 shows the location

of the SPOT images in northeastern Florida. Two SPOT scenes

(#619-290 and #619-291) from May, 1988 were selected for

analysis. The portions of the LSJRB and LGB covered by these

two scenes are shown in Figure 4-2. Each image covers an area
2
of approximately 5400 km2. The SPOT satellite has three high

resolution visible (HRV) spectral bands: green (0.50-0.59 pm);

red (0.61-0.69 pm); and near infrared (0.79-0.89 gm), with a

resolution of 20 m x 20 m, and one panchromatic band (0.51-

0.73 pm) with a resolution of 10 m x 10 m. The near infrared

band is sensitive to reflective and not to thermal infrared

wavelengths. The near infrared band is useful in determining

spectral signatures of similar vegetation types and water

bodies.










































OW SCm E 6-2o

9M SCENM w=-B


Figure 4-1. Location of SPOT images.























































Figure 4-2. Hastings, Palatka, and Seville quadrangle
locations.










Study Areas


The primary ecosystem of the basins is southern Florida

flatwoods (hyperthermic zone). The soils in the area are

mainly Spodosols, which are nearly level, somewhat poorly

drained sandy soils. Smaller areas of Histosols (level,

poorly drained organic soils underlain by marl and/or

limestone) and Entisols (level to sloping, excessively drained

thick sands) also exist in the two basins (Fernald and Patton,

1984).

The land use in the basins historically included forest

(conifers and hardwoods), agriculture (citrus, potatoes,

cabbage, corn, onion, and improved pasture), wetlands,

rangeland, urban, barren, and water. In recent years, fern

operations and improved pasture areas have increased.

For our purposes of examining the fractal dimension,

three subsets were selected to show the range of different

land uses and correspond to USGS quadrangle areas of Hastings,

Palatka, and Seville. Figure 4-2 shows the location of these

areas, while Figures 4-3, 4-4, and 4-5 illustrate the

Hastings, Palakta, and Seville quadrangles, respectively.

The coordinates of the boundaries for each of the three

quadrangles used to extract sub-images for analysis are given

in Table 4-1.













































































Figure 4-3. Photograph of Hastings quadrangle map (reduced
scale).


* 1 MINUTC *cmei irwicinwci




























































Figure 4-4. Photograph of Palatka quadrangle map (reduced
scale).




























































Figure 4-5. Photograph of Seville quadrangle map (reduced
scale).










Table 4-1. Universal Transverse Mercator (UTM zone 19)
boundary coordinates for Hastings, Palatka, and
Seville study areas.


Quadrangle/ X-UTM Y-UTM
Study Area m m

Hastings 439,567 3,291,068
439,493 3,277,218
451,594 3,277,159
451,654 3,291,009
Palatka 427,481 3,291,140
427,391 3,277,289
439,493 3,277,218
439,567 3,291,068
Seville 451,475 3,249,459
451,416 3,235,610
436,562 3,235,565
436,606 3,249,414










Image Processing System



The Earth Resources Laboratory Analysis System (ELAS,

1989) classification software was used to classify the SPOT

images. This program was originally developed by NASA for

analyzing Landsat and other remote sensing data. ELAS has

many image processing capabilities including image

enhancement, registration, rectification, and classification.

Additionally, ELAS can perform basic GIS manipulations.


Geographic Information System


Geographic Information Systems are a recent interactive

mapping technology with widespread applications. Originally

developed on main frame computers, GIS's are now readily

available in versions for the personal computer (PC) and mini-

computer such as the Sun Sparc computer. The Remote Sensing

Applications Laboratory (RSAL) of the Agricultural and

Biological Engineering Department at the University of Florida

uses the Arc/Info GIS package developed by Environmental

System Research Institute (ESRI, 1992). Arc/Info is a vector

based system that can perform overlays, analysis, and graphic

output of spatial databases. A digitizing tablet (CalComp

9100) is used for entering map related data and a Hewlett

Packard Proplot plotter and laserjet printer are used for

output.









Maximum Likelihood Classification Method


ELAS spectrally classifies satellite imagery using a

maximum likelihood classifier which utilizes a Bayesian

statistical procedure (ELAS, 1989). The two satellite images

were classified using the Normal Variation (NVAR), Thematic

Mapper Trainer (TMTR), and Maximum Likelihood Classifier

(M234) modules in ELAS.

The NVAR module determines the normal variation of the

data for each of the three HRV spectral bands. The module fits

the data to a parabola (assuming a Gaussian distribution of

the data) for each band. Curve fitting coefficients are the

outputs for use in the TMTR module.

Training sets are developed in the TMTR module, by use

of a 3 pixel x 3 pixel window to search for near-homogeneous

spectral classes. The output of this module is a set of

spectral classes (the number of which is determined by the

user) and their associated statistical parameters and a-priori

values.

The M234 module classifies all the pixels in the scene.

The digital number for each pixel of each band is compared to

the spectral classes determined by TMTR. Each pixel is then

assigned a spectral class based on the Bayes' Rule decision

making algorithm. The result of this pixel assignment process

is a one channel image. This procedure used an unsupervised

classification process which was done without prior knowledge








36

of the actual ground land-use information. Specifics of these

ELAS modules are given in Appendix A.

Fractal Dimension Calculation


There are varied ways to calculate the fractal

dimension depending on the dataset and purpose of the

analysis. Following is a brief overview of fractals and

different fractal analysis techniques.

The dimension of an object in Euclidian geometry can be

either 1 (line), 2 (plane), or 3 (volume). These dimensions

are often described in terms of X, Y, and Z coordinates.

However, interdimension values for entities can be described

through use of the fractal dimension. A curve possesses a

fractal dimension between 1 and 2, while a surface possesses a

fractal dimension between 2 and 3.

The fractal dimension of a line may be calculated as:


D = log(N)/log(l/r) = fractal dimension............(4-1)


where: N = number of steps and

1/r = similarity ratio.

In practice D for a curve is often calculated by using

different step sizes and can estimated by the following

equation:


log(L) = C + B(log(G)) ........ ..........(4-2)


D = 1 B.............................(4-3)











where: L = length of the curve,
G = step size, and

B,C = regression coefficients.



This can be simply demonstrated (Lam, 1990):


II I I I





N = 4, I/r = 4 N = 8, 1/r = 4

D = log(4)/log(4) = 1 D = log(8)/log(4) = 1.5

For areas the fractal dimension may be calculated using

area and perimeter measurements (De Cola, 1989):

P = C (A0 5)D ......................(4 4)

where: P = perimeter,

A = area, and

C = fractal shape

D = fractal dimension.

Similar to the calculations for the fractal dimension of

a line, the fractal dimension for a set of areas is often

calculated using a regression equation:

ln(P)= ln(C) + D(ln(A05 )) ................. ...... ...(4-5)










There are five methods for measuring the fractal

dimension of surfaces: variograms, Fourier power spectrum, the

walking-divider (box-counting or grid-overlay) method,

triangular prism surface method, and the robust fractal

estimator. For further discussion on measuring D see Shelburg

et al. (1982 and 1983), Shelburg and Moellering (1983), Muller

(1987), Roy et al., (1987), or De Cola (1989).


Varioqrams


The basis for using variograms in estimating the fractal

dimension lies in fractional Brownian motion. This may be

described (using elevation as an example) as (Roy et al.,

1987):


E[(zi + Zi+h)2] = ......................... (4-6)


where: zi = elevation at point i,

zi+h = elevation at point i + distance h,

h = distance between points,

H = coefficient to be calculated

(0 < H < 1).

For lines the fractal dimension is computed as


D = 2 H........................ ............... (4-7)


and for surfaces


D = 3 H..........................................(4-8)












or


D = E + 1 H.............................. ..... (4-9)


where E = Euclidian dimension (Voss, 1988).

Now let


S = E[(zi + Zi+h)2] .................... ....... (4-10)


where S = expected value of the squares of the elevation

points.

To calculate D from actual data we take logs for both

sides of the equation 4-6 and perform a regression analysis

which leads to:


log(S) = log(b) + 2 H log(h)......................(4-11)


In this equation b is the intercept of the regression

equation. If the mean of the squared height differences

(variance) is computed for different distances, then D can be

estimated from the slope of a log-log plot of variance against

distance by


D = 3 (b/2)......................................(4-12)


Mark and Aronson (1984) applied this variogram method by

picking independent random points (32,000) on a map. However,

the map was restricted to an area which could be drawn by the








40

largest circle completely within the map. The measurements

were made for 100 equally spaced distances using pseudo-random

numbers generated by an algorithm developed by Tausworthe

(1965).

For 17 study areas used by Mark and Aronson (1984) only

one was self-similar over all scales. However, all of the

other areas did show self-similarity over certain ranges,

often with sharp breaks between scales. This led them to

conclude different processes were working to shape the

landscape at different scales.


Fourier Power Spectrum


The use of Fourier analysis to calculate the fractal

dimension has been performed by Burrough (1981), Fournier et

al., (1982), Pentland (1984), Pfiefer (1984), and Clarke

(1988). The basis of Fourier analysis is using sines and

cosines, with characteristic wavelengths and amplitudes, to

estimate a certain parameter. The analysis may be either

continuous (in which the function is integrated) or discrete

(in which a summation is performed). The discrete method is

used for fractal analysis.

The fractal dimension is determined by performing a log-

log regression of the power spectrum versus distance. The

slope of the regression line, b, is used to calculate D as,


D = 3 (b/2) .....................................(4-13)











Note the similarity of this equation and the one used in the

variogram analysis.


Walking-Divider


The Walking-divider method (WDM) is based on work

originally developed by Richardson (1961) and later expanded

by Mandelbrot (1967). Richardson measured the length of a line

with a pair of dividers of different lengths, producing pairs

of divider length versus total line length. He plotted the

log-log relationship between these two measurements to examine

the variation between total length and divider length.

Mandelbrot (1977) extended this concept by performing a

regression of the log-log plots and relating the slope in the

regression (b) line with the fractal dimension.


D = 1 b...................... ..... ............ (4-14)


The walking divider method can be applied to both area

and surface fractal calculations.


Triangular Prism Surface


The triangular prism surface method (TPS) was developed

by Clarke (1986a). This method is designed for grid elevation

data (from Digital Elevation Models) and is calculated from

the known geometry.








42

The method uses four elevation points, which form a

square, to calculate an average center elevation. Using the

center point, four triangular prisms are created and their

areas are computed. The surface area for sides of increasing

powers of two are calculated and summed for each side size

area. A log-log regression of surface area versus the side

area (i.e., lxl = 1; 2x2 = 4; 4x4 = 16; etc.). The slope of

the regression line, b, is then used to calculate the fractal

dimension, D, as D = 2 b. Note that as the resolution

measurement area increases, the computed surface area

decreases and thus, b will be negative.


Robust Fractal Estimator


The robust fractal estimator (RFE), developed by Clarke

and Schweizer (1991), is based on the Walking-divider method.

Profiles are taken in east-west and north-south directions for

each pixel of a matrix (this method designed for use with 7.5

minute digital elevation models). This was done based on the

assumption that changes occur gradually in one (or two) of

these directions. The walking divider method is applied in

both directions for pixel, thus a m x n matrix will have 2(m x

n) estimates of D. The surface fractal dimension is then

calculated as the average of the D values plus one. The

addition of one is due to the walking-divider method being a

line estimate.








43

De Cola (1989) used a Landsat Thematic Mapper image of

northwest Vermont to compare fractal dimensions for different

land uses. IDIMS image processing software was used to

perform a supervised classification of the image into eight

land uses. Fractal numbers were calculated for each class

using area-perimeter regression techniques. The equation used

is :

in(pj) =lIn(C) + D*lin(sj05(
ln(pj) = ln(C) + D ln(sj.5).................... (4-15)

where: pj = th perimeter for a given land use
sj = j th area for a given land use

C = fractal shape

D = fractal dimension.

The dominant land use in De Cola's image are hardwoods

(39.5%), hayland (12.8%), and softwoods (12.2%). Other land

uses are water, brush/wetland, grassland, bare ground/corn,

and urban.

This research used classes which had previously been

determined by a supervised classification procedure. The

fractal dimensions were an end product and not used as part of

the classification process.

Lam (1990) used Landsat TM images from Louisiana to

compare fractal dimensions for different land uses. Fractal

analysis was applied to a 5 km by 5 km area for three







44

different images. Each area represented one of three land

uses: urban, rural, or coastal.

An isarithmic line algorithm was used on the digital

numbers of each TM band for each area. Thus, each land use

had seven fractal dimensions (one for each band of the TM

image). Table 4-2 gives the results of the fractal dimension

calculations.

The problem with this research is applying the methods

to classify other areas in the image. This is not readily

possible using the techniques given. Also, the between band

difference of the fractal dimensions is greater than the

difference between the land uses.

Bands 1, 2, and 3 had the highest fractal dimension for

each land use. Bands 4, 5, and 7 were next highest with band

6 (thermal IR) having the lowest fractal number. This is to

be expected since the range of digital numbers is so small for

thermal IR. La Gro (1991) used aerial panchromatic and

color infrared photography to classify forest areas within the

Finger Lakes National Forest area of New York. The forest

areas included both deciduous and coniferous trees. The

fractal dimension was calculated using area-perimeter

methodology (see discussion on De Cola, 1989).

The fractal dimension was calculated for 1938 and 1988

forest areas, with resulting values of 1.222 and 1.243

respectively. No other land uses were analyzed, thus this










Table 4-2. Fractal dimension by Landsat
uses (Lam, 1990).


band for three land


Land Use Landsat Band Fractal Dimension

Urban 1 2.698
2 2.715
3 2.726
4 2.672
5 2.592
6 2.208
7 2.653
Rural 1 2.709
2 2.615
3 2.607
4 2.587
5 2.540
6 2.176
7 2.536
Coastal 1 2.866
2 2.737
3 2.671
4 2.604
5 2.562
6 2.157
7 2.583







46

work can not be compared with other research into classifying

land use with fractals.

Krummel et al. (1987) used NASA UR/RB-57 high altitude

aerial photography to study the fractal dimension of forest

areas. Their study area was the USGS Natchez, Mississippi

quadrangle (1:250,000). The forest areas were deciduous

trees, with conifer areas eliminated. The standard area-

perimeter methodology used by De Cola (1989) was also used by

Krummel et al. (1987).

They divided the forest areas into small (< 55.7 ha) and

large (>100.4 ha) areas and performed the fractal analysis on

each set of areas. The results show the fractal dimension to

be smaller (D=1.20 +/- 0.02) for the smaller areas than for

larger areas (D=1.52 +/-0.1). They theorized that there are

separate constraints which influence the fractal dimension

based on forest area size. The smaller areas are affected

more by nearby agricultural activity and thus are more

rectangular than the larger areas.


Fractal Shape Calculation


The relationship between the fractal dimension and

fractal shape can be best understood by examining the

regression equation. The regression model takes the form

(Haan, 1977) :


Y = a + b*X + e...................................(4-16)











where: Y = dependent variable

X = independent variable

a = intercept

b = slope

e = error term

Solution of this equation for a and b using least

squares is:


b = I(xi*yi)/. (xi2) ............................... (4-17)


a = Ymean b*Xmean ..............................(4-18)


where: xi, Yi = sample points

Mean = mean of y observations

Xmean = mean of x observations.

Thus, a and b are related through the mean of the x and

y data points, which in our case are the ln(sqrt(area)) and

ln(perimeter); respectively.

For this study the fractal dimensions will be calculated

using the area-perimeter method. A log-log regression on the

area and perimeter data will be performed using equation (4-

5). In addition to the fractal dimension, which is the slope

of the regression equation, the intercept, called the fractal

shape, will be used to distinguish the different classes and

land uses which result from the maximum likelihood







48

classification. These data will be used to combine the 59

classes into different land uses.


Statistical Analyses


Three parameters will be used to compare the fractal

dimension with the fractal shape and other comparisons for use

in land use classification. First, the mean is used to locate

the center of the distribution. The mean is an important

factor for analysis. For example, if the fractal dimension is

large it implies more irregularity of the land use, while if

the fractal shape is large it implies a more regular shape of

the land use.

Second, the standard deviation (SD) is used to measure

the spread or range of the individual measurements which is

very important in image processing. A parameter associated

with a larger SD implies that it has a greater capability to

differentiate the land use conditions.

Third, the coefficient of variation (CV) affords a

relative measure of dispersion so that variation can be

compared in features expressed in different units of

measurement. In other words, this parameter is ratioing the

above two parameters in a percentage basis for quantifying the

variation. This also implies that a parameter associated with

a larger CV is better in image processing for differentiating

the land use conditions.










Use of Different Pixel Groupings


Often after classification of satellite images there

are land use areas which consist of only a few pixels which

results in "peppering" of the final image. These small

areas often are the majority of the total number of land use

areas. This effect could unduly affect the value of the

fractal dimension and fractal shape. To resolve this dilemma

two methods are employed, the use of unique area-perimeter

combinations and the use of successively increasing minimum

pixel areas.


Unique Area-Perimeter Combinations


The results of the fractal dimensions in the previous

sections were based on using all area-perimeter information

available for each study area. However, to eliminate the

effect of multiple area-perimeter combinations for each land

use, the fractal dimension was calculated using only the

unique area-perimeter combinations. The reason for doing

this is to examine the types of shape that occur for each

type of land use. For example, the water land use areas

would generally be long areas with narrow widths that

meander, typical of rivers, while the urban land use would

contain areas which are more rectangular.









Using Different Cell Sizes


To examine the use of different cell sizes, the fractal

parameters will be calculated by successively increasing the

minimum number of pixels for any land use group. For

example, if the standard method of fractal calculation

includes land use areas which consist of only one pixel of a
2
SPOT image, an area is only consisting of 400 m For this

analysis the fractal number is calculated eliminating the

land use areas below a given minimum size. This is then done

for increasing number of pixels (and corresponding land use

areas). The results of this will be a relationship between

the fractal dimension and a given minimum pixel land use

area.


Spectral Reflectance and Waveband Combinations


The mean spectral reflectance data were obtained for

channel 1 (green), channel 2 (red), and channel 3 (infrared)

for the Hastings, Palatka, and Seville study areas. These

data will be compared with the different fractal parameters.


Normalized Difference Vegetation Index


The NDVI is calculated for each pixel in the SPOT image

as follows (Price, 1987):


NDVI = (DN3 DN2)/(DN3 + DN2) ....................(4-19)









where : DNi = digital number (reflectance value) for

channel i.

To correlate NDVI with the fractal dimension for each

class and land use the following equation was used:


NDVI = (MR3 MR2)/(MR3 + MR2) .................. (4-20)


where : MRi = mean reflectance for channel i.

To apply a NDVI to an AVHRR scene a ratio is applied to

each pixel as follows (Price, 1987 and Shih, 1994):


NDVI = (DN2 DN1)/(DN2 + DNj) ................... (4-21)


where terms are the same as before, except the wavelength

ranges are different for the AVHRR than the SPOT image.

The use of different waveband combinations and ratios is

used for enhancement of spectral images. Table 4-3 lists the

different combinations used.

A study conducted by Shih (1994), using AVHRR data to

analyze the NDVI within the EAA, showed negative NDVI values

in the non-cropped areas such as water and cleared land. These

negative values are mainly due water having a lower spectral

response in the near infrared region than in the visible

region. In order to avoid this negative value image which may

influence the image processing, 0.5 and 0.3 were added to the

NDVI and called the revised NDVI and the modified revised

NDVI, respectively (Table 4-3).










Table 4-3. Waveband combinations and ratios.


Band Ratio Name Definitiona Status

Normalized Difference
Vegetative Index (NDVI) (B3-B2)/(B3+B2) Old
Revised Normalized
Difference Vegetative NDVI + 0.5
Index (RNDVI) New
Modified Revised
Normalized Difference
Vegetative Index (MRNDVI) NDVI + 0.3 New

Infrared/Red B3/B2 Old


Infrared Red B3 B2 Old


Red/Green B2/B1 Old


aBand 1 = green waveband

Band 2 = red waveband

Band 3 = infrared waveband









Proposed Fractal Analyses


Historical Fractal Analyses


Historically the fractal dimension was not calculated on

an unsupervised maximum likelihood classification image.

DeCola (1989) used a supervised classification in Vermont and

thus started with only eight classes. He only postulated

using fractals as part of the classification scheme. However,

this method is also implemented with unsupervised

classification techniques in this study for examining its

applicability for Florida conditions.

Although significant and interesting progress has been

made by recent researchers, problems of existing fractal

analysis are evident. Lam (1990) calculated fractal dimension

for each band, but did not calculate fractal dimension for

band combinations which are very important in land use

classification. Vasil'yev and Truflin (1992) concluded that

agroengineering geosystems have a fractal character, but they

made no comparisons between urban, forested (hardwood or

conifer), marsh, etc. land uses. Olsen et al. (1993) used a

modified fractal dimension to measure landscape diversity, but

the index cannot be used as a tool for land use

classification. De Jong and Burrough (1995) did not

conclusively relate the fractal dimension to land use.








54

Therefore, the new fractal analyses are proposed in the

following section.


New Fractal Analyses

1. Use of the fractal shape along with the fractal

dimension for land use classification.

2. Use unique area-perimeter combinations greater than

three pixels for fractal parameter calculations.

3. Use of different cell sizes by eliminating the land use

areas below a given minimum size for fractal

calculations.

4. Use of mean reflectance values and fractal parameters

for land use classification.

5. Use of different waveband combinations and/or ratios

with fractal parameters for land use classification.













CHAPTER 5
RESULTS AND DISCUSSION


Conventional Classification of SPOT Images


The ELAS image processing system classified each SPOT

scene into 59 unrelated classes using the maximum likelihood

methodology discussed in Chapter 4. These 59 separate classes

were assigned a land use by "sliding through" the classes.

This was done by assigning each spectral class of interest a

color and viewing it on the computer monitor. The location

and spatial pattern (straight line, rectangular, sinuous,

etc.) were noted and compared with quadrangle maps and through

extensive ground-truthing.

Finally, the 59 classes were grouped into eight land use

categories which are described in Table 5-1. This is a

modification of the Anderson classification system. These

eight land uses are conifers, hardwoods, marsh, pasture, row

crops, urban, water, and clearings. The marsh/shadehouse land

use grouping was based on similar reflectance and included

reed, rush, bullrush, flag, cattail, and some asphalt and

shadehouse used in fern operations. Pastures were both

improved and unimproved. Urban areas included pavement,

buildings, quarries, and landfills. Water included lakes,

ocean, intercoastal waterways, and rivers. Clearings included










Table 5-1. Land use descriptions for SPOT images.



Land Use Description


Urban


Water



Clearings


Pavement
Buildings
Quarries
Landfills
Ocean
Intercoastal Waterway
Rivers
Ponds/Lakes
Fresh Silviculture Clear-Cuts
Beach
Bare Sand Hills


Conifers Primarily Plantation Pine.
Pine Wetland
Pine Scrub
Fired Pine Scrub
Sapling Pine
Red Cedar Stands
Hardwoods Live Oak
Oak Scrub
Oak/Tupelo
Mixed Hardwoods
Marsh Tree-less Wetlands with Growths of:
Reed
Rush
Bullrush
Flag
Cattail
Also includes some Fresh Asphalt and Shade
Houses.
Pasture Improved Pasture
(Tended Pasture, Lawns, Golf Courses)
Unimproved Pasture
(Weedy/Neglected Pasture, Brush Rangeland,
Grassy Fallow Areas. Roadside Grass).
Row Crops Potato Fields
Corn
Cabbage
Onion
Ornamentals--Gladiolus and Canna


Ornamentals--Gladiolus and Canna








57

mainly silviculture clear-cuts and some beach, and bare sand

hills.

Seven distinct classes for the top scene are shown in

Table 5-2 mainly because the clearings class was not shown in

the original 59 classes; and eight distinct classes for the

bottom scene were determined and are shown in Table 5-3.

The spatial distribution of land uses is shown in

Figures 5-1 and 5-2 for images 619-290 and 619-291,

respectively. For our purposes only black and white are shown,

while the land uses can be color coded for ease in

identification of their spatial distribution.

This final processing step consisted of entering ground

control points (GCPs), followed by image geo-correction and

resampling. GCPs were brought into ELAS using a digitizing

tablet and USGS 7.5 Minute Series quadrangle sheets. These

GCPs included intersections of two-lane, paved roads. Dirt

roads and ditch-lines were not used, because they are often

re-routed. Multi-lane highways, utility easements, and urban

road intersections were also not used, since they are usually

too large to pin-down as GCPs.

Once a sufficient GCP set with a sufficient number of

points (3+ per quadrangle) and with an acceptable accuracy

(rms error < 10 m for entire image) was entered, the image

could be geo-corrected and resampled. Because the project









Table 5-2. Land use spectral classes for SPOT image 619-290.


Land Use/Cover


Conifers



Hardwoods

Marsh

Pasture



Row Crops

Urban

Water


ELAS Spectral Class Numbers


1, 2, 6, 7, 9, 13, 15, 16, 19, 23, 27,

33, 38,43, 45

4, 8, 18, 41

17, 22, 34, 35, 36

5, 24, 26, 28, 29, 32, 40, 44, 47, 48,

53, 57, 58

39, 42, 46, 49, 55, 56, 59

31, 50, 52

3, 10, 11, 12, 14, 20, 21, 25, 30, 37,

51, 54









Table 5-3. Land use spectral classes for SPOT image 619-291.


Land Use/Cover


Conifers



Hardwoods

Marsh

Pasture



Row Crops



Clearings

Urban

Water


ELAS Spectral Class Numbers


1, 2, 9, 10, 11, 17, 21, 23, 29, 33, 40,

45, 54, 55

3, 4, 6, 7, 12, 26, 46, 47

15, 38, 57

5, 8, 20, 22, 24, 25, 34, 35, 36, 39, 42,

48, 52, 59

13, 16, 18, 19, 27, 28, 32, 37, 41, 43,

50, 51,56

30, 44, 49

31, 53

14, 58
























































Figure 5-1. SPOT image 619-290 land use classes.


























































Figure 5-2. SPOT image 619-291 land use classes.








62

area contained reasonably low-relief terrain, the first-order

global polynomial surface model was selected. The nearest-

neighbor resampling method was then applied to the images.

This resampling method should be the one chosen for all land-

cover images, since the other resampling methods are limited

in application to single-channel, non-classified images. The

resampling size was chosen to be identical to the original

SPOT pixel size (20 m x 20 m).


Spatial Distribution of Land Uses


The acreages and land-area percentages of the eight

land-use types distinguished within the two SPOT images are

given in Tables 5-4, 5-5, and 5-6. Several conclusions can be

drawn from these tables.

It is evident that most (75.6%) of the project land area

(Table 5-6) is under forested land use, and that pines

comprise 70.8% of forest component. Agriculture (including

pasture and row crops) forms the second largest land use

(19.8% of project land area). The largest agricultural sub-

type is shown to be pasture (80.0% of agriculture). Marsh,

clearings, and urban land use types, although important for

water-management purposes, are relatively small components of

the project land area.

It should also be noted that the total area belonging to

the Ocala National Forest clear-cuts is divided into four








63

Table 5-4. Spatial distribution of land use areas for SPOT
image 619-290.



Land Use Area Total Area Land Area
ha % %


Conifers 142,337 38.6 58.4

Hardwoods 37,066 10.1 15.3

Marsh 5,178 1.4 2.1

Pasture 42,979 11.6 17.6

Row Crops 9,609 2.6 3.9

Urban 6,621 1.8 2.7

Water 125,204 33.9 --

Clearings ---- ---- --



Total land 243,790 66.1 100.0

Total 368,994 100.0 ---







64

Table 5-5. Spatial distribution of land use areas for SPOT
image 619-291.



Land Use Area Total Area Land Area
ha % %


Conifers 185,422 45.0 50.3

Hardwoods 98,281 23.8 26.7

Marsh 4,128 1.0 1.1

Pasture 53,846 13.1 14.6

Row Crops 14,613 3.5 4.0

Urban 986 0.3 2.7

Water 43,812 10.6 --

Clearings 11,132 2.7 3.0



Total land 368,408 89.4 100.0

Total 412,220 100.0 ---








65

Table 5-6. Spatial distribution of land use areas for combined
SPOT images 619-290 and 619-291.



Land Use Area Total Area Land Area
ha % %


Conifers 327,759 42.0 53.5

Hardwoods 135,347 17.3 22.1

Marsh 9,306 1.2 1.5

Pasture 96,825 12.4 15.8

Row Crops 24,222 3.1 4.0

Urban 7,607 1.0 1.3

Water 169,016 21.6 ---

Clearings 11,132 1.4 1.8



Total land 612,198 78.4 100.0

Total 781,214 100.0 ---








66

of the above land-use classes. Those clear-cut areas which

were freshly cut in 1988 fell within the clearing class, while

those with 1-2 years of natural regrowth fell within the

pasture or row crops classes, those with 3-5 years of natural

regrowth fell within the conifer or hardwoods classes, and

those with 3-5 years of pure pine regrowth fell within the

conifer class.


Fractal Dimension by Class and Land Use


Class Analysis


Images resulting from the maximum likelihood

classification process yielded a 59 class image, which was

first analyzed for fractal properties.

As discussed previously, three subsets of the SPOT image

No. 619-290 were used in this research. The areas are the

Hastings, Palatka, and Seville USGS 7.5 minute quadrangle

areas. These areas were selected since they included all land

uses and contained the larger urban areas found in the SPOT

image. For purposes of discussion, the word "study area"

will refer to the quadrangle area (i.e., the Hastings study

area refers to the study area encompassed by the geographic

location of the Hastings USGS quadrangle).

After extraction of these smaller images the fractal

dimension was calculated using the log-log regression







67

techniques discussed earlier (equation 4-5). This method uses

the log of the perimeter and the log of the square root of the

area. The results of the fractal dimension are given in Table

5-7 for the 59 classes of the three study areas. The

statistical analyses of the mean, standard deviation (SD), and

coefficient of variation (CV) are also given in Table 5-7.

Several observations can be made from Table 5-7. First,

of the 59 class images, 13 are for each of three land uses

(pasture, pine, and row crops), eight are for hardwoods, three

each for marsh/shadehouse and clearings, and two each for

urban and water.

Second, the mean fractal dimensions for the 59 class

image for each study area show similar results: 1.325 for

Hastings and Seville, and 1.324 for Palatka.

Third, the standard deviations are 0.042, 0.036, and

0.031 and coefficients of variation are 3.2%, 2.7%, and 2.3%

for Seville, Hastings, and Palatka, respectively. This

indicates that the spread or variation of individual class

measurements for the fractal dimensions are similar for the

three study areas. Furthermore, from this small range of SDs

and CVs it is difficult to differentiate the land use

conditions within a study area using fractal dimension

techniques for analyzing the original 59 classes, in other

words, a further modification is needed.









Table 5-7. Fractal dimension and fractal shape for 59
spectral classes for Hastings, Palatka, and
Seville study areas.



Class Land Use Hastings Palatka Seville


FDa FS b FD FS FD FS

1 Pine 1.351 1.377 1.392 1.199 1.353 1.363
2 Pine 1.345 1.399 1.339 1.427 1.340 1.425
3 Hardwoods 1.383 1.237 1.372 1.285 1.387 1.221
4 Hardwoods 1.374 1.272 1.369 1.298 1.378 1.257
5 Pasture 1.327 1.482 1.333 1.453 1.331 1.461
6 Hardwoods 1.326 1.491 1.330 1.473 1.317 1.534
7 Hardwoods 1.369 1.295 1.363 1.319 1.347 1.392
8 Pasture 1.344 1.404 1.324 1.498 1.339 1.427
9 Pine 1.373 1.280 1.346 1.394 1.365 1.314
10 Pine 1.314 1.547 1.319 1.523 1.349 1.383
11 Pine 1.335 1.441 1.322 1.499 1.333 1.445
12 Hardwoods 1.392 1.202 1.394 1.193 1.377 1.264
13 Row Crops 1.313 1.548 1.322 1.511 1.336 1.439
14 Water 1.243 1.932 1.308 1.584 1.198 2.278
15 Marsh/ 1.308 1.579 1.323 1.509 1.301 1.614
Shadehouse
16 Row Crops 1.341 1.421 1.290 1.669 1.351 1.380
17 Pine 1.327 1.485 1.336 1.443 1.345 1.400
18 Row Crops 1.321 1.511 1.317 1.534 1.324 1.497
19 Row Crops 1.350 1.377 1.303 1.606 1.368 1.309
20 Pasture 1.326 1.489 1.308 1.579 1.330 1.472
21 Pine 1.341 1.419 1.347 1.388 1.359 1.341
22 Pasture 1.313 1.555 1.308 1.579 1.301 1.611
23 Pine 1.316 1.535 1.331 1.465 1.340 1.422
24 Pasture 1.306 1.585 1.300 1.613 1.345 1.401
25 Pasture 1.316 1.535 1.292 1.658 1.349 1.380
26 Hardwoods 1.396 1.186 1.390 1.205 1.397 1.186
27 Row Crops 1.354 1.356 1.269 1.779 1.301 1.617
28 Row Crops 1.317 1.520 1.233 1.986 1.173 2.384
29 Pine 1.319 1.521 1.320 1.514 1.312 1.549
30 Clearings 1.307 1.580 1.321 1.512 1.333 1.456
31 Urban 1.290 1.661 1.340 1.418 1.319 1.517
32 Row Crops 1.358 1.335 1.336 1.445 1.338 1.429
33 Pine 1.360 1.330 1.378 1.261 1.366 1.302
34 Pasture 1.320 1.520 1.303 1.598 1.347 1.392
35 Pasture 1.324 1.499 1.319 1.524 1.344 1.404









Table 5-7. -- continued.


Class Land Use Hastings Palatka Seville


FDa FS b FD FS FD FS

36 Pasture 1.292 1.656 1.316 1.535 1.273 1.744
37 Row Crops 1.330 1.467 1.324 1.506 1.326 1.491
38 Marsh/ 1.290 1.672 1.301 1.607 1.221 2.070
Shadehouse
39 Pasture 1.336 1.440 1.295 1.633 1.319 1.519
40 Pine 1.324 1.497 1.315 1.541 1.354 1.364
41 Row Crops 1.325 1.493 1.295 1.642 1.312 1.552
42 Pasture 1.315 1.539 1.336 1.438 1.339 1.425
43 Row Crops 1.339 1.420 1.300 1.618 1.332 1.458
44 Clearings 1.297 1.632 1.291 1.662 1.315 1.541
45 Pine 1.338 1.433 1.337 1.438 1.344 1.407
46 Hardwoods 1.353 1.366 1.338 1.431 1.352 1.370
47 Hardwoods 1.293 1.648 1.334 1.430 1.341 1.399
48 Pasture 1.297 1.627 1.272 1.761 1.281 1.710
49 Clearings 1.319 1.522 1.312 1.555 1.363 1.324
50 Row Crops 1.272 1.759 1.302 1.611 1.299 1.617
51 Row Crops 1.237 1.969 1.374 1.267 1.290 1.663
52 Pasture 1.329 1.475 1.313 1.549 1.318 1.526
53 Urban 1.230 2.006 1.309 1.551 1.287 1.665
54 Pine 1.303 1.603 1.327 1.490 1.245 1.915
55 Pine 1.322 1.504 1.314 1.545 1.275 1.744
56 Row Crops 1.306 1.579 1.297 1.628 1.304 1.592
57 Marsh/ 1.248 1.906 1.321 1.514 1.315 1.542
Shadehouse
58 Water 1.402 1.168 1.389 1.209 1.374 1.272
59 Pasture 1.352 1.373 1.310 1.570 1.312 1.560

Mean 1.325 1.503 1.324 1.503 1.325 1.504

SD 0.036 0.175 0.031 0.148 0.042 0.223

CV, % 2.7 11.7 2.3 9.8 3.2 14.8


a FD = fractal dimension

b FS = fractal shape







70

Fourth, since the 59 class image is the first output of

the unsupervised classification and the similarity of fractal

dimension among the three study areas, it is difficult to

differentiate actual land use conditions. Thus, after ground

truthing and class combinations, the original 59 classes were

re-grouped into eight land uses (see Table 5-1 for a

description) which are analyzed in the following section.


Land Use Analysis


The fractal dimensions for the eight land use image for

each quadrangle are given in Tables 5-8a, 5-8b, and 5-8c and

plotted in Figures 5-3, 5-4, and 5-5 for Hastings, Palatka,

and Seville, respectively. A complete listing of the

statistical results (number of areas, mean area and perimeter)

used in the fractal analysis is given in Table 5-9. Several

observations can be made from Tables 5-8a, 5-8b, 5-8c, 5-9 and

Figures 5-3, 5-4, and 5-5.

First, the pasture land use has the highest fractal

dimension for all three study areas and varied from 1.396 to

1.414. This implies that boundaries are more irregular in

pastures than in other land uses. This increased complexity of

the boundaries may be partially due to "tree islands" in

pastures. Also, pastures include rangeland, grassy areas, and

roadside grassed areas. The border of some unimproved pastures

have irregular perimeters due to migration of hardwood and










Table 5-8a. Fractal dimension and fractal shape for eight
land uses for the Hastings study area.



Land use FDa FSb CVc

Pine 1.344 1.402 1.6
Hardwoods 1.313 1.536 1.8
Pasture 1.396 1.176 1.9
Row Crops 1.311 1.556 1.8
Marsh/ 1.309 1.569 1.0
Shadehouse
Clearings 1.344 1.405 1.2
Urban 1.264 1.799 1.5
Water 1.139 2.664 1.6

Mean 1.303 1.638

SD 0.076 0.451

CV, % 5.8 27.5

a FD = fractal dimension using all data.

b FS = fractal shape using all data.

c CV = Coefficient of Variation within each land use.









Table 5-8b. Fractal dimension and fractal shape for eight
land uses for the Palatka study area.



Land use FDa FSb CV,

Pine 1.344 1.398 1.6
Hardwoods 1.316 1.522 1.8
Pasture 1.414 1.110 1.9
Row Crops 1.396 1.191 1.5
Marsh/ 1.353 1.364 1.4
Shadehouse
Clearings 1.353 1.364 1.3
Urban 1.290 1.646 1.6
Water 1.189 2.333 2.5

Mean 1.332 1.491

SD 0.070 0.380

CV, % 5.3 25.5

a FD = fractal dimension using all data.

b FS = fractal shape using all data.

c CV = Coefficient of Variation within each land use.










Table 5-8c. Fractal dimension and fractal shape for eight
land uses for the Seville study area.



Land use FDa FSb CVc

Pine 1.371 1.229 2.2
Hardwoods 1.331 1.396 2.3
Pasture 1.410 1.063 2.2
Row Crops 1.320 1.475 1.6
Marsh/ 1.204 2.218 2.1
Shadehouse
Clearings 1.382 1.181 1.8
Urban 1.304 1.540 1.9
Water 1.085 3.540 2.3

Mean 1.301 1.705

SD 0.107 0.821

CV, % 8.2 48.2

a FD = fractal dimension using all data.

b FS = fractal shape using all data.

c CV = Coefficient of Variation within each land use.

















1.400 +


row
crops


marsh/
shadehouse


1.300 -


clearing


urban


1.200 +


water


1.100 +-


1.000 1L _


Land Use


Fractal dimension versus land use for the Hastings study area.


Figure 5-3.
















row
rcrnnc


pine


marsh/
shadehouse clearing


1.100




1.000 -





Figure 5-4.


Land Use


Fractal dimension versus land use for the Palatka study area.


1.400


1.300




1.200


hardwoods


urban


water
















pasture


clearing


Dine


hardwoods


row
crops


marsh/
shadehouse


1.100 -1-


1.000 _1 -


Land Use


Fractal dimension versus land use for the Seville study area.


1.400




1.300


1.200 -I-


urban


water


Figure 5-5.









Table 5-9. Area and perimeter statistics for Hastings,
Palatka, and Seville study areas.



Study Land Use No. of Average Average
Area Areas Aria Perimeter
m m

Hastings Pine 4,320 4,731 258
Hardwoods 2,228 11,774 387
Pasture 3,137 7,664 392
Row Crops 1,885 9,180 339
Marsh/Shadehouse 794 1,246 134
Clearings 3,382 1,344 152
Urban 392 3,148 219
Water 12 2,066,066 5,393
Palatka Pine 4,774 13,589 364
Hardwoods 2,240 19,058 462
Pasture 4,370 5,916 370
Row Crops 3,082 2,439 215
Marsh/Shadehouse 953 1,825 173
Clearings 4,375 1,580 166
Urban 506 3,533 237
Water 78 211,087 1,130
Seville Pine 1,984 32,103 751
Hardwoods 1,165 46,917 946
Pasture 1,317 23,424 812
Row Crops 916 4,699 304
Marsh/Shadehouse 319 6,792 322
Clearings 787 4,823 332
Urban 70 4,331 317
Water 48 172,712 948








78

conifers into old pasture areas. This increases the complexity

of the pasture areas.

Second, water has the lowest fractal dimension which

implies a high regularity of perimeter of the water bodies in

all three study areas.

Third, the greatest range (highest minus lowest value)

of fractal dimensions among land uses occurred between pasture

and water land uses at all three study areas (Table 5-8). For

example, the fractal dimension at Seville for pasture compared

with water is 30% higher.

Fourth, the fractal dimension technique clearly

separates water from urban land use at all locations (Table 5-

8). For example, the fractal dimension for urban compared to

water land use at Seville is 20% higher.

Fifth, the pine and clearings have similar fractal

dimensions in each study area. This similarity could be due to

the high correlation between clearings and pine land use

areas. For example, after harvest of pines, areas become

clearings, or vice versa.

Sixth, the fractal dimensions for pine and clearings are

higher, i.e., more perimeter irregularity, for Seville than

for Hastings and Palatka. This could be due to the more

interior location of Seville which contains less water bodies

as shown in Table 5-9, which can contribute to less regular

boundaries. Also, pine and clearing areas are less likely to








79

be adjacent to water bodies in the Seville area than in the

other two areas, thus causing a higher fractal dimension at

Seville.

Seventh, the fractal dimensions are similar for

hardwoods at all study locations. However, the fractal

dimensions for row crops and hardwoods are similar in the

Hastings and Seville study areas, but the fractal dimension

for row crops is higher than for hardwoods in the Palatka

area. This could be due to the row crops in the Palatka area

being of smaller size per number of row crop areas, i.e. about
2 2
2,400 m compared to about 4,700 m or higher for the other

two areas (Table 5-9). This could contribute to the higher

fractal dimension for row crops in the Palatka area.

Eighth, fractal dimension was slightly but consistently

higher for pines compared to hardwood land use for all three

study areas (Table 5-8). For example, the fractal dimension at

Seville for pine compared to hardwood is 3% higher. Both pine

and hardwood have natural boundaries which are non-

rectangular, but the reason for the slightly lower fractal

dimension for hardwoods may be due to hardwoods being located

near water bodies, which have a lower fractal dimension, and

pines are located in upland sites.

Ninth, the lower fractal dimension for marsh/shadehouse

land use in the Seville area compared to Hastings and Palatka

areas may be due to a larger sized marsh/shadehouse area in









2 2
the Seville area (6,800 m2 compared to 1,800 m2 or less for

the other areas). This feature creates a more regular shaped

marsh/shadehouse area for the Seville area. Additionally, the

lower fractal dimension for Seville could be due to more

shadehouses present in the Seville area compared to the

Hastings and Palatka areas. These shadehouses are rectangular

and thus would lower the fractal dimension.

Tenth, the higher overall mean fractal dimension (1.332)

for the Palatka area could be mainly due to the higher fractal

dimension (1.396) for row crops and the higher fractal

dimension (1.414) for pasture as mentioned above.

Eleventh, after comparing Table 5-7 with Table 5-8, it

is evident that the SDs and CVs for fractal dimensions in

eight land uses are higher than in the 59 classes. This

implies, as mentioned in the statistical analysis section,

that the eight land uses are better for differentiating land

use conditions than the 59 classes.

Twelfth, as Table 5-8 shows, the CVs for fractal

dimensions for all three study areas only varied from 5.3% to

8.2%. This small magnitude of CVs still makes it difficult to

differentiate among land uses using fractal dimensions. In

other words, another parameter which has a higher CV is

urgently needed.

Thirteenth, the coefficients for fractal dimensions and

fractal shapes are given in Tables 5-8a, 5-8b, and 5-8c for








81

Hastings, Palatka, and Seville, respectively. These results

afford a relative measure of dispersion within a given land

use. The CVs among land uses ranged from 1.0 to 1.9% for

Hastings, 1.3 to 2.5% for Palatka, and 1.6 to 2.3% for

Seville. These relatively low CVs suggest validity of the

experimental method and that the spectral signatures were

similar within a given land use. The CV is ratioing the

standard deviation and the mean in a percentage basis for

quantifying the variation. This implies that a parameter with

a smaller CV is better for the unsupervised maximum likelihood

classification within a given land use.

In summary, application of the fractal dimension

technique for differentiating among land uses is only

partially successful. The technique separates pasture from

other land uses, water from other land uses, urban from water,

and pine from hardwood. However, clearings, hardwoods, and row

crops may have similar fractal dimensions at some locations.

The above shortcomings or disadvantages suggest the need for a

different parameter to differentiate among land uses. This

leads to an analysis of fractal shape.










Fractal Shape by Class and Land Use


Class Analysis


Three observations pertaining to fractal shape can be

made from Table 5-7. First, the mean fractal shapes for the 59

class image show similar results for each study area: 1.503

for Palatka and Hastings; and 1.504 for Seville. This close

relationship among study areas also was shown previously for

the fractal dimension.

Second, the SDs for fractal shape for the 59 classes are

0.148, 0.175, and 0.223 for Palatka, Hastings, and Seville,

respectively. Whereas the SDs for fractal dimensions only

range from 0.031 to 0.042, these four times larger SDs for

fractal shape are desirable in image processing for

differentiating among land uses.

Third, the CVs for fractal shape for the 59 classes are

9.8%, 11.7%, and 14.8% for Palatka, Hastings, and Seville,

respectively. Whereas the CVs for fractal dimension only range

from 2.3% to 3.2%, these four times larger CVs for fractal

shape are desirable in image processing for differentiating

among land uses. In other words, using the fractal shape

technique is better than the fractal dimension technique in

land use classification.

The fractal shape is the intercept of the log-log

regression. The fractal shape versus the fractal dimension is








83

plotted in Figures C-l, C-2, and C-3 in Appendix C for the 59

class images for Hastings, Palatka, and Seville, respectively.

These figures show a negative linear relationship between the

intercept (fractal shape) and the slope (fractal dimension),

i.e., the higher the fractal dimension, the lower the fractal

shape.


Land Use Analysis


The fractal shapes for the eight land use image for each

study area are given in Tables 5-8a, 5-8b, and 5-8c and

plotted in Figures 5-6, 5-7, and 5-8 for Hastings, Palatka,

and Seville, respectively. Several observations can be made as

follows.

First, pasture land use has the lowest fractal shape for

all three study areas and varies from 1.063 for Seville to

1.176 for Hastings. This implies that boundaries are more

irregular, or less regular, for pastures compared with other

land uses. A similar conclusion was reached based on the high

fractal dimension for the pasture land use. However, the

difference based on fractal dimension among three areas was

only 1%, whereas the difference based on fractal shape was

11%. This means that the pasture land use among land uses is

similar based on fractal dimension, whereas there is a large

difference based on fractal shape analysis. This could be due

to the smaller farms (Table 5-9) with more improved pasture in