<%BANNER%>

Detection of Fluvial Landforms Underneath Forests Using Lidar Data

Permanent Link: http://ufdc.ufl.edu/UFE0022862/00001

Material Information

Title: Detection of Fluvial Landforms Underneath Forests Using Lidar Data
Physical Description: 1 online resource (82 p.)
Language: english
Creator: Cho, Hyun-Chong
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: digital, dmp, lidar, mathematical, stream
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Airborne Laser Swath Mapping (ALSM) instrument technology and subsequent algorithm advances have made it possible over the last several years to map the earth s surface and landcover at unprecedented resolution. The ability of ALSM technology to densely sample ground elevations beneath forest canopies is particularly important because forested watersheds have traditionally been difficult to study with remote sensing techniques. Extraction of stream networks from digital elevation models (DEMs) plays a fundamental role in modeling local and spatially distributed hydrological processes. To detect stream channels, we have developed two approaches. The first approach is based on an encoding of mathematical morphological operators and is shown to systematically and accurately extract stream channel locations, forms, and incipient incisions in a forested watershed. The accuracy of the method is verified using a set of error measures over simulated terrain and also over real terrain where the site was manually surveyed. The second approach represents an alternative to the first, and it consists of three steps. First, the composition of geodesic tophat and bothat operations of different sizes is used in order to build a differential morphological profile that records image structural information. The use of morphological operations at multiple scales can capture a wider variety of surface forms, but it also leads to a high-dimensional parameter space that often contains redundant information. Therefore, in the second step, feature selection is investigated using both Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). Third, a Bayesian classification is used to classify the features resulting from the second step. In experiments, the two proposed methods perform well in terms of detection results and classification accuracies. The second approach is more general than the first, but also requires training and more computation. It will be shown that the second method is better suited for analyzing complex watersheds that contain numerous channels or other surface forms at multiple scales.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Hyun-Chong Cho.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Slatton, Kenneth C.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0022862:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022862/00001

Material Information

Title: Detection of Fluvial Landforms Underneath Forests Using Lidar Data
Physical Description: 1 online resource (82 p.)
Language: english
Creator: Cho, Hyun-Chong
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: digital, dmp, lidar, mathematical, stream
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Airborne Laser Swath Mapping (ALSM) instrument technology and subsequent algorithm advances have made it possible over the last several years to map the earth s surface and landcover at unprecedented resolution. The ability of ALSM technology to densely sample ground elevations beneath forest canopies is particularly important because forested watersheds have traditionally been difficult to study with remote sensing techniques. Extraction of stream networks from digital elevation models (DEMs) plays a fundamental role in modeling local and spatially distributed hydrological processes. To detect stream channels, we have developed two approaches. The first approach is based on an encoding of mathematical morphological operators and is shown to systematically and accurately extract stream channel locations, forms, and incipient incisions in a forested watershed. The accuracy of the method is verified using a set of error measures over simulated terrain and also over real terrain where the site was manually surveyed. The second approach represents an alternative to the first, and it consists of three steps. First, the composition of geodesic tophat and bothat operations of different sizes is used in order to build a differential morphological profile that records image structural information. The use of morphological operations at multiple scales can capture a wider variety of surface forms, but it also leads to a high-dimensional parameter space that often contains redundant information. Therefore, in the second step, feature selection is investigated using both Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). Third, a Bayesian classification is used to classify the features resulting from the second step. In experiments, the two proposed methods perform well in terms of detection results and classification accuracies. The second approach is more general than the first, but also requires training and more computation. It will be shown that the second method is better suited for analyzing complex watersheds that contain numerous channels or other surface forms at multiple scales.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Hyun-Chong Cho.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Slatton, Kenneth C.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0022862:00001


This item has the following downloads:


Full Text

PAGE 1

DETECTION OF FLUVIAL LANDFORMS UNDERNEATH FORESTS USING LIDAR DATA By HYUN-CHONG CHO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009 1

PAGE 2

2009 Hyun-chong Cho 2

PAGE 3

To my father, mother, sister and brother 3

PAGE 4

ACKNOWLEDGMENTS First of all, I would like to express the deepest gr atitude to my advisor, Dr. K. Clint Slatton. I have been amazingly fortunate to have an advi sor who gave me the freedom to explore on my own and at the same time the guidance to recover when my steps faltered. He taught me how to question thoughts and express ideas His patience and support helped me overcome many crisis situations and finish this di ssertation. I hope one day to b ecome as good an advisor to my students as he has been to me. I am also grateful to Dr. Ramesh Shrestha, Dr. Fred J. Taylor, and Dr. John G. Harris for their valuable time and in terest in serving on my supervisory committee, as well as their comments, which helped improve the quality of this dissertation. I have been very fortunate to work with many outstanding graduate students in the Adaptive Signal Processing Laboratory (ASPL). My special acknowledgement goes to Sweungwon Cheung, Pravesh Kumari, Heezin L ee, Carolyn Krekeler, Kristofer Shrestha, Michael Starek, Kittipat Kampa, Abhinav Si nghania, Bidhyananda Yadav, Hojin Jhee, John Caceres, Juan Carlos, Karthik Nagarajan, Kuei -Tsung Shih, Michael Sartori, Pang-wei Liu, Raghavendra Kumar, Thelma Epperson, Tory Cobb, and Tristan Cossio for their help, collaboration and valuable discussions. Th ey also brought me continuous fun, which was essential during my PhD study. I owe much to them all. Finally, my utmost appreciation goes to my sist er and brother for alwa ys believing in me. Their unceasing love and whole-he arted support made finishing th is work possible. Last but most, I thank my parents, for their love, support, patience, and late-night prayers. 4

PAGE 5

TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4LIST OF TABLES................................................................................................................. ..........6LIST OF FIGURES.........................................................................................................................7CHAPTER 1 INTRODUCTION................................................................................................................. .111.1 Background.......................................................................................................................111.2 Measurement.....................................................................................................................151.3 Site Description................................................................................................................162 STREAM CHANNEL DETECTION USI NG MATHEMATICAL MORPHOLOGY.........202.1 C-Star Algorithm..............................................................................................................202.1.1 Basic Algorithm......................................................................................................202.1.2 Connecting Stream Segments.................................................................................222.2 Filter Parameter Selecti on using Simulated Terrain.........................................................252.2.1 Simulated Data.......................................................................................................252.2.2 Error Metrics..........................................................................................................262.3 Simulation and Real Data Result......................................................................................272.3.1 Simulated Data Result............................................................................................272.3.2 Stream Channels Detection in Real Data...............................................................282.3.3 Features of Stream Channels..................................................................................303 STREAM AND ROAD DETECTION US ING DIFFERENTIAL MORPHOLOGICAL PROFILES....................................................................................................................... .......503.1 Background of Differential Morphological Profiles.........................................................503.2 Differential Morphological Profiles.................................................................................523.3 Principal Component Analysis.........................................................................................543.4 Linear Discriminant Analysis...........................................................................................553.5 Bayesian Classification.....................................................................................................583.6 Result and Discussion.......................................................................................................603.7 Comparison of C* Algorithm, DMP, and D8...................................................................624 CONCLUSION AND FUTURE WORK...............................................................................75LIST OF REFERENCES...............................................................................................................78BIOGRAPHICAL SKETCH.........................................................................................................82 5

PAGE 6

LIST OF TABLES Table page 2-1. Error metrics vs. sizes of disk shape SE for simulated data...................................................492-2. Error metrics vs. shapes for the best size of 7 for simulated data..................................493-1. Information classes, training, and test samples for Hogtown Creek site................................733-2. Test accuracies in percentages w ith variances for Hogtown Creek site.................................733-3. Information classes, training, and test samples for Hatchett Creek........................................733-4. Test accuracies in percentage with variances for Hatchett Creek..........................................733-5. Information classes, training, and test samples for Red Wall Canyon...................................733-6. Test accuracies in percentage with variances for Red Wall Canyon......................................743-7. Error metrics vs. a ll methods on simulation...........................................................................743-8. Error metrics vs. all methods on Hogtown Creek..................................................................743-9. Error metrics vs. all methods on Hatchett Creek....................................................................743-10. Error metrics vs. all methods on Red Wall Canyon.............................................................74 6

PAGE 7

LIST OF FIGURES Figure page 1-1. Bare-surface DEMG3 and DEMDS of Hogtown Creek...........................................................181-2. Hogtown Creek and Hatchett Creek.......................................................................................192-1. A 7 disk-shaped bina ry structuring element.......................................................................362-2. Hogtown Creek DEMs of each process in C* algorithm.......................................................362-3. The 3x3 pixel neighborhood used in the eight-connectivity algorithm..................................372-4. Minimum-cost path extraction process for a 3 x 3 image......................................................372-5. The connection results of DEMDS over the Hogtown site......................................................382-6. Simulated DEM of a 200mm ALSM image.................................................................382-7. Definitions of detection errors........................................................................................... .....392-8. Testing algorithm on simulated terrain...................................................................................3 92-9. Testing algorithm on another simulated terrain......................................................................402-10. Planform channel detection results at the Hogtown Creek...................................................412-11. Detection result of C-star al gorithm at the Hatchett Creek..................................................422-12. Detection result of Cstar algorithm at the Red Wall Canyon, Death Valley......................432-13. Stream channel cross-sections..............................................................................................442-14. Cross-sections of survey result, DEMG3 and DEMDS...........................................................452-15. Results of ROC, bank slope asymmetry and tree density in DEMG3...................................462-16. 1-D plots of Hogtown Creek features...................................................................................472-17. 2-D figures of Hogtown Creek features...............................................................................483-1. Morphological Profile for the Hogtown Creek site................................................................673-2. Example of a DMP for a pixel on a stream in the Hogtown DEM.........................................673-3. Ground truth over the Hogtown site.......................................................................................6 83-4. Ground truth of Hatchett: Stream (blue), Outside Stream (red).............................................68 7

PAGE 8

3-5. Ground truth of Red Wall Canyon: Stre am (blue), Outside Stream (red)..............................693-6. Detection results on simulated data....................................................................................... .693-7. Detection results on Hogtown Creek......................................................................................703-8. Detection results on Hatchett Creek.......................................................................................713-9. Detection result s on Red Wall Canyon...................................................................................72 8

PAGE 9

Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DETECTION OF FLUVIAL LANDFORMS UNDERNEATH FORESTS USING LIDAR DATA By Hyun-chong Cho May 2009 Chair: K. Clint Slatton Major: Electrical and Computer Engineering Airborne Laser Swath Mapping (ALSM) instru ment technology and subsequent algorithm advances have made it possible over the last several years to map th e earths surface and landcover at unprecedented resolution. The abil ity of ALSM technology to densely sample ground elevations beneath forest canopies is part icularly important because forested watersheds have traditionally been difficult to study with remote sensing techniques. Extrac tion of stream networks from digital elevation models (DEMs) plays a fundamental role in modeling local and spatially distributed hydrological processes. To de tect stream channels, we have developed two approaches. The first approach is based on an encoding of mathematical morphological operators and is shown to systematically and accurately extract stream channe l locations, forms, and incipient incisions in a forested watershed. The accuracy of the me thod is verified using a set of error measures over simulated terrain and also over real terrain where the site was manually surveyed. The second approach represents an alternat ive to the first, and it c onsists of three steps. First, the composition of geodesic tophat and bothat operations of diffe rent sizes is used in order to build a differential morphological profile that records image stru ctural information. The use of morphological operations at multiple scales can ca pture a wider variety of surface forms, but it also leads to a high-dimensional parameter sp ace that often contains redundant information. 9

PAGE 10

Therefore, in the second step, feature selecti on is investigated using both Principal Component Analysis (PCA) and Linear Discriminant Analys is (LDA). Third, a Bayesian classification is used to classify the features resulting from the second step. In experiments, the two proposed methods perform well in terms of detection re sults and classification accuracies. The second approach is more general than th e first, but also requires traini ng and more computation. It will be shown that the second method is better suited for analyzing complex watersheds that contain numerous channels or other surface forms at multiple scales. 10

PAGE 11

CHAPTER 1 INTRODUCTION 1.1 Background Accurate stream channel delineation is vita l for understanding th e flow of water over terrain and flood mitigation. Extracting accurate representations of streams from Digital Elevation Models (DEMs) is ofte n a required step in predicting the effects of flowing water on surficial processes such as erosion, sediment transport and sha llow landslides, and thus facilitates better decision making and planning in wa ter resource management (Knighton, 1998). Similar to our stream channel extraction app lication, some researchers have used LiDAR data to extract different kinds of channel networks. Those applic ations include the recognition of channel-bed morphology (Cavalli et al ., 2007), mapping gully and rill channels (James et al ., 2007), exploiting topographic signatures (Lashermes et al ., 2007), mapping tidal zone areas (Mason et al ., 2006), mapping geomorphological units in mountain areas (Asselen et al ., 2006), and mapping river valley environments (Jones et al ., 2007), for example. In the recognition of channel-bed morphology, Cavalli et al (2007) used indicators of the local variability of elevation and slope to disti nguish step-pool and riffle-pool reaches, which are continuous parts of streams betw een two specified points. A he uristic approach was employed using indexes of surface roughness to classify th e different morphological units (land forms). Reliance on surface roughness, however, will not generally succeed when extracting small streams (e.g. 2-5 m across) under forest canopy. Th is is because a non-trivial fraction of LiDAR returns can come from shrubs and the lower parts of tree trunks, thereby modulating the estimated surface roughness. The ability of LiDAR data to map gullies and rill channels in a forested landscape, as investigated in James et al (2007), could potentially impr ove channel-network maps and 11

PAGE 12

topological models. At the gully reach scale (i.e 2 m), their attempts to use LiDAR data to extract gully cross-section shap es under forest canopy were less successful due to systematic underestimation of gully depths and overestimation of gully t op widths. Limited morphologic accuracy of the data set at this scale may be due to low bare-Earth LiDAR point densities, shadowing of gully bottoms, a nd filtering of topographic disc ontinuities during post-processing. In an effort to exploit topographic signatures, Lashermes et al (2007) showed that certain useful features can be found only when using high resolution (i.e. about 2. 6 m average bare earth data spacing, gridded to 1 m) t opography, such as that derived from LiDAR. They were able to reveal topographic transitional ar eas of weak convergence, such as the transitions between hillslopes and valleys. They used wavelet analysis to locally filter elevation data and to detect thresholds in topographic curvat ure and slope-direction change for defining valleys and probable channelized portions of the valley. This method, however, is only suitable for landforms that are significantly larger than the sm all stream channels we are interested in detecting. Mason et al (2006) mapped tidal zone areas base d on data from two study sites: River Ems, Germany and Venice Lagoon, Italy. It is se en to give reasonably good results in areas which are not significantly complicated. The algorithm for channel extraction from fused LiDAR and spectral data did not reduce the total error substantially from that using LiDAR data alone due to the higher signal-to-n oise ratio present in the LiDAR data compared to that in the spectral data. Asselen et al (2006) concluded that hi gh-resolution topographical da ta derived from laser Digital Terrain Models (DTMs) are useful for extracting ge omorphological units (e.g. deep incised channel, shallow incised channel a nd fluvial terrace) in mountainous areas. The geomorphological units extracted from laser elevation data not only represent homogeneous 12

PAGE 13

surface characteristics but can also indicate similar material and genesis (land formation process), but only once interpreted by a geomorphological expert. In mapping river valley environments, Jones et al (2007) found that sometimes unfiltered LiDAR data, including vegetation and buildin gs, are more suitable for geomorphological mapping than data that have been filtered to remove these features. This approach relied heavily on visual interpretation, and they found that using derivatives of the original LiDAR data, such as grids of slope gradient or aspect, did not always significantly improve the results of mapping the survey area of interest. This approach, howev er, is totally inappropria te for heavily forested regions, such as ours, because 85% of the Li DAR returns come from the canopy, and the bare ground is completely obscured in the unfiltered LiDAR data. The above proposed methods make contributions to several application fields for geomorphological mapping, but they do not focus on extraction of small scale (e.g. 2-5 m across) stream channels under heavy forest canopy. Our proposed approach is a new method to automatically and accurately extract stream channe l locations, forms, and incipient incisions in forested watersheds. Another important issue is the accuracy and sensitivity of LiDAR data extraction, which was examined in (Bowen et al ., 2002) and (Lindsay, 2006), respect ively. Elevation errors based on measurements over all terrain types are larg ely attributable to horizontal positioning limitations in areas with variable terrain and large topographic relief. Those indicating crosssectional profile algorithms that were effective for removing vegetation in relatively flat terrain were less effective near the active channel where dense vegetation was found in a narrow band along a low terrace. Accuracy of LiDAR elevation data varies depending on terrain type. Most published estimates of LiDAR accur acy reflect values obtained in relatively flat, homogeneous 13

PAGE 14

terrain. Although LiDAR is capable of producing 15 to 20 cm RMSE ( z ) elevation data, horizontal positioning limitations (1 to 2 m RMSE ( x y )) associated with each laser return increase the probability of larger observed elevat ion errors in areas with variable terrain and large topographic relief. LiDAR elevation data are based on systematic random sampling by a scanning laser. This limits the user's ability to define linear features, such as the top of a steep bank, at a resolution smaller than the distance between sample points, which can be as large as 1 to 5 m in many LiDAR data sets (Bowen et al ., 2002). A series of stochastic simulations was used to evaluate the sensitivity of DEM based channel mapping techniques to the magnitude and sp atial autocorrelation of elevation error, even before the advent of high resolution LiDAR data. Those automated channel extraction techniques that utilize digital te rrain data can be categorized as valley recognition (VR) methods, channel initiation (CI) methods, or combinations of the two. The channel-mapping algorithms in (Lindsay, 2006), (Douglas, 1986), (Johnston et al ., 1975), and (Peucker et al ., 1975) are based on identifying patterns in surface morphology and are pa rticularly susceptible to errors resulting from surface roughness. Algorithms in (OCallaghan et al ., 1984), and (Montgomery et al ., 1993) are based on simulating overland flow and are also hindered by the greater number of surface depressions occurring on ro ugh surfaces. Although LiDAR data were found to provide a sufficient resolution for mapping fine-scale h eadwater channels, the greater surface roughness did present challenges for automated channel-mapping techniques (Lindsay, 2006). River system analysis has traditionally b een limited to conventional ground surveys and repeated field measurements. Advances in the mapping and remote sensing technology gradually led to the advent of using aerial phot ography, digital imagery, and radar data for the delineation of streams. Laliberte et al (2001) used aerial photographs of different time periods 14

PAGE 15

to compare the changes in channel outlines and st ream widths over a yearly period. The task of identifying the stream boundaries in planform was generally li mited to manual digitization of imagery, and in most cases, three-dimensional (3D) stream cross-section measurements still had to be collected through field observations, unless in ferred from stereo optical or interferometric radar methods, each of which has significant 3D resolution limitations at meter scales. Furthermore, neither passive optical nor rada r techniques could accurately detect streams covered over by dense forest canopy. Thus, the st udy of fluvial and erosional processes in many forested watersheds remains problematic. Ai rborne Laser Swath Mapping (ALSM), also known as LiDAR, with its high 3D spatial resolution and vegetation penetrati on capability, offers a powerful new technology that can be applied to th is problem. However, the ALSM data must be combined with specialized algorithms to systematically extract the channels. 1.2 Measurement Before 2007, National Center for Airborne Laser Mapping (NCALM) operated an Optech 1233 model ALSM system. It was capable of a 33 kHz laser pulse rate, recorded two returns (first and last) per laser shot, and had a fixed be am divergence of 0.25 milliradians. In February 2007, NCALM took delivery of and has since calibra ted a new generation of ALSM instrument (Shrestha et al ., 2007). The Optech Gemini model is capab le of laser pulse rates up to 167 kHz, records four returns (including fi rst and last) per shot, and has a switchable beam divergence of 0.25 mrad and 0.80 mrad. Early testing of the Gemini unit by NCALM re vealed an upward trend in elevation error rms with increasing laser pulse rate (Shrestha et al ., 2007). Furthermore, it was desired to characterize the bare-surface sampling capability of the Gemini system at different pulse rates and beam divergences. In a series of experiment s, the Gemini was operated at different settings for three repeat passes of a forested test site. The laser pulse rate and beam divergence settings 15

PAGE 16

for the three flights were (1st) 142 kHz and 0.25 mrad, (2nd) 125 kHz and 0.25 mrad, (3rd) 125 kHz and 0.80 mrad. The Above Ground Level (AGL) flying altitude was 600 m in all cases. The average spot spacing at ground level was be tween 40 50 cm for each flight, resulting in almost 30 points per square meter when the point clouds from the three flights were merged. However, vegetation filtering tests revealed that only about 17% of the laser shots resulted in returns from the ground, yielding about 5 actual gr ound points per square meter in the forest. While valuable for algorithm validation, the DEM that results from this high grade data set (DEMG3) is not necessarily representative of othe r ALSM-derived DEMs to which researchers might have access (e.g. pre-2007 NCALM data sets). In order to generate a rigorous estimation of what might be possible with a more typica l ALSM acquisition, the data files from the two narrow-beam flights were downsampled via the time stamps on each shot to mimic a two-pass acquisition with a laser pulse ra te of 33 kHz. A two-pass scenario was assumed since NCALM normally flies all paralle l lines with 50% overlap, thus yi elding double coverage except on the two bounding flight lines. The downsampled data were filtered to produce a bare-earth DEM (Kampa et al ., 2004), which we will refer to as DEMDS. Figure 1-1 shows the bare-surface of DEMG3 and DEMDS at Hogtown Creek in Florida, USA. DEMG3 has less noise and clearer stream views. 1.3 Site Description Two forested watersheds (Hogtown Creek a nd Hatchett Creek) located within roughly 10km of each other in North-Central Florida, USA and the deformed landforms along the northern Death Valley fault zone (i.e. Red Wall Canyon) are examined. The Hogtown Creek Watershed drains 20 square miles of mostly urban and suburban development along with some greenbelt while the Hatchett Creek Watershed drains nearly 65 sq. mi. of rural forests. Both watersheds have low topographic relief on the order of 10m overa ll. The portions of Hogtown 16

PAGE 17

examined here are heavily forested floodplain lo cated in a greenbelt with mixed southern pine and hardwoods, and significant saw palmetto (Ser enoa repens) understory. The bottomland soils are generally sandy, but range in sand and orga nic content. Hogtown Creek ALSM data was acquired by Gemini model in March 2007 and Ha tchett Creek ALSM data was collected by Optech 1233 model in February 2007, at which ti me the trees had undergone significant budding, but were far from maximum leafout. Figure 1-2 shows pictures of Hogtown Creek and Hatchett Creek. Red Wall Canyon ALSM data is collected fo r the study on the northern Death Valley and Fish Lake Valley fault zones, the largest fault system in the region, extending over 300 km from the Garlock fault in the Mojave Desert northward into southwestern Nevada. NCALM (National Center for Airborne Laser Mapping) acquired ap proximately 2 km 10 km of LiDAR data at sites centered on 36.87N/117.26W and 37.09 N/117.47W in northern Death Valley, California in February 2005. It is available on the Web [http://calm.geo.berkeley.edu/ncalm/ddc.html]. The paper is organized as follows. In Chapter 2, we describe the basi c characteristics of a stream channel detection algorithm, which is our first approach, and discuss the experimental results. For validating the approach used in this work, the filter pa rameter selection using simulated terrain is also discussed. In Chapter 3, we explain the Di fferential Morphological Profile (DMP) method used to ex tract streams and roads. To reduce the dimension of DMP, Principal Component Analysis (PCA) and Linear Discriminant An alysis (LDA) are applied. The experimental results of this second approach will also be presented and analyzed. In Chapter 4, the conclusions and future wo rk are described, respectively. 17

PAGE 18

Figure 1-1. Bare-surface DEMG3 (A) and DEMDS (B) derived from filtered ALSM data of the Hogtown study site near Gainesville, FL. Th e imaged area is oriented with North pointing up along the y-axis, and covers an area of 290mm with 1mm pixels. Total elevation range is 7 meters. 18

PAGE 19

Figure 1-2. Hogtown Creek (A, B, and C) and Hatchett Creek (D, E, and F). They have about 35m tall forest with dense understory. (Irregular tree spacing and structure and uneven-aged: multiple layers of undergro wth and canopy). Channel width at water level is 2-3 m and channe l depth is about 10-20 cm. 19

PAGE 20

CHAPTER 2 STREAM CHANNEL DETECTION USI NG MATHEMATICAL MORPHOLOGY 2.1 C-Star Algorithm 2.1.1 Basic Algorithm Raw ALSM data comes in the form of an i rregularly spaced cloud of discrete laser returns. Each point is associated with a 3D coordinate. The ALSM point cloud data is first segmented into ground and non-ground points using the method developed by Kampa and Slatton (Kampa et al ., 2004). The term non-ground points refers to laser returns from the foliage, light poles, or any houses or other structures in the forest that occlude the ground. The set of ground points is then interpolated to yiel d a bare-ground DEM or elevation image. Before applying the stream detection algor ithm to the data, the georeferenced elevation values in meters are converted to gray level values from 0 to 255. This input elevation image is smoothed by convolution with a 7 disk-shape d (i.e. radius 3) structuring element (SE), (see Figure 2-1). We will discuss how we choose the size and shape of SE in Sections 2.2 and 2.3. Then, the Log Transformation and contrast stretching (i.e. hist ogram normalization) is used (Equation 2-1). )1log( rcs (2-1) where c is constant (here c =1), and the input r represents the elevation va lues of the pixels after converting to gray-level (i.e. 0255). This transformation maps a narrow range of low gray-level values in the input image into a wider range of output levels. Thus, th e small variations in elevation between stream channels and the surrounding stream banks are emphasized in the resulting image sMorphology theory (Goutsias et al. 2000) has been effectively applied in image processing for many purposes, including feature extraction. In graysc ale morphology theory, 20

PAGE 21

two fundamental operations (dilation and erosion) for an image (Gonzalez et al ., 2002, Soille 2002) are defined as follows: f}),(;),( ),(),(max{),)(( :b fDyxDytxs yxbytxsftsbf Dilation (2-2) }),(;),( ),(),(min{),)( ( :b fDyxDytxs yxbytxsftsbf Erosion (2-3) where and are the domains of image and structuring element respectively, are the row and column pixel indicesinf, a), y are the indices in b. From these bas operations, we can define additional operations. fDbD fb),( ts nd( xic bbfbf Opening ) ( : (2-4) bfbf Closing )( : (2-5) The bothat operation is define d as the closing of the image minus the image. The term bothat is short for bottom-hat, which is so na med because it is the i nverse of the better known top-hat operation. It emphasizes local minima in pixel values at the scale of the SE. fbfh Bothat )( : (2-6) The bothat morphological operator (Gonzalez et al., 2002) is then applied using the same disk-shaped SE to isolate stream features. In many urban watersheds, roads are present in the imaged areas, in addition to streams. So it is im portant that the stream de tection algorithm not be prone to detecting roads. In our data sets, ro ads are not detected by this algorithm because they do not exhibit as much variation in elevation as do streams. The result of this step is an image 21

PAGE 22

that emphasizes the stream positions as local maxi ma, but it has a very lo w contrast. Histogram equalization is therefore performed to exaggerate the pixel value ra nge. The stream channels are finally segmented from the surrounding terrain by applying Otsus method (Otsu, 1979) to the grayscale image to form a binary image that de picts the two classes stream and non-stream. Otsus method is a simple unsupervised clustering method that finds the pixel value threshold that maximizes the distance between the two resu lting pixel value clusters. Therefore, their combined spread (intra-class variance ) is minimal. The resulting binary image contains the detected streams, but it also contains a small nu mber of short stray regions, a common artifact of morphological filters and edge filters. The stray regions ar e not streams because they do not satisfy the criterion for the minimum size of a stream. These are removed using the simple area binary morphological operator that removes connected pixel groups of insufficient area. In this work, the DEMs are gridded to a pixel size of 1 m 1 m, and the minimum area considered for a detected stream segment is ba sed on general stream physical dimensions. To precisely locate the streams, the centerlines are then found using the thinning algorithm in (Gonzalez et al., 2002). Thinning is the process of changi ng a large group of pixels into a single, one-pixel wide line. It preserves the Euler number (E): the number of holes (H) and connected components (C) in a figure, E=C-H. Figure 2-2 shows Hogtown Cr eek DEM of each process in C* algorithm. 2.1.2 Connecting Stream Segments Because locally dense foliage can preclude ALSM returns from reaching the ground over small areas, it is possible to have some breaks in the detected stream paths. For flow routing, however, hydrologists desire unbroken stream path s. Therefore, we must link the stream segments. Several image processing approaches have been developed to link edges or contours in images (Dillabaugh et al., 2002). In classic edge linking, it is often assumed that two 22

PAGE 23

disconnected lines have the same orientation or direction. Ho wever, for connecting irregular pixel paths, such as stream centerlines, we use a more general notion of connectedness. We use Connectivity Number (CN) to join disconnected stream centerlines. In the binary image, the CN of the stream pixel is given one of five values: CN = 0: inner point, CN = 1: end point, CN = 2: connected point, CN = 3: branch point, and CN = 4: cross point (Japan Industry Technology Center, 1993). In binary images, the Connectivity Number of the black pixel (i.e. values = 1) is the number of the connected black pixels in the ne ighborhood of the considered pixel. There are two kinds of connectivities: the 4connectivity (horizontal and ve rtical directions) and the 8connectivity (horizontal, vertical, and two diagonal directions ). The 8-connectivity gives better visual performance with irregular paths. Therefore, only the 8-c onnectivity is discussed here and is defined in Equation 2-7 (Japan Industry Technology Center, 1993). Se e also Figure 2-3. Connectivity Number (8-connectivity): 1)()()()()(2 1 0 )8( Sx k kk k CkxfxfxfxfxN (2-7) where }7,5,3,1{1 S )(1)(i ixfxf 19xx For the criteria of the connecting process, distances between end points are used. The distances between all end points are calculated. E ach end point is associated with its nearest neighbor end point which is not in the same 8-conn ected label. If these end points are within a user defined bound (15 meter in this case), they become candidates for linking. The criterion of 15 m comes about because of the occlusions in the LiDAR point cloud induced by tree canopies. 15 m is approximately three times the smallest stream widths and is also the approximate maximum diameter of dense clumps of inter-mingled tree canopies. Where these clumps occur, very few LiDAR points reach the ground, and ther efore the stream is not detected. The 23

PAGE 24

candidate end point pair is then conn ected by the A-star algorithm (Fischler et al., 1981), which is described below. Connection Condition Rules: i. For each end point in the end point list find all end points within distance D (where D=15m). ii. Of those candidates, find the closest end point that is not in same stream line (i.e. same label). iii. Then connect them by the A-star algorithm. In computer graphic theory, A-star is a best-first graph search algorithm that finds the least-cost path from a starting point to an endi ng point to be linked. It allows non-straight-line links. Before applying A-star we generate a Cost Image (Equation 2-8) to reveal the similarities between the input image and the average of the detected stream pixels. In the Cost Image, a small pixel value indicates a higher possibi lity of being a stream pixel. Therefore, Astar finds the least-cost path through the Cost Image, finding the channel path with minimal error cost. Cost Image = |Input Image Average of det ected streams pixels| (2-8) where the input image is connecting area of elev ation image and the average of all detected stream pixels is a scalar value. Figure 2-4 depicts how we can employ the Co st Image to find the minimum-cost path connecting two pixels, i.e. the Starting Point (S ) and Ending Point (E). In this process, two images, the Cost Image and a Step Image, are used. The Step Image shows the cumulative minimum cost of the path leading to the next pixel on the path from S. 24

PAGE 25

First, every pixel in the Step Image is set to infinity, except for the S position. At the S position in the Step Image, we input the corresponding pixel value of the Cost Image. In each iteration of the Step Image, we sum Cost Image pi xels in pixels adjacent to the current pixel in the 8-connectivity directions (i.e. horizontal, vertical, and two di agonal directions) and follow the path resulting in the lowest sum. We replace the infinity values in Step Image with the path sum values. When the pixel value of the E position in Step Image is reached and replaced with a finite value, the process stops. We then trace ba ck from E to S following smallest values to find the minimum-cost path in the final Step Imag e. Figure 2-5 shows th e connection results of DEMDS over the Hogtown study site. It is better to use A-st ar rather than pure gradient (like D8) because the LiDAR typically hits trees between stream points and those points will be higher than the stream. Actually they may be not downw ard gradient. Therefore, A-star is better since it looks at a cost image (both pos itive and negative differences). From this point on, we will refer to the entire process of detecting and connecting stream channel segments given a DEM as the C* algorithm, signifying the first complete generation of a channel extraction operator C* suitable for high-resolution LiDAR-derived DEMs. 2.2 Filter Parameter Selection using Simulated Terrain The shape and size of the SE is very important in mathematical morphology. Therefore, after developing the basi c algorithm to detect stream centerlines, a sensitivity analysis was performed with respect to th e shape and size of the SE. 2.2.1 Simulated Data We generate simulated elevation images usi ng a 2D fractal process and embed meandering stream channels of different widt hs and depths (see, for example, Figure 2-6). We then calculate a nominal ALSM scan pattern over this terrain and randomly remove 80% to 90% of these simulated ALSM points to mimic the occluding e ffects of a dense forest canopy. The remaining 25

PAGE 26

samples represent the ground points and are in terpolated to simulate a bare-surface DEM obtained from ALSM data over forested terrain. 2.2.2 Error Metrics The output of mathematical morphological op erators strongly depends on the SE size and shape. Therefore, we needed to analyze the al gorithms performance over the simulated data as a function of SE size and shape via four E rror Metrics (EM) enumerated as EM1 EM4. Our stream detection algorithm can make two kinds of errors: false negatives and false positives. A false positive occurs when the code classifies a detected stream centerline pixel as belonging to the stream class but the true stream centerline does not pass through that location. A false negative is when the code fails to classi fy a pixel as stream ev en though the true stream centerline passes through that loca tion (See Figure 2-7). Let in Figure 2-7 denote a pixel that was detected (classified) as a stream centerline pixel by the algorithm, and denote a pixel that is on the true stream centerline. We associate each with the nearest (nearest neighbor rule). This will esta blish a one-way 1-to-1 correspo ndence between detected stream centerline pixels and true stream centerline pixels. For each of these pairs, we compute the straight line (Euclidean) di stance between them in 2D as 2 mino 2 mino mino y x d (2-9) We then label all s outside of a defined band around the true stream centerline of width 2 (i.e. min od) as false positives. Based on the know n ALSM resolution and nominal stream sizes, we set the width parameter of this search band to be 5 m. EM1 is the total number of false negative pixels, There is no distance associated with this error measure since there is no detected stream centerline pixel in this case. The true stream fnN 26

PAGE 27

centerline pixels that have no corr esponding detected pixel within the -band are simply counted. EM2 is the total number of false positives, These are simply the pixels that lie outside of the fpN -band. No distance is associated with this measure since closeness does not count if the is outside of the -band. For those detected points that remain, i. e. for pixels that lie inside the -band, we sum the distances to the nearest It is possible to have a false positive inside the -band, however, we will not consid er that an error since was chosen small to tightly conform to the stream. This gives TD xoNdmin for EM3, where is the number of true detected pixels. This is simply the mean absolute error. TDNFor EM4, we simply define the sum of thes e three errors, normalized by the number of pixels in the true stream centerline oN ) ()()(4min TD xo ofp ofnNdNNNNEM (2-10) 2.3 Simulation and Real Data Result 2.3.1 Simulated Data Result Figure 2-8 and Figure 2-9 show detection results of simulated da ta. Figure 2-8 is the same data which is shown in Figure 2-6 and is used to calculate Error Metrics. In Table 2-1, we see that larger SEs result in more false positives (l arger EM2) and are less likely to have disconnects in the stream (smaller EM1). In Table 2-2, we see the disk shape SE is more less sensitive to changes in stream direction, as implied by the low EM4 score. Different SEs were tested by varying its size and shape and it wa s found that the 7 disk-shaped (i .e. disk with radius 3) SE yields the smallest total error (EM4). The disk shape as a structure element has the property of being isotropic, i.e. the pr operty of being independent to changes of orientation. 27

PAGE 28

2.3.2 Stream Channel Detection in Real Data While it is the 3D shape of the stream channels that C* is sensitive to, it is convenient to focus first on the detection results in a planfo rm, or top view. The detection results of DEMG3 and DEMDS over the Hogtown site are shown in Figure 210. The forest is predominantly in the eastern (right) portion of the image. Many shallo w geometric features associated with roads and residential yards are visible in the western portio n. The C* algorithm was designed to not detect roads (alternative algor ithms are used for that purpose), so that in urban watersheds it does not confuse streams with roads. The most striking feature in the DEMs is an almost rectangular shaped depression in the forested area. This is an old borrow pit, from which sand was extr acted, when roads were expanded in this area many years ago. It has since become densely vegetated and exhibits a complex network of short channel forms, some na tural and some modified intentionally. Such forms can make low-relief and urban watersheds particularly problematic to analyze with more traditional approaches based on contributing area which is simply a method of counting the number of pixels that would drain water into a given pixe l using the watershed algorithm (Beucher et al., 1979). The algorithm (Jenson et al., 1988, and O'Callaghan et al., 1984) is an example of this that is well known in the hydrologic literature. The C* algorithm readily detects these small channel forms. But for this study, the channels detected in that area are excluded so that focus may be placed on the tw o main stream channels: Possum Creek entering from the north and Hogtown Creek entering from the east. The two creeks merge near the southern edge of the DEM, below which it is simply referred to as Hogtown Creek. D8In the DEMG3 (Figure 2-10), we see that the C* extr acted stream channels agree very well overall with the hand digitized channels. True stream center line is made by hand watching DEMG3. We checked accuracy of stream detectio n using Global Positioning System (GPS) at 28

PAGE 29

discrete points. However, for continuous ground truth, we had to do hand digitized since GPS signal is not good enough under canopy to do kinematic GPS. A zoom view over the stream confluence reveals that agreement is often better than one meter in th e main channel. In fact, the Mean Absolute Error (MAE) between the hand digi tized main channel and the detected channel centerline is only 1.31m (each pixel is 1mm). However, in the zoom view we can see small off shoots from the main channel that are det ected by the C* algorithm. Visits to the site revealed that these smaller channels are in fact real features and not algo rithmic artifacts. These small incisions are often fewer than 6m long and only 1-2 m across. They tend to occur between the root balls of individual tr ees on this forested fl oodplain. We speculate that they may have formed in response to high runoff events when the floodplain experien ces large volumes of standing water. As the water level over th e floodplain recedes, water flows through these incipient incisions into the main stream. Given the density of understory and lower canopy foliage, these features are often not even visible to an observer until one has practically stepped into them, and therefore represent a dramatic adva nce in channel detection in forested watersheds from remote sensing platforms. In the DEMDS overview in Figure 2-10, we see that C* still manages to extract stream channels well overall, in spite of the lower LiDAR point density. The zoom view over the stream confluence reveals that agreement is better than a meter in much of the main channel. Also, many of the incipient incision features are still detected. The MA E between the detected channel centerline and the hand digiti zed channel (which is based on DEMG3) is 1.54m. This rather small increase in MAE between DEMG3 and DEMDS suggests that applying C* to other forested watersheds that were imaged with older NCALM data could also yield satisfactory stream extractions in planform. We do see in th e zoom view of Figure2-1 0 that the narrow neck 29

PAGE 30

of an isthmus in DEMG3 is detected as a channel in DEMDS, thus changing the small isthmus to a small island. Results from using the C* algorithm, detection results at two other study sites (Hatchett Creek in northern Florida and Red Wall Canyon in Death Valley) are s hown in Figure 2-11 and Figure 2-12, respectively. Based on our str eam detection results, C* algorithm gives good performance at all sites. 2.3.3 Features of Stream Channels Most available ALSM measurements (inclu ding those from NCALM) are based on an Nd:YAG laser that emits pulses in the near-infra red (1064 nanometers) portion of the spectrum. The optical properties of water are such that lig ht in the near-IR does not significantly penetrate below the water surface. Thus, these ALSM sensors cannot directly observe the true channel bottoms if water is present. In the Hogtown site during late winter and early spring, the water stage is often quite low (less than 20cm in pl aces). Furthermore, in March 2007, this area was still experiencing a significant droug ht. So channel depths estimated from this particular LiDAR data set are likely to be within a few decime ters of the true bottom depth (except over small scour holes and fallen trees in th e channel). The same is true for nearby Hatchett Creek and the very dry Red Wall Canyon in Death Valley. Thus, for the purposes of this work, the channel depth-to-the-water-surface measured by ALSM will be referred to as simply the depth. With the channel centerlines extracted, it is straightforward to automatically extract the locally orthogonal channel cross-se ctions at every centerline pixel. Two extracted cross-sections are shown in Figure 2-13. The locations from which they originate are indicated in the DEM overviews in Figure 2-10. Cross-section (or trans ect) T1 comes from a relatively straight section of Possum Creek, whereas transect T2 come s from a pronounced meander bend in Hogtown Creek. One would generally expect the channel cr oss-section in the meander to exhibit greater 30

PAGE 31

asymmetry between the outer a nd inner bank slopes based on typical erosion and sediment deposition patterns that arise from the fluvial processes that form and maintain the streams (Knighton, 1998). This is, in fact, rev ealed in the transects in Figure 2-13. To compare between cross-sections of DEMs in real terrain, six crosssections (four over straight portions of the streams and two over cu rved portions) were measured in the field using total station, which is an optical instrument used in modern surv eying, at the Hogtown site. Each cross-section had more than tw enty shots with distances between shot positions of about 20-50 cm. The MAE (Mean Absolute Error) between DEMs (DEMG3, and DEMDS) and survey results are 0.1212 m and 0.23 m, respectively. Figure 2-14 shows two of the cro ss-section survey results usi ng the total station and a 3D view of one of the cross-sections. It validat es that our estimated cross-sections in DEMG3 are closer to the real terrain than DEMDS, yet both DEMs lead to very good results when one considers the nominal absolute accuracy of LiDAR poi nts stated earlier and th e fact that this is obtained through dense forest canopy. In spite of the close over all agreement between DEMG3 and survey elevations, care should be taken in any attempt to extract channel mo rphology at submeter scales from ALSM data because the point spacing on the ground is highly non-uniform due to the complex occlusions of the vegetation. Terrestrial (g round-based) LiDAR would be pr eferred when robust submeter channel form morphology is required in forested areas. Relative errors in the cross-sections extracted from DEMG3 and DEMDS were examined. In the case of the T1 transect, the relative MAE in elevation was only 11.3 cm and the standard deviation of the signed error was 15.6 cm. For transect T2, th e relative MAE in elevation was only 21.3 cm and the standard deviation of th e signed error was 20.8 cm. Based on survey 31

PAGE 32

results, we know that the DEMG3 is very close to the real terr ain. It may be that a 10 20 cm loss in precision from DEMDS is significant for some fluvial morphology applications. In such cases, this result suggests that state-of-the-art high pulse rate ALSM data may be required along with C* to adequately extract channel forms. As a general rule of thumb, it would be reasonable to say that older LiDAR poi nt densities (as in DEMDS) are quite sufficient for general extraction of channels in planform, and th at higher densities (as in DEMG3) should be used when trying to extract 3D channel forms. With the capability to now systematically extract channels in planform and in cross-section all along their paths, it becomes possible to charac terize channel form parameters, such as Radius of Curvature (ROC), width, depth, and bank slope asymmetry m ~ Normalized bank slope asymmetry was calculated as maxRLRLRLmnormmmmmmm (2-11) where m ~ is the normalized bank slope asymmetry, and are the estimated slopes of the right and left banks, respectively. RmLmUnder normal fluvial processes, one genera lly expects an inverse relation between m ~ and ROC (Knighton, 1998). In other words, where ther e are sharp bends in the stream (small ROC), we expect larger slope asymmetry. In Figure 2-1 5, there are ten white circles. The numbers 1, 2, 5, 8, and 10 are at curved stream positions and the numbers 3, 4, 6, 7, and 9 are at straight stream positions. It shows the expected inverse rela tion between ROC and bank asymmetry except at number 8. The highest tree densit y occurs at number 8. This is quite interesting because it indicates that the presence of trees near the banks can modulate the expected channel forms. This is intuitive since the root balls of trees can be seen to retain much soil (see Figure 1-2). Nonetheless, this is a significant finding sinc e most books on fluvial proc esses only consider the 32

PAGE 33

case of streams in open terrain, where the sedi ment and erosion patterns are not modulated by vegetation. Figure 2-16 shows 1-D plots of ROC, bank asymmetry, de pth and width of Hogtown Creek following the stream from left to right in the DEM imag e. Width is similar throughout this entire stream segment and depth is increasing from right to left. The stream flows from right to left and merges with Possum Creek at the left. This explains why depth is larger on the left side (more runoff accumulates as you move further down stream). From distance indices 0 to 15, and 85 to 105 along the horizontal-axis, bank as ymmetry values are uns table and a little bit higher. Also along this section, th e tree density is high for a long in terval. If tree density is low in short intervals, it does not appear to affect the invers e relation between ROC and slope asymmetry very much, but if it is low in a long interval, it has a larger a ffect on the bank asymmetry values (i.e. from 0 to 15 and 85 to 10 5 in horizontal-axis). From distance indices 180 to 190 along the horizontal-axis, the inverse rela tion is not strong, because the tree density is highest. Figure 2-17 shows 2-D figures of RO C, asymmetry of bank slope, depth and width following Hogtown Creek. We can easily find that ROC and slope asymmetry have an inverse relation. Computing lengths of the small in cipient channel features in DEMG3 yielded the following statistics: a detected mean valu e of 2.6m with standard deviati on of 1.2m. Detected channels longer than 6m were not included so as to focus on the small incision features. Width and depth of these features were not estimated since the f eatures are often only one or two meters wide and the DEM resolution was 1mm. The length statistics could, howev er, prove very useful to hydrologists trying to charac terize a channel network. 33

PAGE 34

Flow speed and rate of the stream waters depend on the channels characteristics. A channels slope, size and surface roughness can all in fluence a streams flow. The relationship between flow and these channel characteristics is shown in the Manni ng equation (or Mannings empirical formula, Gauckler, 1867), which is we ll known in hydrologic literature and can be adapted to determine both flow speed and flow ra te. Mannings empirical formula for the mean cross section velocity of grav ity-driven, uniform, fully develo ped turbulent flows in rough open channels is among the better known expression s used by hydrologists, geomorphologists, and hydraulic engineers (Gioia et al., 2002). Lacking a better solu tion, it is assumed that the equation is also valid for non-unifo rm reaches that are invariably encountered in natural channels if the energy gradient is modified to reflect only the losses due to boundary friction (Dalrymple et al., 1967). The formula is customarily used to determine the capacity of natural streams and flood plains, and to design artifi cial channels (Dooge, 1992 and C how, 1988). It has also been used to quantify the vast flows wh ich appear to have occurred on Ma rs in the distant past (Carr, 1979). Because it embodies a larg e body of experimental resu lts (Dooge, 1992), and it produces good performance in general, Mannings formula o ffers a simple parameterization of channels useful for many applications. In spite of the fact that there is little deta iled theory justifying Mannings formula, the following assertion, made in a classical text on geomorphology (Leopold et al., 1964), remains accepted after thirty-seven year s: It is truly surpri sing that engineering practice has depended to such an extent on a formula as empirical as this one, derived nearly a century ago (Gioia et al., 2002). Mannings formula is written as: 2 1 3 2SR n k V (2-12) 34

PAGE 35

ASR n k Q 2 1 3 2 (2-13) where V is the velocity ( ), Q is the flow rate ( ), k is a conversion constant equal to 1.0 for International System of Units (i.e. SI un its), n is the Manning coefficient of roughness (independent of units), A is the cross sectional area of flow ( ), P is wetted perimeter (m), R is the hydraulic radius (m) given by sm /sm /32m P A, and S is the along-track slope of the water surface or the linear hydraulic head loss. Appropriate values of n have been measured for different types of channel walls, and tabulated (Chow, 1988). For Hogtown Creek, we assumed it approximates a rectangular open channel, water is fully loaded in channel shape with a Manning coefficient of 0.035 for the winding (meandering) stream or rivers. The resulting calcula ted Hogtown stream velocity is 1.9046 ( ) and flow rate is 11.5986 ( ). It was not possible to verify th ese velocity estimates since it would require placing flow meters in situ (which we do not have) into th e stream and field expertise for making such measurements. Yet, we have demons trated for the first time that the high resolution channel widths and depths derived from the LiDAR data can now be used in conjunction with Mannings formula to produce such estimates. sm /sm /3 35

PAGE 36

Figure 2-1. A 7 disk-shaped bi nary structuring element. Figure 2-2. Hogtown Creek DEMs of each process in C* algorithm. A) After log transform and contrast stretching. B) After bothat operation. C) After Otsus method. 36

PAGE 37

Figure 2-3. The 3x3 pixel neighborhood used in the eight-conn ectivity algorithm. Figure 2-4. Minimum-cost path ex traction process for a 3 x 3 imag e. The cost image is in the upper left. The starting point (i.e. 4) and ending point (i.e. 2) ar e shown. The steps are continued until the goal pixel is added in the process. Once the ending point is reached, a path is traced back from the e nding point to the starting point following the smallest values to find the minimum-cost path 37

PAGE 38

Figure 2-5. The connection results of DEMDS over the Hogtown site. Detection results before applying connecting algorithm (A, B, and C). Detection results after applying connecting algorithm (D, E, and F). Figure 2-6. Simulated DEM of a 200mm ALSM imaging swath over a meandering stream. Elevations are in meters and pixel size is 1mm. Minimal topographic relief is used to simulate a Florida flood pl ain test site. Bright pixels are high elevations, whereas dark pixels are low elevations. 38

PAGE 39

Figure 2-7. Definitions of detec tion errors. The gray area repr esents a thin band around the stream center line of width 2 Figure 2-8. Testing algorithm on simulated te rrain. A) Simulated DEM of a 200mm ALSM imaging swath over a meanderi ng stream before applying connection algorithm. B) Simulated DEM with detected channel center line (white line) after applying connection algorithm. Connected stream segments are indicated by red circles. 39

PAGE 40

Figure 2-9. Testing algorithm on another simula ted terrain. A) Simulated small meandering stream in low-relief terrain (1000mm). It is a 1m x 1m fractal surface with embedded channel. B) True path of the simulated stream. C) Detected channel center line. Mean absolute error between true and detected channel centerline pixels is only 0.32 pixels. 40

PAGE 41

Figure 2-10. Planform channel detection results at the Hogtown Creek. A) DEMG3 showing the true (hand digitized) main channel (solid line) and th e channel detected by the C*algorithm (dotted line). Very little differe nce is visible in the overview, suggesting good performance overall. The imaged area is 290mm with 1mm pixels (total elevation range is 7 meters). B) DEMDS showing the true main channel (derived from DEMG3) and the detected channel derived from running C* on DEMDS. Overall performance is still quite good. C) A 47m46 m zoom view onto a channel confluence from the top left result. D) Corresponding area from the top right result. At this scale, detection differences between the DEMs become apparent. 41

PAGE 42

Figure 2-11.A) A satellite image of the Hatche tt Creek area near the Gainesville Regional Airport from Google Earth. B) A bare-surf ace DEM of the Hatchett Creek, FL site. C) Detection result of the C* algorithm. D) The same area as in C, without the detected stream (425 m x 510 m, 1mm pixels, and total el evation range is 7 meters) for comparison. 42

PAGE 43

Figure 2-12. A) A satellite pict ure of Red Wall Canyon in Death Valley, CA from Google Earth. B) a zoom view of the area showing the bare-surface DEM derived from LiDAR. C) a further zoom in to show channel details. D) Detection result of C* algorithm (601 m x 382 m, 1m1m pixels, and total elevation range is 90 meters). Although Death Valley is very dry, short flood events known as cl oud bursts can result in channel formation in the soil. 43

PAGE 44

Figure 2-13. Stream channel cross-sections. A) A comparison between the cross-sections automatically extracted from location T1 in DEMG3 and DEMDS from Figure 2-10. B) A similar plot for location T2 from Figure 210. In this case, the bank slopes clearly display more asymmetry in B, which is often associated with bends in meandering channels in which erosion dominates th e outer bank and deposition dominates the inner bank. The detection algor ithm enables the systematic mining of the DEM data to detect asymmetric por tions of the channel. 44

PAGE 45

Figure 2-14. Cross-sections of survey result, DEMG3 and DEMDS in Hogtown Creek (B and D). Both right figures show DEMG3 is closer to the survey result than DEMDS. C) 3D cross-section view of white rectangular area. 45

PAGE 46

Figure 2-15. Results of ROC, bank slope asymmetry and tree density in DEMG3. A) Small white circles show the positions along Hogtown Creek where ROC, bank slope asymmetry, and tree density were calculated in DEMG3. Numbers 1, 2, 5, 8, and 10 are at curved stream positions and numbers 3, 4, 6, 7, and 9 are at straight stream positions. B) The plots of normalized ROC. C) Normalized bank slope asymmetry. D) Normalized tree density. 46

PAGE 47

Figure 2-16. 1-D plots of Hogtown Creek featur es. A) ROC. B) Bank asymmetry. C) Width (m). D) Depth (m). E) A superposition plot of ROC (red), bank asymmetry (blue), and tree density (green). 47

PAGE 48

Figure 2-17. 2-D figures of H ogtown Creek features. A) Hogt own Creek. B) ROC. C) Bank asymmetry. D) Depth (m). E) Width (m). 48

PAGE 49

Table 2-1. Error metrics vs. sizes of disk shape SE for simulated data EM 1 EM2 EM3 EM4 TDN Radius 2 (5 by 5) 785 18 1.6843 2.0722 1222 Radius 3 (7 by 7) 581 22 1.6713 1.9626 1406 Radius 4 (9 by 9) 588 130 1.8277 2.1601 1473 oN: 2070 (Number of pixels in th e true stream centerline) TDN: Number of true detected pixels Table 2-2. Error metrics vs. shapes for th e best size of 7 for simulated data EM 1 EM2 EM3 EM4 TDN SE Rectangle (3 by 7) 1559 7 1.5676 2.3241 535 SE Diamond (7 by 7) 655 22 1.7072 2.0342 1347 SE Square (7 by 7) 545 97 1.7855 2.0956 1483 SE Disk (7 by 7, Radius 3) 581 22 1.6713 1.9626 1406 TDN: Number of true detected pixels 49

PAGE 50

CHAPTER 3 STREAM AND ROAD DETECTION US ING DIFFERENTIAL MORPHOLOGICAL PROFILES 3.1 Background of Differential Morphological Profiles Opening and closing are commonly used in morphological operations because, unlike dilation or erosion alone, they generally maintain the size of the features in the image. The open operation dilates an eroded image, whereas th e close operation erodes a dilated image. The morphological top-hat operator for grayscal e images is also a well known morphological operator. Its function is to detect local maxi ma on non-uniform backgrounds. The top-hat is the difference between an image f and its opening, i.e. tophat (f) = f which extracts bright structures or large pixel values. The bothat ope rator was mentioned in Chapter 2. It is the difference between image f and its closing, bothat(f) =bf bf f, and it extracts dark structures or small pixel values (i.e. local minima). Regardless of the particular morphological operation, the response of an image object to that operator depends strongly on the SE. A simple structure of a particular size may have a high response for one SE size, and a low response for ot her SE sizes. For example, consider a DEM image of a large bowl-shaped depression that is 200 pixels in diameter. While the center of that bowl is certainly a local, if not a global minimum, a bothat operator defined on a SE that is 10 pixels wide will respond to small random fluctuati ons in the elevations rather than to the large topographic depression. In some applications, such as photographic inspection of parts in a factory, the sizes of the structures to be detected are known. Another example is that shown in Chapter 2, in which a small urban flood plain was studied a nd most of the main stream channels were of similar widths. But in the general case where la rge complex landscapes are imaged, it is not always possible to 50

PAGE 51

know the size of the channels in advance. Furt hermore, no single SE size may adequately detect all of the channels if they vary greatly in width. Therefore, in such cases, a multi-scale approach based on a range of different SE sizes is approp riate. A range of different hypothetical spatial domains is analyzed, and the highest (best) response of the structures in the image is used for the classification procedure. The idea to use a composition of opening tran sforms for a morphologi cal segmentation of satellite data was origin ally proposed for the detection of diffe rent urban structures in (Bianchin et al., 1994) and (Pesaresi, 1993). By the simple arith metic addition of a series of openings with an increasing SE, segmentation labels we re acquired in the method in (Bianchin et al., 1994) and (Pesaresi, 1993). Those methods are only useful to binary images, and the geodesic metric is not used. In Pesaresi et al. (1999), a composition of geodesic opening and closing operations of different sizes for building a morphologi cal profile is applied. In Pesaresi et al. (2001), Pesaresi and Benediktsson suggested the differential composition of geodesic opening and closing operations of different sizes, which are both more general and more robust than the methods in (Bianchin et al., 1994), (Pesaresi, 1993), and (Pesaresi et al., 1999). Since the tophat and bothat operations are efficient segmentation tools for ex tracting bright and dar k, respectively, objects from an uneven background, we replace opening a nd closing with tophat and bothat operations for our work. We refer to the differential comp osition of geodesic tophat and bothat operations of different sizes as Morphological Profiles (MPs ). We then apply Differential Morphological Profiles (DMPs) to the classificatio n of landforms in the DEMs. It is first time that the tophatbothat filters have been employed with DMPs. A potential disadvantage of these methods (MPs or DMPs) is th at they can lead to large feature sets because a series of tophat and bothat operations occu r. The MP method produces an 51

PAGE 52

image feature set which can help classify the feat ure data very effectively, but it also leads to many redundancies in the feature set. Thus, we would like to see if the MP and DMP feature selection can be combined with f eature reduction to help to find the most important features in the feature space and if similar classification performances can be acquired with a reduced feature set. We will use two feature extraction methods: Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). After feature extracti on, Bayesian clas sification will be used to classify the data assuming Gaussian distribution. 3.2 Differential Morphological Profiles The Morphological Profiles (MPs) and their derivatives, the Differential Morphological Profiles (DMPs), are used to create a feature vector from a single image I. Both methods are based on the repeated use of in our case, the tophat and bothat operators. A Morphological Profile is comprised of the topha t profile (TP) and th e bothat profile (BP). The TP at pixel x of image I is defined as an -dimensional vector: n],0[),()()(nixxTPi R i (3-1) where is a morphological tophat op erator by reconstruction usi ng structuring element (SE) of size i, and n is the total number of topha ts. Also, the BP at pixel x of image I is defined as an -dimensional vector: )(i Rn],0[),()()(nixxBPi R i (3-2) where is a morphological bothat operator by reconstructi on with an SE of size i, and n is the total number of bothats. By definition of the tophat and bothat by reconstruction, we have Given Equation 3-1 and 3-2, the topha t profile can also be defined as a granulometry made with the tophat by reconstruc tion, while the bothat profile can be defined as )(i R)()()(0 0xIxTPxBP 52

PAGE 53

antigranulometry made with botha t by dual reconstructi on. By connecting the TP and the BP together, the MP of image I is defined as the following 12 n dimensional vector: )(),...,(),...,()(xTPxIxBPxMPn n (3-3) ninifTP niifxI niifBP xMPi in i2 )( 0 )( (3-4) The MP for each pixel is the response of the considered pixel to tophat or bothat by reconstruction with a structuring element of increasing size. Ex amples of the tophat and bothat operations for a particular SE size are shown in Figure 3-1. We can see that the bothat emphasizes local minima, such as streams, wher eas the tophat emphasizes local maxima, such as berms. The derivative (difference equa tion actually since the MP is discrete) of the morphological profile is defined as a vector where the measure of the slope of the tophatbothat profile is stored for every step of an increasing SE series. Sp ecifically, the derivative of the tophat profile, is defined as the vector )( xTP nixTPxTPxTPi i i,1,)()()(1 (3-5) Similarly, the derivativ e of the bothat profile )( xBP is defined as the vector nixBPxBPxBPi i i,1,)()()(1 (3-6) We can then define the DMP as the vector njnifxTP njifxBP xDMPnj jn j21 )( 1 )( )(1 (3-7) where 2n is the total number of iterations, j is SE size. From Equation 3-7, if the high responses are near the central position of th e DMP vector, there are mainly sm all structures in the image. 53

PAGE 54

By contrast, high responses either towards the left or the right impl y there are large structures in the image. These larger struct ures are either darker (i.e. hi gh response in th e bothat profile ) or lighter (i.e. high res ponse in the tophat profile )( xBP )( xTP ) than the surroundings. Basically, the DMP provides the information about the size and type of the structure (darker or lighter) in the image by the respons e location in the DMP histogram. The size and type of the structures can be determined by the distance from the center to peak response position in the profile and on which side the peak occurs in the histogram of the DMP values (see Figure 3-2). While the above mentioned approaches do not require a particular metric for the morphological tran sforms, the DMP approach require s the use of the tophat and bothat pair by reconstruction, using a geodesic metric. 3.3 Principal Component Analysis The DMP is a rather high dimensional repres entation (Section 3.2), leading to a length profile for every single pixel in the DEM. Principal Componen t Analysis (PCA) is a well known technique that can be used to reduce multidimensiona l data sets to lower dimensions for analysis. Depending on the field of applicatio n, it is also named the discrete Karhunen-Love transform, the Hotelling transform or Proper Orthogonal Decomposition (POD) (Gonzalez et al., 2002). PCA attempts to find the least redundant set of bases (with respect to seco nd order statistical moments) in which to represent the data by projecting the data in the directions of maximum variance. 2 nLet the training set of DMPs be M ,...,,,321, where M is the number of training and is the DMP vector for pixel in an image. The size of nMn 1nn is1 L where L is the total number of iterations in DMP. The average DMP of the set is defined by 54

PAGE 55

M n nM11 (3-8) Each DMP differs from the average by the vector ii. The vector and scalarskuk are the eigenvectors and eigenvalues, re spectively, of the covariance matrix, Lk 1 M n T nnM C11 (3-9) After sorting eigenvalues, we chose some largest eigenvectors corresponding to the eigenvalues. To classify the classes (new DMP vectors) efficiently, the proper value of k must be chosen. Since the eigenvalues are close to ze ro after the 13th largest eigenvalue, we chose 13 here. The new DMP is transformed into its eigenvector components (proj ected into DMP space) by a simple operation, )( T kkuw for (3-10) ',...,1 Lk where L L '1. 3.4 Linear Discriminant Analysis Linear Discriminant Analysis (LDA) optimizes the ratio of between-class variance to within-class variance in any particular data se t, thereby guaranteeing optim al separability with respect to the second orde r statistical moments (Duda et al., 2001). PCA projec ts data in the directions of maximum variance, however, th e direction of maximum variance may not be optimal for classification. LDA projects to a sp ace which preserves directions useful for data separability, and therefore classification. The object of LDA is to perform dimensionality reduction while preserving as much of the class discriminatory information as possible. For the C-class problem, the projection is from a L-dimensional space to a (C-1)-dimensional space, and it is assumed that CL 55

PAGE 56

In C-classes, we will seek (C-1) projections, ],...,,[1 21 cyyyy, by means of (C-1) projection vectors ,iw11 Ci, which can be arranged by columns into a projection matrix : and (3-11) ]|...||[1 21 CwwwWxwyT iixWyTwhere y is the projected vector, Wis projection matrix and x is the input vector. The generalization of the within-class scatter is C i i wSS1 (3-12) where Cis the total number of classes and ix T i i ixxS))( ( (3-13) i is mean vector of class i, i is the class i label ix i ix N1 (3-14) where is total number of samples from class i. iNThe generalization of the between-class scatter is C i T i ii BNS1))(( (3-15) and ix ii xN N x N 11 (3-16) where N is total number of samples from all classes. Then WBTSSS is called the total scatter matrix. The mean vector and scatter matrices fo r the projected samples are defined as 56

PAGE 57

iy i iy N1 ~ (3-17) C iy T i i Wiyy S1) ~ )( ~ ( ~ (3-18) yy N 1 ~ (3-19) C i T i ii BNS1) ~~ )( ~~ ( ~ (3-20) We can re-write these using a projection matrix W: WSWSW T W ~ (3-21) WSWSB T B ~ (3-22) We are looking for a projection that optimizes the ratio of between-class to within-class scatter. Since the projection is no longer a scalar (it has C-1 dimensions), we then use the determinant of the scatter matrices to obtain a scalar objective function, WSW WSW S S WJW T B T W B ~ ~ )( (3-23) We seek the optimal projection matrix that maximizes this ratio. It can be shown that the optimal projection matrix is the one whose co lumns are the eigenvectors corresponding to the largest eigenvalues of the followi ng generalized eigenvalue problem (Duda et al., 2001). *W*W WSW WSW wwwWW T B T Cmaxarg]|...||[* 1 2 1 *0)(*iWiBwSS (3-24) where i represents the eigenvalues. BS is the sum of C matrices of rank one or less and the mean vectors are constrained by 57

PAGE 58

C i iC11 (3-25) Therefore, will be of rank (C-1) or less. This means that only (C-1) of the eigenvalues BSi will be non-zero. The projections with maximum cla ss separability information are the eigenvectors corresponding to the la rgest eigenvalues of BWSS13.5 Bayesian Classification Bayesian classification is a simple probabilistic classifi cation based on applying Bayes' theorem. If the gi ven class labels are j where ranges from 1 to the number of classes, and j x is the vector of features de rived from the data, we have )( )()|( )|( xp pxp xPjj j (3-26) where j jjpxpxp )()|()(In words, we can re-write, evidence prior likelihood posteriror (3-27) The prior probability reflects know ledge of the relative frequenc y of instances of a class. The likelihood is the probability distribution that a given value occurs in a given class. The evidence is a scaling term to ensure 0(|)1jPx In its most basic form, we choose the class label that yields the maximum a posteriori (MAP) probability for a gi ven sample. For forming a more general classifier, discriminant functions can be specified for each class We assign a sample )( XgiCi ,...,1 X to class if for all k) ()(XgXgj kjk For a minimum error classifier, )|()( XPXgi i If is a monotone increasi ng function, the collection f 58

PAGE 59

()(()),1,...,jihXfgXiC forms an equivalent family of discriminant functions (Duda et al., 2001), e.g., c j ii ii i ipXp pXp XPXg1)()|( )()|( )|()( (3-28) )()|()(ii ipXpXg (3-29) )(ln)|(ln)(i i ipXpXg (3-30) This expression is the well known log likelihood, and it can be read ily evaluated if the densities )|(iXp are multivariate normal, that is, if ),(~)|(ii iNXp where X is a d dimensional vector, is the mean vector, and is the d x d covariance matrix. The general multivariate normal density in d dimensions is written as )()( 2 1 exp )2( 1 )(1 2/1 2/ X X Xpt d (3-31) In this case, we can re-write the discriminant function, )(lnln 2 1 2ln 2 )()( 2 1 )(1 i i i i t i iP d X XXg (3-32) In the general multivariate normal case, the covariance matrices are different for each category. The only term that can be dr opped from Equation 3-32 is the 2ln 2d term because it does not depend on the data, making the resulting discri minant functions inherently quadratic in X : 0)(i t ii t iXwXWXXg (3-33) where 12 1i iW (3-34) 59

PAGE 60

iiiw1 (3-35) and )(lnln 2 1 2 11 0 i i ii t i iP (3-36) 3.6 Result and Discussion To build the Morphological Profiles (MPs), it is necessary to choose a shape and a range of sizes for the Structure Element (SE). A disk shap e is often used because it has the property of being independent to changes of or ientation (i.e. isotropi c). Here, we use a disk. The number of different SE sizes and their increments in size ar e to be chosen to cover all the structures of interest in the image. This is chosen in accordance with the re solution of the data and the range of possible variations in the size of the structures of interest. In the case presented here, a 21dimensional morphological profile was created (ten bothats, ten t ophats, along with the original image) using a circular morphol ogical structuring element with an increasing radius. A 20dimensional DMP (Differential Morphological Profile ) was then generated. Thus, each pixel in the DEM gets associated with a 20-dimensional feature vector. We employ 6 classes in the Hogtown Creek site: 1.Stream, 2. Unstructured watery areas (e.g. ponds, borrow pits, and sink holes), 3. Fore st floor outside of the stream, 4.Road, 5. Suburban area that is not a road, 6.Earthen Berms (See Figure 3-3). PCA (with 13 eigenvectors) and LDA are applied for feature extraction and reduction in the Bayesian classifier. The classification accuracies for the differe nt feature sets were compared to accuracies achieved for the full differential morphological profile. The test image of Hogtown Creek in this experiment is bare-surface DEMG3. The imaged area is 290mm, with 1mm pixels. Approxim ately half of the samples were used for training and the rest for testi ng the approaches (See Table 3-1). We ran the experiment one 60

PAGE 61

hundred times with randomly selected samples fo r training and found the mean and variance of detection percentages. Table 3-2 shows the experimental results. From Table 3-2, we can see the stream is very successfully classified in all three cases. The berm class is also successfully classified. Considering the fact th at the elevation ranges across most roads are considerably smaller th an those across streams or berms, the road accuracies are acceptable. LDA reduces the dimensionality to, at most, C-1, where C is the number of classes (C=6). But in PCA, the dime nsion is changed from 1 to N dimensions (in this case, N was equal to twenty). Here, LDA uses only 5 dimensions. PCA can project up to the original dimensionality of the data (20 in this case), but the top 13 PCA channels, which have most of the variance information (about 97%), were used (i.e. the eigenvalues are close to zero after the 13th largest eigenvalue). So in this case, PCA requires more information than LDA. Often times LDA is expected to be superior to PCA because it deals directly with class discrimination. But this is not always the case. When the training data set is small, PCA can outperform LDA and, also, PCA is sometimes le ss sensitive to different training data sets (Martinez et al., 2001). Here, PCA contains almost all of the information and the berm class has a particularly small amount of available training data, and so it is not surprising that LDA results suffer somewhat. The detection percentages of other classes (classes 2, 3, and 5) are low because they are easily confused with each other. This is perhap s not surprising given th at the classification was based on local morphology at the scale of the stru cturing elements. One would not necessarily expect a morphological operator that detects st reams to differentiate between non-road city terrain and non-stream forested terrain. In the future, we will likely merge some of those classes 61

PAGE 62

because the main intent here is to extract roads and streams fro m the DEM, not to classify all kinds of terrain. In the Hatchett data, we have two classes: 1. Stream, 2. Outside Stream (forest terrain that is not a stream) (See Figure 3-4) since the other classes were not present. We applied the same procedures to Hatchett Creek as we did to Hogtown Creek. Table 3-3 shows the number of samples used for training and testing. The expe rimental results of Hatchett Creek can be found in Table 3-4. Streams are classified well in fu ll DMP, PCA, and LDA. The result of LDA is slightly lower than other two approaches, likely due to the reduced dimensionality. Red Wall Canyon in Death Valley has two clas ses: 1. Stream, 2. Outside Stream (See Figure 3-5). Like Hogtown Creek and Hatchett Creek, the sa me procedures are applied to Red Wall Canyon data and the results are shown in Table 3-6. Table 3-5 shows the number of samples used for training and testing. As it works in Hogtown Creek and Hatchett Creek, the streams are classified well in all cases. In the Hogtown Creek and Red Wall Canyon cas es, the performance difference between PCA and LDA is trivial. However, in the Hatc hett case, there is a pe rformance difference of about 5% between PCA and LDA. One po ssible reason is LDA does not have enough information for the separation because of total number of classes, C (C=2). Red Wall Canyon outperforms than Hogtown Cr eek and Hatchett Creek with regards to non-stream detection performance. This may be due to the use of the vegetation filter on Hogtown Creek and Hatchett Creek. It is mo re difficult to perfectly remove the non-ground LiDAR points in densely vegetated forests than in sparsely vegetated areas like Red Wall Canyon. 62

PAGE 63

3.7 Comparison of C* Algorithm, DMP, and D8 In the field of hydrology, the most commonly used approach to infer the locations of streams is the algorithm known as D8 (TauDE M, 2005). The name derives from the 8 neighboring pixels around the cen ter pixel of a 3 sliding wi ndow. The algorithm was created to be used on the types of DEM data that have been most often used to date. These DEMs are typically generated from stereo aerial photography, such as the USGS National Elevation Dataset (USGS, 2006), or from interferometric radar, such as the NASA Shuttle Radar Topography Mission (SRTM, 2006). They generally have spatial resolutions of 30 m, but in some cases the resolutions are as fine as 10 m. Regardless of the resolution, however, these sensing modalities generally fail to explicitly image stream channels. Thus, the D8 algorithm is predicated on local gradients rather than on stream channel morphology. Rainwater is assumed to flow from a given pixel towards the neighbori ng pixel that offers the steepest gradient descent. The class of stream locating al gorithms to which D8 belongs is generally referred to as watershed algorithms (TauDEM, 2005). Slight va riations exist in the hydrologic literature, including the D algorithm (TauDEM, 2005), but they all work in the same general manner. While D8 works well on coarse-scale DEMs with large topographic relief it often does not work well on flat areas with small closed watersheds, which are common in the coastal plains of the southeastern United States. Yet, these watershed algorithms are still used widely because they are considered to be the best ava ilable. With the greater availabi lity of fine resolution (5m down to 1m) DEMs derived from air borne LiDAR, it is now possible to explicitly image stream channels and automatically detect them. The C* and DMP algorithms are able to exploit this new DEM technology and resolution and detect st reams in a fundamentally different manner than the D8 class of algorithms. 63

PAGE 64

We wish to compare the performance of the C* and DMP approaches for stream detection to each other and to the widely used D8 algorithm We measured the det ection performances of the C* algorithm, DMP, and D8 on simulated da ta, Hogtown Creek data, Hatchett Creek data, and Red Wall Canyon data. To implement the D8 algorithm, we used the TauDEM software package, which is available on the Web [http://hydrology.neng.usu.edu/taudem/]. The D8 flow direction grid defines a network of flow directions that extends to each grid cell (i.e. pixel) in the DEM. Then TauDEM orders the network accord ing to the Strahler (TauDEM, 2005) ordering system. In the Strahler method, pixels that do not have any other pixels draining into them are order Higher order numbers designate pixels that have increasingly higher numbers of pixels from which water would drain into them. When two (or more) flow paths of different order converge, the order of the downstream flow path is the order of th e highest incoming flow path. When two (or more) flow paths of equal orde r converge the downstream flow path is increased by 1. This is implemented as 1orderS highest input flow path order, max second highest input flow path order 1orderS (3-37) which generalizes the common defi nition to cases where more than two flow paths converge at a point. Intuitively, we can see that locations, such as stream channels, into which water that has accumulated over a large area flows, will have relativ ely high Strahler orders. So if one displays all of the DEM pixels with a Strahler order over a certain value, the locations of streams and ponds can be indirectly estimated. Unfortunately, there is no mechanism in the D8 algorithm to automatically determine the optimal threshold for th e Strahler order. A us er-specified threshold is typically chosen that yields a stream map that appears to be the most reasonable based on knowledge of the local hydrology (TauDEM, 2005). In this comparison, we thresholded the D8 64

PAGE 65

result at Strahler order 5 on the simulated DEM, and at order 6 on the Hogtown Creek, Hatchett Creek and Red Wall Canyon sites to produce the best agreement with gro und truth and informed visual interpretation of the DEMs. Figure 3-6 shows results from the three algo rithms on the simulated data, and Table 3-7 shows the corresponding Error Metrics. What we see in Figure 3-6 is that the D8 clearly fails to detect the stream channel in many locations. Furthermore, it erroneously detects false streams in some locations simply because of the presence of local minima in the DEM. The C* and DMP results both appear to match the true stream well As one might expect, the multiscale nature of the DMP responds to a greater variety of channe l widths than does C*, which uses a single SE size. This is evidenced by the greater number of small feeder channels that are detected in the DMP result. In Table 3-7, we see that the C* algorithm has a slightly lower value for EM4 than does DMP, but it also has a lower value for This is because the small numerous feeder paths that direct water into the stream were not explicitly encoded into the simulated stream. So when the DMP detects them, many are counted as false positives (EM2). In this case, we interpret the C* algorithm as giving a slightly better performance than DM P in detecting only the main stream channel, while the DMP gives a slightly better performance than C* in detecting a wider variety of incision features. TDNFigure 3-7 shows analogous results to Figure 36 for the Hogtown site, and Table 3-8 lists the error performances. Again, the D8 has the worst overall detection result. In fact, it mistakenly detects part of a ro ad running from (270 in vertical axis, 98 in horizontal axis) up to (100, 98) and another road running from (170, 1 80) up to (50, 180). The C* algorithm and DMP method give fairly similar results to each othe r. DMP still detects more true pixels (higher ) than C*, but has slightly larger EM3 and EM4 values. TDN 65

PAGE 66

Figure 3-8 demonstrates similar results to Figure 3-6 and Figu re 3-7 for the Hatchett site, and Table 3-9 shows the error performances. Once more, comparing all methods, D8 has the worst overall detection performance. The D8 er roneously detects low elev ation terrain as having sufficient Strahler order to be considered stream. The C* algorithm and DMP methods produce similar and good results with relatively small EM4 values. DMP detects more true pixels than C*, however, it has only minimally larger EM4 values. Finally, Figure 3-9 displays detection resu lts for Red Wall Canyon. The D8 method does not have a lot of erroneous stream detections, as was the case in the other test sites. Table 3-10 gives the error performances for all methods. Unlik e previous sites, there is not a big difference between the EM 4 values of all 3 methods. On e should recall that the vegetation filter has a harder time perfectly reconstruc ting the bare-surface DEM in densely forested regions where only 10% 20% of the LiDAR points typically r each the ground, as in the simulated site, Hogtown Creek, and Hatchett Creek. The i nput bare-surface DEM for Red Wall Canyon is therefore a better representation of the true gr ound surface. Based on results of Hogtown Creek, Hatchett Creek, and Red Wall Canyon, C* and DM P are found to work well for stream detection in the most challenging case of densely fore sted areas. All three methods, including the conventional D8 technique, produce acceptable resu lts in non-forested areas only. The relatively wide and straight nature of the channels in Red Wall Canyon, may also play a role in the improved performance of D8. The DMP algorithm tends to pick up more incision features and small pits in the surface than the other two, which may be useful for understanding incipient channel formation. 66

PAGE 67

Figure 3-1. Morphological Profile fo r the Hogtown Creek site. The st ructuring elements are disks. A) Bothat profile with SE (disk radius 3). B) Original DEM generated from LiDAR ground points gridded to 1m 1m pixel sizes. C) Tophat profile with SE (disk radius 3). All image sizes are 290 m x 521 m. Figure 3-2. Example of a DMP for a pixel on a stream in the Hogtown DEM. A circular morphological structuring element was used w ith an increasing radius from 1 to 10. The peak response is on the bothat side, as one would expect for a stream. 67

PAGE 68

Figure 3-3. Ground truth over the H ogtown site based on image inte rpretation and repeated field surveys: 1.Stream, 2.Unstructured watery ar ea (borrow pit), 3.Fore st floor outside of the stream, 4.Road, 5.Suburban area that is not a road, 6. Earthen berm created for flood control. Figure 3-4. A) Bare-surface DE M of Hatchett Creek. The imag ed area is 425mm, with 1mm pixels. Elevations are in meters. B) A two-class ground truth of Hatchett: Stream (blue), Outside Stream (red). 68

PAGE 69

Figure 3-5. A) Bare-surface DEM of Red Wall Canyon. The imaged area is 601mm, with 1mm pixels. Elevations are in mete rs. B) Ground truth of Red Wall Canyon: Stream (blue), Outside Stream (red) Figure 3-6. Detection results on simulated data. The DEM is 200 m 1000m, with an elevation range of 4m. The DMP result is shown in tw o blocks because it requires training. The left DMP block was used for training when the right DMP block is the test block and vice versa. In A, the white line is the t rue and main stream in the Simulated Data. It does not include the small incipient inci sion features that we see picked up by the algorithms. 69

PAGE 70

Figure 3-7. Detection results on Hogtown Creek. The DEM is 290m 521m, with an elevation range of 7 m. Similar to Figure 3-6, the top DMP block was used for training when the bottom DMP block is the test block and vi ce versa. White line in A is the true and main stream in the Hogtown Creek deri ved from close visual inspection of the DEM and trips to the field site. It does not include the small convergent incipient incision features that we see picked up by the algorithms. 70

PAGE 71

Figure 3-8. Detection results on Hatchett Creek The DEM is 510m 425m, with an elevation range of 7 m. Similar to Figure 3-6 and Fi gure 3-7, the left DMP block was used for training when the right DMP block is the test block and vice versa. White line is the true and main stream in the Hatchett Creek. 71

PAGE 72

Figure 3-9. Detection results on Red Wall Canyon. The DEM is 601m m, with an elevation range of 90m. Similar to Figure 3-6, Figur e 3-7 and Figure 3-8, the left DMP block was used for training when th e right DMP block is the test block and vice versa. The white line in A is the true and main stream in the Red Wall Canyon. 72

PAGE 73

Table 3-1. Information cla sses, training, and test samples for Hogtown Creek site Class No. Information Class Number of Training Samples Number of Test Samples 1 Stream 2101 2100 2 Watery Area 9497 9496 3 Outside Stream 35375 35375 4 Road 4415 4414 5 Outside Road 22556 22555 6 Earthen Berm 1063 1063 Table 3-2. Test accuracies in percenta ges with variances for Hogtown Creek site Class No. Information Class Full DMP (%) PCA (%) LDA (%) 1 Stream 94.17 (1.19) 93.75 (0.14) 92.91 (0.21) 2 Watery Area 28.74 (0.32) 23.92 (0.12) 26.00 (0.18) 3 Outside Stream 13.80 (1.13) 16.24 (0.09) 15.56 (0.06) 4 Road 89.82 (0.26) 89.18 (0.18) 86.22 (0.37) 5 Outside Road 36.30 (0.39) 37.54 (0.08) 36.64 (0.14) 6 Earthen Berm 88.14 (1.26) 86.92 (0.52) 80.38 (0.93) Table 3-3. Information cla sses, training, and test samples for Hatchett Creek Class No. Information Class Number of Training Samples Number of Test Samples 1 Stream 2240 2239 2 Outside Stream 106136 105135 Table 3-4. Test accuracies in percenta ge with variances for Hatchett Creek Class No. Information Class Full DMP (%) PCA (%) LDA (%) 1 Stream 90.30 (0.47) 89.70 (0.43) 84.47 (0.49) 2 Outside Stream 81.28 (0.31) 83.76 (0.14) 91.67 (0.01) Table 3-5. Information cla sses, training, and test samples for Red Wall Canyon Class No. Information Class Number of Training Samples Number of Test Samples 1 Stream 22820 22820 2 Outside Stream 91971 91971 73

PAGE 74

Table 3-6. Test accuracies in percenta ge with variances for Red Wall Canyon Class No. Information Class Full DMP (%) PCA (%) LDA (%) 1 Stream 92.60 (0.02) 92.39 (0.02) 90.07 (0.03) 2 Outside Stream 93.53 (0.01) 93.69(0.008) 95.83(0.005) Table 3-7. Error metrics vs. all methods on simulation EM 1 EM2 EM3 EM4 TDN C* Algorithm 581 22 1.6713 1.9626 1406 D8(TauDEM) 856 1741 1.9677 3.2223 1317 DMP 510 772 2.1621 2.7814 1756 TDN: Number of true detected pixels Table 3-8. Error metrics vs. all methods on Hogtown Creek EM 1 EM2 EM3 EM4 TDN C* Algorithm 78 740 1.3179 2.5861 315 D8 (TauDEM) 281 2187 1.2615 5.0878 201 DMP 83 558 1.7498 2.7436 485 TDN: Number of true detected pixels Table 3-9. Error metrics vs. all methods on Hatchett Creek EM 1 EM2 EM3 EM4 TDN C* Algorithm 135 8 1.4332 1.6642 249 D8(TauDEM) 365 3212 2.3664 8.1451 297 DMP 69 6 1.7132 1.8344 382 TDN: Number of true detected pixels Table 3-10. Error metrics vs. all methods on Red Wall Canyon EM 1 EM2 EM3 EM4 TDN C* Algorithm 609 128 1.7856 2.008 1975 D8(TauDEM) 1018 1239 1.7658 2.4474 1924 DMP 144 360 2.2686 2.4208 1184 TDN: Number of true detected pixels 74

PAGE 75

CHAPTER 4 CONCLUSIONS AND FUTURE WORK To date, the ability to accurately detect a nd parameterize small stre ams, such as those examined here, in forested terrain has been problematic. In situ methods are extremely labor intensive, thus limiting their spatial density and coverage. High-resolution remote sensing methods offer the potential to ch aracterize watersheds much more efficiently than direct field sampling. However, traditional remote sensing technologies, such as passive optical and radar, are not able to extract the neces sary 3D information on surfaces below forest canopies at the required spatial resolutions to reveal streams. While modern ALSM (Airborne Laser Swath Mapping) technology offers the possibi lity of detecting such stream channels in forests, a method is still needed to systematically extract str eam channels and estimate their characteristics. In this work, a set of morphological operations are specified that pe rform this detection, demonstrating for the first time the robust extracti on of small channels in low topographic relief dense forest canopies. The C* algorithm discusse d and demonstrated here allows us to mine ALSM-derived DEMs for these important hydrologic f eatures in a systematic way. From C*, we can extract Radius of Curvature (ROC), bank sl ope asymmetry, width an d depth so that we determine both the planform paths of the channels as well as their 3D forms. This is valuable information for hydrologists or researchers who are studying stream channels. Of particular interest is the discovery of small features that appear to reveal incipient inci sion on floodplains. The detection of such features will likely pr ove very useful for studies of where and how channels initiate in forested watersheds. In a second approach, we used the Differen tial Morphological Profile (DMP) method to determine the optimal size of the structuring element for channel detection. Additionally, we found that the morphological transformations used to build a DM P could be used as a feature set 75

PAGE 76

for Bayesian classification of bot h channels and roads. This is critically important in urban watersheds where the stream network can be cris scrossed with numerous roads. Knowing where the roads are enables us to separate earthen da ms (where the water does not pass) in the DEM from small bridges (where the water can pass). Additionally, we explored ways to reduce the dimensionality of the DMPs. The considered ap proaches were Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). The use of the differential profiles in classification proved valuable, a nd good overall accuracies of str eam detection were achieved, while the detection of roads and earthen berms also shows promis e in the Hogtown Creek data. This reduction in dimensionality is motivated by the desire to run this type of stream detection on larger areas. We can also apply the DMP method to detect streams with different widths because it is a multi-scale approach. Of primary importance is to more fully unde rstand the performance of C* and DMP under different conditions, such as locatio n, data density, and training, so that clear conclusions can be drawn as to their relative merits and when to use C* versus when to use DMP. Experiments should be run in the future on simulated and real data to accomplish this. The C* and DMP algorithms are compared w ith a conventional algorithm (i.e. D8). Unlike our algorithms, D8 requires a user-specifi ed threshold to obtain a result, and is quite sensitive to the choice of threshold. We used user-thresholds too in C* (e.g. when it connects segments, etc.). The main difference is th at those thresholds are only on intermediate calculations and small changes in them probabl y dont dramatically chan ge the final stream detection. In contrast, the threshold in D8 is on the final stream detection and has a huge impact on the D8 results. Also, it doesnt seem to have a clear relation to the physical sizes of the streams as our C* thresholds do. The C* a nd DMP have good performance for stream channel 76

PAGE 77

detection especially in forested areas, while the conventional technique, D8, yields acceptable results in non-forested areas only. In our Hogtown Creek classificati on experiment, we initially used six classes: 1. Stream, 2. Watery Area, 3. Outside Stream, 4. Road, 5. Ou tside Road, 6. Earthen Berm. The features of three of those classes (2: Watery Area, 3: Ou tside Stream, and 5: Outside Road) are not well suited for the small-scale morphology approach we us e to detect steams and roads. Furthermore, detecting those classes are not ce ntral to our topic here, so one may wish change the taxonomy in future classifications so that it focuses more on detecting roads and streams from the background and worries less about classifying that background. In addition, a different approach altogether could be us ed to classify the remaining terrain once streams and roads are classified by C* or DMP. To reduce the dime nsionality of DMP, we examined two well known feature extraction methods, PCA and LDA. While these did produce good stream detection results, the impact of using more or fewer co mponents in PCA on the eventual accuracy should be explored more for different types of terrain. We may also look at more modern feature extraction methods in the future. Finally, we plan to investigate th e classifiers sensitivity to the amount and distribution of trai ning data through more extens ive areas and randomized resampling methods. With the detected streams fully connected, we can begin to characte rize the actual stream network rather than just the location, form of local stream channels and simple features. We could then extract network features such as total volume, ratio of streams of different orders, the evolution of cross-section width and depth with stream order, number and spacing of convergent points (two streams becoming one), etc as one moves downstream. The systematic extraction of these features from LiDAR DEMs woul d be very important for hydrologists. 77

PAGE 78

LIST OF REFERENCES Asselen, S. V., and Seijmonsbergen, A. C., 2006, Expert-driven semi-automated geomorphological mapping for a mountainous area using a laser DTM. Geomorphology 78, pp. 309-320. Beucher, S., and Lantuejoul, C., 1979, Use of watersheds in contour detection, International workshop on image processing, real-time edge and motion detection. Bianchin, A. and Pesaresi, M., 1994, Outils de morphologie mathmatique appliqu aux images satellite pour lanalyze de lurbanization diffuse. In Processing EGIS-MARI 94 Conference, Paris, France, March 29April 1, pp. 2085-2094. Bowen, Z. H. and Waltermire, R. G., 2002, Ev aluation of light detec tion and ranging (LiDAR) for measuring river corridor topography. Journal of The American Water Resources Association, 38, pp. 33-41. Carr, M.H., 1979, Formation of Martian flood f eatures by release of water from confined aquifers, J. Geophys. Res., 84, 2995-3007 Cavalli, M., Tarolli, P., Marchi, L. and Fontan a, G. D., 2007, The effectiveness of airborne LiDAR data in the recognition of channel-bed morphology. Catena, 73, pp. 249-260. Chow, V. T., 1988, Open-Channel Hydraulics (New York: McGraw-Hill) Crespo, J., Serra, J. and Schafer, R., 1995, Th eoretical aspects of morphological filters by reconstruction. Signal Processing, 47, pp. 201-225. Dalrymple, T., and Benson, M.A., 1967, Measur ement of peak discharge by the slope-area method. Techniques of Water-Resources In vestigations Report, Chapter A2. US Government Printing Office. Dillabaugh, C.R., Niemann, K. O ., and Richardson, D.E., 2002, Semi-automatic extraction of rivers from digital imagery, GeoInfomatica, 6, pp. 263-284 Dooge, J. C. I., 1992, Channel Wall Resistance: Cente nnial of Mannings Formula, edited by B. C. Yen (Littleton, Colorado: Wa ter Resources Publications). Douglas, D.H., 1986, Experiments to locate ridges a nd channels to create a new type of digital elevation model. Cartographica, 23, pp. 29-61 Duda, O. R., Hart, P.E., and Stork, D.G., 2001, Pattern Classification, 2nd ed (New York: A Wiley-Interscience Publication) Fischler, M.A., Tenenbaum, J.M. and Wolf, H.C., 1981, Detection of roads and linear structures in low-resolution aerial imagery using a multisource knowledge integration technique. Computer Graphics and Image Processing, 15, pp. 201-223. 78

PAGE 79

Gauckler, P., 1867, Etudes Thoriques et Pratique s sur l'Ecoulement et le Mouvement des Eaux, Comptes Rendues de l'Acadmie des Sciences, Paris, France, Tome 64, pp. 818-822 Gioia1 G. and Bombardelli F. A., 2002, Sca ling and Similarity in Rough Channel Flows, PHYSICAL REVIEW LETTERS, 88, 014501. Gonzalez, R. C. and Woods, R.E., 2002, Digital Image Processing, 2nd ed (New Jersey: Prentice-Hall) Goutsias, J., Vincent, L., and Bloomberg, D. S., 2000, Mathematical Morphology and Its Applications to Image and Signal Processing (Kluwer: Academic Publishers) James, L. A., Watson, D. G., and Hansen, W. F., 2007, Using LiDAR data to map gullies and headwater streams under forest canopy: South Carolina, USA. Catena, 71, pp. 132-144. Japan Industry Technology Center, 1993, Introduction of Computer Image Processing (Korean version) (Seoul: Mechanics Research Press). Jenson, S.K. and Domingue, J.O., 1988, Extracting topographic structure from digital elevation data for geographic information system analysis, Photogrammetric Engineering and Remote Sensing 54(11), 1593-1600. Johnston, E.G. and Rosenfeld, A., 1975, Digital detection of pits, peaks, ridges and ravines. IEEE Transactions on Systems, Man and Cybernetics, 5, pp. 472-480. Jones, A. F., Brewer, P. A., Johnstone, E. and Macklin, M. G., 2007, High-resolution interpretative geomorphological mapping of ri ver valley environments using airborne LiDAR data. Earth Surface Processes and Landforms, 32, pp. 1574-1592. Kampa, K. and Slatton, K. C ., 2004, An adaptive multiscale filter for segmenting vegetation in ALSM data. In Proceeding IEEE 2004 International Geoscience and Remote Sensing Symposium (IGARSS), 20-24 September, 6, pp. 3837-3840. Knighton, D., 1998, Fluvial Forms and Processes: A New Perspective (Arnold Press). Laliberte, A.S., Johnson, D.E., Harris, N.R., a nd Casady, G.M., 2001, Stream change analysis using remote sensing and Geographic Information Systems (GIS). Journal of Range Management, 54: pp. 22-50. Lashermes, B., Georgiou, E. F. and Dietrich, W. E., 2007, Channel netw ork extraction from high resolution topography using wavelets. Geophysical Research Letters, 34, L23S04. Leopold, L. B., Wolman, M. G. and Miller, J. P., 1964, Fluvial Processes in Geomorphology (San Francisco: W. H. Freeman and Co.) Lindsay, J. B., 2006, Sensitivity of channel ma pping techniques to uncertainty in digital elevation data. International Journal of Geogr aphical Information Science, 20, pp. 669692. 79

PAGE 80

Martinez, A. M. and Kak, A. C., 2001, PCA versus LDA. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23, pp. 228-233. Mason, D. C., Scott, T. R. and Wang, H. J., 2006, Extraction of tidal channel networks from airborne scanning laser altimetry. ISPRS Journal of Photogrammetry & Remote Sensing 61, pp. 67-83. Montgomery, D.R. and FoufoulaGeorgiou, E., 1993, Channel network source representation using digital elevation models. Water Resources Research, 29, pp. 3925-3934. OCallaghan, J.F. and Mark, D.M., 1984, The extr action of drainage networks from digital elevation data. Computer Vision, Graphi cs, & Image Processing, 28, pp. 323-344. Otsu, N., 1979, A threshold selection method from gray-level histograms. IEEE Transactions on Systems, Man, and Cybernetics, 9, pp. 62-66. Pesaresi, M., 1993, Analisi Numerica dello spazio edificato nella citt diffusa (Venice, Italy: Techical Report. IUAV DAEST) Pesaresi, M. and Benediktsson, J. A., 2001, A new approach for the morphological segmentation of high-resolution satellite imagery. IEEE Transactions on Geoscience Remote Sensing, 39, pp. 309-320. Pesaresi, M. and Kannellopulos, I., 1999, Detecti on of urban features us ing morphological based segmentation and very high resolution remotely sensed data. Machine Vision and Advanced Image Processing in Remote Sensing, Kanellopoulos, I., Wilkinson, G. G. and Moons, T., Eds. (Berlin, Germany: Springer-Verlag). Peucker, T.K. and Douglas, D.H., 1975, Detecti on of surface-specific po ints by local parallel processing of discrete terrain elevation data. Computer Graphics and Image Processing, 4, pp. 375-387. Shrestha, R., Carter, W., Slatt on, K.C., Dietrich, W., 2007, Res earch-Quality Airborne Laser Swath Mapping: The Defining Factors, ver. 1.1. National Center for Airborne Laser Mapping (NCALM), http://www.ncalm.ufl.edu /, (accessed 22 June 2007). Soille, P. and Pesaresi, M., 2002, Advances in mathematical morphology applied to geosciences and remote sensing. IEEE Transactions on. Geoscience Remote Sensing, 40, pp. 20422055 Soille, P., 2003, Morphological Image Analysis Principles and Applications, 2nd ed. (Berlin, Germany: Springer-Verlag). NASA Shuttle Radar Topography Mission (SRTM), 2006, URL: http://www2.jpl.nasa.gov/srtm/ (accessed 05 June 2008) Terrain Analysis Using Digital Elev ation Models (TauDEM), 2005, URL: http://hydrology.neng.usu.edu/taudem/ (accessed 05 June 2008) 80

PAGE 81

USGS National Elevatio n Dataset, 2006, URL http://ned.usgs.gov/ (accessed 05 June 2008) 81

PAGE 82

BIOGRAPHICAL SKETCH Hyun-chong Cho was born in Suwon, South Korea. He received his B.S. and M.S. degrees in electrical and electronic engineering from Gyeongsang Nati onal University, South Korea in 1999 and 2001 respectively. From 1997 to 1998, he was an exchange student with a full scholarship in information and electronic engi neering from Nagoya Univ ersity, Japan. Since 2002, he has been working toward his Ph.D. degree in electrical and computer engineering at the University of Florida, Gainesville. He bega n working under the supervision of Dr. K. Clint Slatton in 2005. His research interests include remote sensing, image processing, and adaptive signal processing, especially re lated to airborne laser swath mapping (ALSM) applications. 82