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3D Feature Extraction and Geometric Mappings for Improved Parameter Estimation in Forested Terrain Using Airborne LiDAR Data

Permanent Link: http://ufdc.ufl.edu/UFE0021923/00001

Material Information

Title: 3D Feature Extraction and Geometric Mappings for Improved Parameter Estimation in Forested Terrain Using Airborne LiDAR Data
Physical Description: 1 online resource (127 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: 3d–point–data, airborne–lidar, feature–extraction, forestry, remote–sensing
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: Scanning laser ranging technology is well suited for measuring point-to-point distances because of its ability to generate small beam divergences. As a result, many of the laser pulses emitted from airborne light detection and ranging (LiDAR) systems are able to reach the ground underneath tree canopies through small (10 cm scale) gaps in the foliage. Using high pulse rate lasers and fast optical scanners, airborne LiDAR systems can provide both high spatial resolution and canopy penetration, and these data have become more widely available in recent years for use in environmental and forestry applications. The small-footprint, discrete-return Airborne Laser Swath Mapping (ALSM) system at the University of Florida (UF) is used to directly measure ground surface elevations and the three-dimensional (3D) distribution of the vegetative material above the soil surface. Field of view geometric mappings are explored to find optical gaps inside forests. First, a method is developed to detect walking trails in natural forests that are obscured from above by the canopy. Several features are derived from the ALSM data and used to constrain the search space and infer the location of trails. Second, a robust and simple procedure for estimating intercepted photosynthetically active radiation (IPAR), which is an important measure of forest timber productivity and of daylight visibility in forested terrain, is presented. Simple scope functions that isolate the relevant LiDAR reflections between observer locations and the sun are defined and shown to give good agreement between the LiDAR-derived estimates and values of IPAR measured in situ. A conical scope function with an angular divergence from the centerline of 7 degree provided the best agreement with the in situ measurements. This scope function yielded remarkably consistent IPAR estimates for different pine species and growing conditions. The developed idea could be extended, through potential future work, to characterize the spatial distribution of attenuation of GPS (L-band) microwave signals and of detectability from the sky for military personnel operating in forested terrain. Measuring individual trees can provide valuable information about forests, and airborne LiDAR sensors have been recently used to identify individual trees and measure structural tree parameters. Past results, however, have been mixed because of reliance on interpolated (image) versions of the LiDAR measurements and search methods that do not adapt to variations in canopies. In this work, an adaptive clustering method is developed using 3D airborne LiDAR data acquired over two distinctly different managed pine forests in North-Central Florida, USA. A critical issue in isolating individual trees is determining the appropriate size of the moving window (search radius) when locating seed points. The proposed approach works directly on the 3D cloud of LiDAR points and adapts to irregular canopy sizes. The region growing step yields collectively exhaustive sets in an initial segmentation of tree canopies. An agglomerative clustering step is then used to merge clusters that represent parts of whole canopies using the locally varying height distribution. The overall tree detection accuracy achieved is 95.1% with no significant bias. The tree detection enables subsequent estimation of tree height and vertical crown length to an accuracy of better than 0.8 m and 1.5 m, respectively. Lastly, a compact representation of the different geometric characteristics of the segmented LiDAR points is introduced using spin images as a new tool that can potentially help tree detection in complex natural forests.
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.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Slatton, Kenneth C.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021923:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021923/00001

Material Information

Title: 3D Feature Extraction and Geometric Mappings for Improved Parameter Estimation in Forested Terrain Using Airborne LiDAR Data
Physical Description: 1 online resource (127 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: 3d–point–data, airborne–lidar, feature–extraction, forestry, remote–sensing
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: Scanning laser ranging technology is well suited for measuring point-to-point distances because of its ability to generate small beam divergences. As a result, many of the laser pulses emitted from airborne light detection and ranging (LiDAR) systems are able to reach the ground underneath tree canopies through small (10 cm scale) gaps in the foliage. Using high pulse rate lasers and fast optical scanners, airborne LiDAR systems can provide both high spatial resolution and canopy penetration, and these data have become more widely available in recent years for use in environmental and forestry applications. The small-footprint, discrete-return Airborne Laser Swath Mapping (ALSM) system at the University of Florida (UF) is used to directly measure ground surface elevations and the three-dimensional (3D) distribution of the vegetative material above the soil surface. Field of view geometric mappings are explored to find optical gaps inside forests. First, a method is developed to detect walking trails in natural forests that are obscured from above by the canopy. Several features are derived from the ALSM data and used to constrain the search space and infer the location of trails. Second, a robust and simple procedure for estimating intercepted photosynthetically active radiation (IPAR), which is an important measure of forest timber productivity and of daylight visibility in forested terrain, is presented. Simple scope functions that isolate the relevant LiDAR reflections between observer locations and the sun are defined and shown to give good agreement between the LiDAR-derived estimates and values of IPAR measured in situ. A conical scope function with an angular divergence from the centerline of 7 degree provided the best agreement with the in situ measurements. This scope function yielded remarkably consistent IPAR estimates for different pine species and growing conditions. The developed idea could be extended, through potential future work, to characterize the spatial distribution of attenuation of GPS (L-band) microwave signals and of detectability from the sky for military personnel operating in forested terrain. Measuring individual trees can provide valuable information about forests, and airborne LiDAR sensors have been recently used to identify individual trees and measure structural tree parameters. Past results, however, have been mixed because of reliance on interpolated (image) versions of the LiDAR measurements and search methods that do not adapt to variations in canopies. In this work, an adaptive clustering method is developed using 3D airborne LiDAR data acquired over two distinctly different managed pine forests in North-Central Florida, USA. A critical issue in isolating individual trees is determining the appropriate size of the moving window (search radius) when locating seed points. The proposed approach works directly on the 3D cloud of LiDAR points and adapts to irregular canopy sizes. The region growing step yields collectively exhaustive sets in an initial segmentation of tree canopies. An agglomerative clustering step is then used to merge clusters that represent parts of whole canopies using the locally varying height distribution. The overall tree detection accuracy achieved is 95.1% with no significant bias. The tree detection enables subsequent estimation of tree height and vertical crown length to an accuracy of better than 0.8 m and 1.5 m, respectively. Lastly, a compact representation of the different geometric characteristics of the segmented LiDAR points is introduced using spin images as a new tool that can potentially help tree detection in complex natural forests.
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.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Slatton, Kenneth C.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021923:00001


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1 3D FEATURE EXTRACTION AND GEOMETRIC MAPPINGS FOR IMPROVED PARAMETER ESTIMATION IN FORESTED TERRAIN USING AIRBORNE LIDAR DATA By HEEZIN LEE 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 2008

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2 2008 Heezin Lee

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3 To my parents and wife

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4 ACKNOWLEDGMENTS First of all, I would like to express m y gratitude to my advisor, Dr. K. Clint Slatton, for his great inspiration, support, and guidance over my studies. His supervision gave me a lot of opportunities to explore my research interests. I am also grateful to Dr. Ramesh Shresha, Dr. John G. Harris, Dr. Jianbo Gao, and Dr. Wendell P. Cropper Jr. for their valuable time and interest in serving on my supervisory committee, as well as their comments, which helped improve the quality of this dissertation. My special acknowledgement goes to all of my ALSM and ASPL lab colleagues, Dr. William E. Carter, Abhinav Singhania, Bidhyana nda Yadav, Carolyn Krekeler, Hojin Jhee, Hyunchong Cho, John Caceres, Juan Carlos Fernand ez Diaz, Karthik Nagarajan, Kittipat Kampa, Kristofer Shrestha, Kuei-Tsung Shih, Michael Sa rtori, Michael Starek, Pang-wei Liu, Pravesh Kumari, Raghavendra Kumar, Sweungwon Che ung, Thelma Epperson, Tory Cobb, Tristan Cossio, and William Wright, for their help, collab oration and valuable discussions. They also brought me continuous fun, which was essential dur ing my PhD study. I owe much to them all. Finally, my utmost appreciation goes to my parents for always believing in me. Their unceasing love and whole-hearted support made fini shing this work possible. Last but most, I thank my wife, Hyeja, for her love, suppor t, patience, and la te night prayers.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES.........................................................................................................................9 LIST OF ABBREVIATIONS........................................................................................................ 12 ABSTRACT...................................................................................................................................14 CHAP TER 1 INTRODUCTION..................................................................................................................17 1.1 Airborne Laser Scanning .............................................................................................17 1.2 3D Airborne Laser Data over Forested Terrain ........................................................... 21 1.3 Organization of this Study and Contributions .............................................................23 2 STUDY SITES AND DATA ACQUISITIONS..................................................................... 27 2.1 Study Sites ...................................................................................................................27 2.2 Ground Truth and ALSM Data Acquisitions ............................................................... 30 2.3 Preprocessing ...............................................................................................................32 3 FIELD OF VIEW GEOMETRIC MAPPINGS...................................................................... 34 3.1 IPAR Estimation ..........................................................................................................34 3.1.1 Motivation .......................................................................................................... 34 3.1.2 Estim ation of In-Situ IPAR................................................................................38 3.1.3 Isolating the Vegetative Contribution to IPAR .................................................. 40 3.1.4 Optical Scope Functions ....................................................................................41 3.1.5 Estim ation of IPAR from ALSM....................................................................... 44 3.1.6 Results ................................................................................................................ 46 3.1.6.1 Selection of the Best Scope Function ........................................................ 47 3.1.6.2 Variation in IPAR ...................................................................................... 48 3.1.6.3 Residual Analysis ...................................................................................... 49 3.1.7 Discussion .......................................................................................................... 50 3.1.7.1 Factors Influencing in situ IPAR ............................................................... 50 3.1.7.2 Potential Sources of Error .........................................................................51 3.1.7.3 Bias Between Species ................................................................................52 3.1.7.4 Spatia l Variations of IPARALSM................................................................53 3.2 Detecting Forest Trails ................................................................................................. 54 3.2.1 Introduction ........................................................................................................ 54 3.2.2 Study Area and Data Acquisition ...................................................................... 56

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6 3.2.3 Data Segm entation.............................................................................................56 3.2.4 Visibility V ectors and Geometric Constraints................................................... 59 3.2.5 Result on Test Sites ............................................................................................61 4 A CLUSTERING APPROACH TO INDIVIDUAL TREE DETECTION ............................ 62 4.1 Introduction .................................................................................................................. 62 4.2 Scale-Space Method.....................................................................................................65 4.3 Proposed Algorithm .....................................................................................................70 4.3.1 Finding Seed Locations......................................................................................70 4.3.2 The Effect of R on Finding Seed Points............................................................. 71 4.3.3 Region Growing Process....................................................................................74 4.3.4 Agglom erative Hierarchical Clustering............................................................. 77 4.4 Results and Com parison.............................................................................................. 82 4.5 Discussion ....................................................................................................................86 5 FOREST PARAMETER ESTIMATION...............................................................................90 5.1 Introduction .................................................................................................................. 90 5.2 Estim ation of Tree Height and Crown Length............................................................. 90 5.2.1 Tree Height (HT) ............................................................................................... 90 5.2.2 Crown Length (CL)............................................................................................90 5.3 Results and Discussion ................................................................................................92 5.3.1 Tree Height ........................................................................................................ 92 5.3.2 Crown Length ....................................................................................................94 5.3.3 Underestim ation of the Parameters.................................................................... 94 5.3.4 Impact of LiDAR Point Density........................................................................ 95 5.4 Other Param eters.......................................................................................................... 95 5.4.1 Crown Area ........................................................................................................95 5.4.2 Diam eter at Breast Height (DBH)...................................................................... 96 5.4.3 2-Dim ensional Open Gaps................................................................................. 96 5.4.4 3-Dim ensional Open Gaps................................................................................. 97 6 SPIN IMAGES OF DIFFUSE TARGETS.............................................................................99 6.1 Motivation ....................................................................................................................99 6.2 Spin Im ages................................................................................................................ 100 6.3 Creating Spin Im ages from ALSM Points................................................................. 101 6.4 Spin Im ages of Canopy Clusters................................................................................ 104 6.5 Reducing Com putati onal Complexity........................................................................ 110 6.5.1 Num ber of Bins................................................................................................ 110 6.5.2 Num ber of Points on an Object........................................................................ 110 6.5.3 Num ber of Spin Images................................................................................... 111 7 CONCLUSIONS AND FUTURE WORK ........................................................................... 112 7.1 Conclusions ................................................................................................................112 7.2 Future W ork...............................................................................................................114

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7 7.2.1 Extension to Different Forest Types ................................................................ 114 7.2.2 Line-of-Sight Visibility .................................................................................... 115 7.2.3 Multi-feature Spin Im ages............................................................................... 116 7.2.4 New ALSM Technology.................................................................................. 117 LIST OF REFERENCES.............................................................................................................118 BIOGRAPHICAL SKETCH.......................................................................................................127

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8 LIST OF TABLES Table page 1-1 Typical performance specifications for UF-ALSM system .............................................. 19 2-1 February, 2006 in situ field data from across the study sites describing general information about the sites.................................................................................................29 3-1 Plot level inventory data detailing tre e survival and solar angles at the time of the in situ PAR measurements..................................................................................................... 38 3-2 Analysis of Variance (ANOVA) table for in situ and estim ated IPAR............................. 49 3-3 Least Squares estimates of IPAR measured in situ and estim ated from ALSM................ 49 4-1 Algorithm of finding seed points....................................................................................... 71 4-2 Region growing algorithm................................................................................................. 76 4-3 Agglomerative clustering algorithm.................................................................................. 80 4-4 Results of individua l tree segm entation............................................................................. 84 4-5 Results of individual tree segm entation by the scale-space m ethod.................................. 86 5-1 The mean differences between the ground tr uth values and the estim ates of HT and CL......................................................................................................................................93 6-1 The mean value of the correlation coefficients for each case in Figure 6-4.................... 109 6-2 The mean value of the correlation coefficients for each case in Figure 6-5.................... 110

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9 LIST OF FIGURES Figure page 1-1 Illustration of a small footpr int LiD AR system in operation............................................. 20 1-2 An example of undersampling in LiDAR data over a natural forest................................. 23 2-1 The locations of the study sites (PPINE S and IMPAC) with the geographic range of slash pine shaded................................................................................................................28 2-2 A schematic layout of a si ngle p lot from each study site.................................................. 29 2-3 Top view of first-stop LiDAR point heights of a typical plo t from each cultural intensity at each site...........................................................................................................30 2-4 Segmented ground laser points and the estim ated ground elevation at the IMPAC site... 33 2-5 Raw and flattened first/ last stop elevation points ..............................................................33 3-1 The spatial arrangement of the plots in the IMPAC site.................................................... 37 3-2 Solar angles ( ) defined relative to an observer point at the origin of a local spherical coordinate frame.................................................................................................39 3-3 Different types of scope functions investigated ................................................................. 42 3-4 The weighting functions for the cone scopes..................................................................... 43 3-5 Residual analysis comparing the two types of scope functions as dim ensions change, where average absolute difference is simp ly the average absolute value of ALSM IPAR estimates minus in situ IPAR measurements........................................................... 48 3-6 Relationship between observed ( in situ ) and estim ated IPAR (from ALSM) using the cone function with =7 and weighted by distance.........................................................50 3-7 A side view of a plot wi th a hypothetical position of the sun and a scope function .......... 52 3-8 IPARALSM distribution for contrasting sun angles at an observer elevation of 2 m, illustrating the spatial resolution of IPARALSM computed in equation 7-2......................... 53 3-9 Shaded relief image and ground photos of the study area................................................. 57 3-10 Point cloud from the training site....................................................................................... 57 3-11 ALSM data points between 1 m and 4 m elevation (blue dots), tree trunks (black double circles), sm ooth surface points (red small circles), and GPS trail (yellow circles)................................................................................................................................58

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10 3-12 All acquired visibility vectors and the wi nning trail candidate in the training site ........... 60 3-13 The winning trail candida te in the testing site ................................................................... 61 4-1 Aerial photos illustrating the variatio n of canopy morphology even within managed pine forests................................................................................................................... ......63 4-2 Creation of 2D height imag e from 3D LiDAR point clouds............................................. 66 4-3 An example of a scale-space representation...................................................................... 67 4-4 The detected blobs and strength of th eir scale-sp ace signatures at each scale.................. 68 4-5 The mean blob signature.................................................................................................... 69 4-6 The result of individual tree detection by the scale-space m ethod....................................69 4-7 Identifying the seed points in two different cases.............................................................. 71 4-8 Sensitivity of the detection result to the search region R ...................................................72 4-9 The number of detected seeds depending on R in a sm all selected area............................ 73 4-10 The changes in detected seed point s that occur by changing the size of R from 10 m to 1 m.................................................................................................................................73 4-11 An illustration of a case where T is necessary ...................................................................75 4-12 An example of the region growing result.......................................................................... 76 4-13 An example of hierarchical tree and me rged clusters a t specific levels of R ....................78 4-14 Probability density func tions of the two classes ( w1: partial tree clusters, w2: complete tree clusters) estimated by the Parzen windowing method................................ 81 4-15 The segmentation resu lt over the sm all area ...................................................................... 82 4-16 Methodology overview of the proposed algorithm............................................................ 83 4-17 An example of the segmentation result s (a plot with high culture at PPINES) ................. 85 4-18 Performance comparison between the pr oposed method and the scale-space m ethod...... 86 4-19 A top view of the low culture PPINES plot shown in Figure 2-3...................................... 89 5-1 An illustration of estimates of HT, HTLC, and CL on segm ented LiDAR points............ 98 5-2 An example of the maximum possible open angles at locations on the ground ................ 98

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11 6-1 The object centered 3D coordinate system to create a spin image................................. 101 6-2 Selection of the size of spin image.................................................................................. 102 6-3 An example of a spin image of a full tree cluster............................................................104 6-4 Spin images of each cluster in Figure 3-9........................................................................ 106 6-5 Spin images of tree clusters from three different classes................................................. 107

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12 LIST OF ABBREVIATIONS AGL Above Ground Level ALSM Airborne Laser Swath Mapping ANOVA Analysis of Variance CD Crown Diameter CL the length of live crown DBH Diameter at Breast Height DEM Digital Elevation Model DSM Digital Surface Model EAARL Experimental Advanced Airborne Research LiDAR FBRC Forest Biology Research Cooperative FOV Field Of View FWHM Full Width Half Maximum GMM Gaussian Mixture Model GPS Global Positioning System HT Tree Height HTLC the height to the base of the live crown IFAS Institute of Food and Agricultural Sciences IMPAC Intensive Management Practices Assessment Center INS Inertial Navigation System InSAR Interferometric Synthetic Aperture Radar IPAR Intercepted Photosynthe tically Active Radiation IR InfraRed KARS Kinematic And Rapid Static KL Kullback-Leibler

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13 LAI Leaf Area Index LiDAR Light Detection and Ranging LVIS Laser Vegetation Imaging Sensor MI Mutual Information PAR Photosynthetically Active Radiation PCA Principle Component Analysis pdf probability density function PPINES Pine Productivity INterac tions on Experimental Sites RF Radio Frequency RMS Root-Mean-Square ROI Region Of Interest SLICER Scanning LiDAR Imager of Canopies by Echo Recovery UF-ALSM University of Florida Airborne Laser Swath Mapping UTM Universal Transverse Mercator

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14 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 3D FEATURE EXTRACTION AND GEOMETRIC MAPPINGS FOR IMPROVED PARAMETER ESTIMATION IN FORESTED TERRAIN USING AIRBORNE LIDAR DATA By Heezin Lee May 2008 Chair: K. Clint Slatton Major: Electrical and Computer Engineering Scanning laser ranging technology is well suit ed for measuring point-to-point distances because of its ability to genera te small beam divergences. As a result, many of the laser pulses emitted from airborne light detection and ranging (LiDAR) systems are able to reach the ground underneath tree canopies through small (10 cm scale) gaps in the foliage. Using high pulse rate lasers and fast optical scanners airborne LiDAR systems can provi de both high spatial resolution and canopy penetration, and these data have become more widely available in recent years for use in environmental and forestry applications. The small-footprint, discrete-return Airborne Laser Swath Mapping (ALSM) system at the Univer sity of Florida (UF) is used to directly measure ground surface elevations a nd the three-dimensional (3D) distribution of the vegetative material above the soil surface. Field of view geometric mappings are explored to find optical ga ps inside forests. First, a method is developed to detect walking trails in natural forests that are obscured from above by the canopy. Several features are derived from the ALSM data and used to constrain the search space and infer the location of trails. Second, a robust and simple procedure for estimating intercepted photosynthetically active radiation (IPAR), which is an important measure of forest timber productivity and of daylight visibility in forested terra in, is presented. Simple scope

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15 functions that isolate the relevant LiDAR reflec tions between observer locations and the sun are defined and shown to give good agreement between the LiDAR-derived estimates and values of IPAR measured in situ A conical scope function with an an gular divergence from the centerline of provided the best agreement with the in situ measurements. This scope function yielded remarkably consistent IPAR estimates for diffe rent pine species and growing conditions. The developed idea could be extended, through potentia l future work, to characterize the spatial distribution of attenuation of G PS (L-band) microwave signals and of detectability from the sky for military personnel operat ing in forested terrain. Measuring individual trees can provide valuable information about forests, and airborne LiDAR sensors have been recently used to identif y individual trees and measure structural tree parameters. Past results, however, have been mixed because of reliance on interpolated (image) versions of the LiDAR measurem ents and search methods that do not adapt to variations in canopies. In this work, an adaptive clustering method is developed usi ng 3D airborne LiDAR data acquired over two distinctly different manage d pine forests in North-Central Florida, USA. A critical issue in isolating i ndividual trees is determining th e appropriate size of the moving window (search radius) when locating seed points. The proposed approach works directly on the 3D cloud of LiDAR points and adapts to irregular canopy sizes. Th e region growing step yields collectively exhaustive sets in an initia l segmentation of tree canopies. An agglomerative clustering step is then used to merge clusters that represent parts of whole canopies using the locally varying height distribution. The overall tr ee detection accuracy achi eved is 95.1% with no significant bias. The tree detec tion enables subsequent estimation of tree height and vertical crown length to an accuracy of better than 0.8 m and 1.5 m, respectively. Lastly, a compact representation of the different geometric char acteristics of the segmented LiDAR points is

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16 introduced using spin images as a new tool that can potentially help tr ee detection in complex natural forests.

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17 CHAPTER 1 INTRODUCTION 1.1 Airborne Laser Scanning There are tw o major classes of airborne laser ranging technologies cu rrently in use: (1) large-footprint, full-waveform systems; and (2) small-footprint, discrete-return systems. Largefootprint LiDAR systems, such as the NASA Laser Vegetation Imaging Sensor (LVIS) (Drake et al ., 2002) and Scanning Lidar Imager of Canopi es by Echo Recovery (SLICER) (Lefsky et al ., 1999a), generally have footprint diameters of tens of meters. The return si gnal is finely sampled over a long range gate, yielding a digitized reflec ted laser waveform. Because the large footprint spreads the transmitted photons over a wide ar ea, many photons penetrate deep into the canopy, providing a densely sampled vertic al profile. While, large-footprin t systems have been used to estimate forest biophysical parameters (Lefsky et al ., 1999a; Lefsky et al ., 1999b; Means et al ., 1999; Ni-Meister et al ., 2001; Parker et al ., 2001; Hyde et al ., 2005), they are incapable of sensing structure over meter-scale spatial (horizontal) extent since the received waveform represents an integrated response for the entire area illuminated by the f ootprint. This limitation also leads to non-unique functi onal mappings from the received waveforms back to forest structure because an infinite number of structural configurations can, in principle, result in the same waveform shape. Consider, for example, a patch of forest illuminated by the circular footprint. Rotating that patch 180 about the laser bore sight will not change the received waveform. Also, full-waveform LiDAR sensors primarily remain research tools due to the excessive data volumes and associated pe r unit area acquisition costs (Flood, 2002). The experimental NASA system, Experimental Adva nced Airborne Research Lidar (EAARL), combines waveform digitization with small-footprints (Brock et al ., 2002). However, the laser pulse rate is comparatively low, which further reduces terrain sampling rates. The LiDAR data

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18 used in this work belongs to the small-footprint class of airborne laser-ranging technologies, which is more accessible to the wider research and forest management communities. Small-footprint LiDAR systems, such as Ai rborne Laser Swath Mapping (ALSM) system at the University of Florida (UF), can provide sp atially dense (decimeter scale) sampling of the foliage and surface in three-dimensions (3D) The point location accuracy of the UF-ALSM system is nominally 15-20 cm horizontally a nd 5-10 cm vertically. The UF-ALSM unit was dramatically upgraded in February 2007, but the unit that was in use prior to that was used to collect all data in this work. It records both firs t and last laser reflections per outgoing pulse at a rate of 33 kHz with a transmitted pulse duration ( ) of 10 ns (3 m path length) at a near-infrared laser wavelength ( ) of 1064 nm. It also records a relative intensity of each reflection where the intensity of the reflected signal depends primarily on the surface material of the target (Carter et al ., 2001), but also on the incidence angle. Highresolution multispectral imagery is acquired concurrently. The system records the ranges of the first and last return puls es using a constant fraction discriminator at the output of an avalan che photodiode detector to detect the Full Width Half Maximum (FWHM) poi nts on the returned laser waveform (Slatton et al ., 2005). As with all discrete-return ALSM systems, the pulse length imposes a lower limit on the vertical resolution between return pulses. The approxi mate minimum vertical distance for which separable first and last return s can be recorded, given the 10 ns pulse duration, is 2.5 m. The distribution of laser spots on the terrain is created by a single-ax is oscillating mirror. Together with the forward motion of the aircraft, it cr eates a saw-toothed patte rn on the ground along the flight path. The half-angle laser beam diverg ence is 0.125 mrad, resultin g in a laser footprint that is approximately 15 cm in diameter when the system flies at an Above Ground Level (AGL) altitude of 600 m. At this fl ying altitude, the swath width is a pproximately 400 m. Typical flying

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19 altitudes, scan rates, max scan angles, and laser pulse rates of 600 m, 30 Hz, and 30 kHz, respectively, provide roughly 1 laser shot per square meter on the ground. The typical performance of UF-ALSM is depicted in Table 1-1. Much higher point densities are readily achieved using overlapping flightlines, by flying lower and slower, and by using a narrower scan angle. Table 1-1. Typical performance specificati ons for UF-ALSM system (a 1233 ALSM model manufactured by Optech, Inc.) prior to Febr uary 2007. This unit provided all of the LiDAR data used in this work. Parameter Flying height Flying speed Swath width Scan rate Laser pulse rate Scan angle range Data recording Specification 600 m 60 m/s 400 m 30 Hz 33 kHz 20 First and last return with intensities In order to georeference each laser return into an earth-fixed x, y, z coordinate frame, ALSM incorporates three main technologies. (1) An onboard global positioning system (GPS) receiver: Location solutions for the aircraft are determined at a rate of 1 Hz. Given a precise measurement of the physical displacement (i.e. th e lever arm) between the sensor head and the GPS receiver, the precise position of the LiDAR se nsor head can then be estimated using one or more GPS ground reference stations near the area of study. This allows differential correction of the aircraft trajectory, resulting in a root-mean-square (rms) error to within a few centimeters. (2) An inertial navigation system (INS): A Litton LN200A INS unit integrat es accelerometers and horizontal and vertical gyroscopes to record the roll, pitch, and yaw of the aircraft at a rate of 50 Hz. This information is used to compute the exac t orientation of the aircraft relative to the coordinate system being used. (3) Scanning laser rangefinder: The laser transmitter installed in the bottom of an aircraft sends pulses of la ser light towards the gr ound, and laser light is

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20 reflected from an object (terrai n, building, or foliage) to the la ser receiver following the reverse optical path. By timing the round-trip travel of a returned pulse between the laser transmitter, a target, and the laser receiver, th e range distance is determined us ing the velocity of light (38 m/s). The scanning mirror inside the sensor head is used to emit the laser pulses across a wide swath along the path of the aircraft Scan angles recorded from the scanner, together with aircraft orientation and location, are used to convert raw laser ranges in to the earth-fixed coordinate frame. An illustration of an ALSM system at work is shown in Figure 1-1. The ALSM data acquired for this study were processed using R ealm 3.2c (Optech, Inc.), the GPS data were processed using the kinematic and rapid sta tic (KARS) software (Mader, 1992), and the trajectory was computed using PosPac 4.02 (Applanix). Figure 1-1. Illustration of a small footprint LiDAR system in operation, from (Roth et al ., 2007).

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21 1.2 3D Airborne Laser Data over Forested Terrain Forests are important ecosystem s because th ey strongly modulate stores and fluxes of water and carbon near the earths surface. Natu ral and managed forests also comprise an important renewable resource for the timber and pa per industries. Several tree characteristics, such as stem number, density, stem volume, tree height, and canopy architect ure, are of interest to forest resource managers. These parameters are utilized to estimate forest yield, describe structural characteristics for wildlife habitat, model future growth and yield, and evaluate the effectiveness of past (and need for future) silv icultural activities. Traditionally, most of these parameters have been measured using direct ( in situ ) field methods (Czaplewski, 1999). However, traditional ground-base d forest inventories are expensive and time-consuming and as a result, are often limited to relatively small sample areas within the landscape of interest. Efforts have been made to extract informati on about forests more efficiently using remote sensing methods. The majority of this work to date has employed multispectral (passive optical) or microwave (radar) methods. Visual interpre tation from high-resolu tion multispectral aerial images (Brandtberg and Walter, 1998; Gong et al ., 2002) is often time consuming and subjective since the 2D representati on in the narrow optical portion of the spectrum does not possess direct information about the 3D structure of the canop y. Radar methods have the ability to partially penetrate forest canopies, because of their l onger wavelengths and wide ly separated frequency bands, and thus can provide some direct information about canopy density and structure (Hyypp et al. 1997; Hyypp et al. 2000, Slatton et al ., 2001). However, radar-based approaches are typically limited to spatial resolutions at the fe w meter scale (airborne) or few tens of meters scale (spaceborne), which are too coarse to robustly segment individual trees, making it problematic to estimate tree-based parameters fr om such data. Data from LiDAR systems have become more widely available in recent years fo r use in ecologic and fore stry applications, and

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22 these LiDAR sensors can potentially allow for accurate, precise, and automatic identification and measurement of individual trees composing the canopy (Andersen et al ., 2001). For most of applications using LiDAR data, th e range observations are interpolated to form 2D elevation images because one can then apply traditional image processing techniques to filter or classify the data. These images are sometimes called 2.5-dimensional maps since the laser is not capable of detecting objects hidden under opaque solid objects. However, collapsing the 3D point data into a height image early in the proces sing can lead to a signif icant loss of information when attempting to characterize landcover with structural variations in all three spatial dimensions. All algorithms in this work are de veloped to operate direc tly on the 3D raw point cloud data to avoid this information loss, which is one of the contributions in this work. By doing so, many issues associated with converting the data into 2D images, such as selecting the appropriate pixel size and an in terpolation method, are avoided. Small footprint ALSM technology can penetr ate dense canopy by illuminating the ground and understory through small gaps in the crown la yer. While this leads to precisely located measurements under the canopy, the fraction of la ser pulses reflected back from below the canopy is small (Figure 1-2). For example, in our natural forest test site at Hogtown, which is a generally closed canopy, only about 15% of th e laser returns are from the ground. The lower canopy layer just above the ground is particular ly afflicted by spare sampling with LiDAR systems that only record first and last returns, such as the system used in this work. These sparse measurements lead to a condition of undersam pling where the tree stems and understory vegetation are not adequately observed. This is no t critical in forests with relatively wide tree spacings, like managed forests, but can be a factor in denser natural forests. This problem can be ameliorated by estimating volumetric probability dens ity functions (pdfs) of tree features or by

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23 using LiDAR systems that have higher laser pulse ra tes and/or that record more than just the first and last returns. In this wo rk, however, I am focused on detecting the main canopy (crown) in managed forests, and since each canopy is uniquely associated with one trunk, this issue does not pose a severe problem in this work. Figure 1-2. An example of undersampling in LiDAR data over a natural forest. A) An actual photograph taken from a part of Hogtown Greenway in Gainesville, FL. B) 3D probability density function (pdf) of the vegetation of the area (estimated by the Parzen windowing method and shown as a stacked contour plot for easy visualization). The LiDAR data were co llected from the 33 kHz UF-ALSM. The ground returns were removed so that the pdf represents the above-ground material. Notice how the region below about 10 m exhibi ts lower probabilities in the pdf, yet the photograph indicates significan t foliage in that region. 1.3 Organization of this Study and Contributions Chapter 1 serves as necessary background inform ation to the study in th is dissertation. The UF-ALSM s ystem, a small footprin t discrete return LiDAR sens or, and its measurements are described. Three-dimensional point data over fo rests are described, a nd the issue of LiDAR undersampling is presented. The main contributions are also listed at the end of the chapter. A B

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24 Chapter 2 describes the study site and data acquisition. The study sites, PPINES and IMPAC, are used for most of the work except in section 3.2. The study site for that section, Hogtown Greenway, is briefly explained in that section. The ALSM data and ground truth data acquisitions over the study sites are also explained. Chapter 3 presents two geometric mapping a pproaches, in which the relevant LiDAR points between points of interest ar e isolated to find optical gaps inside forests. Firstly, a robust and simple procedure is presented for estimating IPAR. Second, a method is developed to detect walking trails in natural forests that are obscu red from above by the canopy. In both of these applications, the primary structuring elemen ts are field-of-view scope functions. While appropriate for line-of-sight estimation, thes e mappings are not optimal for estimating many important forestry parameters. In Chapter 4, I describe a technique for detec ting individual trees usi ng 3D laser point data. Detecting and segmenting individu al trees opens up the possibility for the direct estimation of structural parameters of paramount interest to forest managers and researchers. An adaptive clustering method is developed to merge the partia l-tree clusters that are segmented by the region growing process, and the performance is compared with the scale-space method. Chapter 5 presents results from estimating so me important tree (or plot) parameters and compares the estimates with ground truth data from a field survey. Th e height, location, and crown length of individual trees are extracted from the segmented points. Some possible methods are introduced to compute gap di stributions that are relevant to the spatial distribution of attenuation of GPS microwav e signals and detectability of personnel from the sky. In Chapter 6, a novel method for the compact re presentation of the geometric features of segmented LiDAR points from tree canopies is expl ored that uses a 3D point matching method

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25 known as spin images. Finally, conclusions a nd discussion of suggested future works are presented in Chapter 7. The main goal of this work is the developm ent of an approach to detect individual tree canopies using 3D point data, which then allows the subsequent estimation of several important tree structural parameters. Geometric mappings, including visibility scope functions, inside forests are also developed to find optical gaps. These mappings allow the estimation of additional forest parameters, such as IPAR, and other parameters that strongly impact tactical operations, such as line-of-sight visibility and locations of obscured walking trails. Specific contributions in this dissertation are: First, a new geometrical method for accurate ly estimating IPAR under forest canopies is developed. This is the first ap plication of small-footprint di screte-return LiDAR to estimate IPAR. This is done by defining field-of-view (sco pe) functions between ob server points in the forest and the sun that parameterize the light penetration through the canopy. These simple scope functions that isolate the relevant LiDAR refl ections between observer points and the sun are shown to give good agreement between the LiDAR-derived estimates and the in situ values of IPAR. This idea can be extended to estimate si gnal attenuation for s ky-ground communication or telemetry transmission. Second, the concept of line-of-si ght visibility is employed to detect walking trails in natural forests that are obscured from above by the canopy. To our knowledge, this is the first and only work using airborne LiDAR data to dete ct occluded forest trails As such, there are no prior methods with which to compare. So estimated trail locations are ve rified using GPS data collected in situ There is an absence of understory biomass on narrow irregular walking trails, but in many cases, these voids correspond to the region that is most severely undersampled by

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26 airborne LiDAR sensors. Instead of direct detection of trails based on density variations in LiDAR point clouds, several features from the AL SM data are extracted and used to constrain the search space and infer the location of trails The visibility vectors, as a byproduct in the process, indicate potent ial lines-of-fire for tactical scen arios and pathways through forested terrain that can potentially minimize traversal times. Third, an improved method for segmenting tr ees in LiDAR data is developed. Unlike previous methods that gridded the LiDAR data into a height image and used image processing techniques to detect trees, the whole process is based on Li DAR point cloud data without the need for a gridding (interpolation) step. This avoi ds the significant loss of information associated with interpolating the 3D data to image data. Furthermore, very few works have focused on principled (non-empirical) methods for dealing with the search radius R even though R is the most important parameter in tree detection via overhead remote sensing. An adaptive clustering method, that adapts to variations in canopy sh apes and sizes, is developed to merge canopy clusters initially segmented by a region growi ng algorithm. This contribution subsequently allows the vastly higher spatial resolution estimation of forest parameters.

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27 CHAPTER 2 STUDY SITES AND DATA ACQUISITIONS 2.1 Study Sites Managed forests com prise an important subset of all forests due to the economic capital invested in them and the resources derived from them. Data were collected for tree detection algorithm development at an installation of the Pine Productivity INteractions on Experimental Sites (PPINES), located in North-Central Florida (30 14' N, 82 18' W) (Figure 2-1). The site was established by the Forest Biology Research Cooperative (FBRC), located at the University of Florida, in January of 2000. A series of field research installations were designed to examine the interactions of full-sib (contro lled ancestry) loblolly pine (Pinus taeda L.) and slash pine (P. elliottii Engelm. var. elliottii) families with several environmental factors, such as location, silvicultural treatment intens ity, and planting density (Roth et al., 2007a). The topography in North-Central Florida is generally very flat, with ground elevations in the study site varying as little as 2 m. In this work, a total of 16 plots at PPINES were se lected where all plots have the same species (loblolly pine), number of planting positions in the measurement plot (48), and spacing between trees (2.74 m2.74 m) arranged in six rows (beds) of eight trees each. A schematic layout of a typical plot is shown in Figure 2-2 (A). However, the plots are split into two different culture treatments (high and low). High cultural intensity attempts to maximize growth and health of the growing stock by unde rstory vegetation control and fertilization. Another managed forest, the Intensive Ma nagement Practices Assessment Center (IMPAC) (Swindel et al., 1988; Jokela and Martin, 2000), loca ted near Gainesville, Florida (29 45' N, 82 17' W) is used in this study (Fi gure 2-1). The IMPAC plots were established in January 1983 as a 2 factorial of species (loblolly pine vs. slash pine), understory vegetation control (none vs. complete and sustained), and fertilization (none vs. a nnual with macroand

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28 micronutrients). A total of 12 plots were sampled consisting of 3 replicates for each of the species by fertilization treatment combinations. The 12 plots are where the understory vegetation was controlled. Each measurement plot was 0.027 ha in size consisting of 40 planting positions on a 3.66 m 1.83 m spacing arranged in five rows (beds) of eight trees each. A schematic layout of a typical plot is shown in Figure 2-2 (B). Figure 2-1. The locations of th e study sites (PPINES and IMPAC) with the geographic range of slash pine shaded. The PPINES site is denoted by #1, and the IMAC site is denoted by #2. The biophysical parameters for the trees in each site are listed in Table 2-1. Over the 16 PPINES plots, the trees averaged 7.9 m tall w ith a live crown length of 5.5 m. Over the 12 IMPAC plots, the average tree height was 21.3 m and the average live crown length was 6.2 m. Due to their advanced stage, the tree stands at IMPAC are at or near maximum carrying capacity, resulting in significant tree morality in some of the plots. As a result, the number of trees, tree heights, and the sizes of canopi es at IMPAC vary significantly Unlike the conical shape of crowns in PPINES, the trees in IMPAC exhibit a wider range of shapes. The percentage of living trees (relative to those originally planted) in PPINES is 91.8 %, and 65.6 % in IMPAC. So even 500 k m 12

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29 in a single pine plantation, th ere can be significant variability in canopies, especially in older plots. Thus, an adaptive segmen tation approach is needed, even for managed forests, to capture such variations within and across different sites. A top view of LiDAR data of a typical plot from each culture treatment is shown in Figure 2-3. Figure 2-2. A schematic layout of a single pl ot from each study site, (A) PPINES and (B) IMPAC. Shaded circles indicate approxima te stem locations. Dimensions of tShe inner measurement plot (shaded) are shown. Table 2-1. February, 2006 in situ field data from across the study sites describing general information about the sites. The trees at PPINES were 6 years old, and those at IMPAC were 23 years old at the time of th e investigation. The number of planted trees was 48 in PPINES and 40 in IMPAC for each measurement plot. Here, Lob = Loblolly pine, Slash = Slash pine, H = high culture, L = low culture. The tree dimensions (tree height and crown length) are written in the order of the maximum, mean, and minimum from the top in each case. Site Tree Species TreatmentsNumber of Plots Number of Living Trees Tree Height (m) Crown Length (m) PPINES Lob H, L 16 705 10.7 m 7.9 m 4.4 m 7.9 m 5.5 m 2.9 m IMPAC Lob, Slash H, L 12 315 26.1 m 21.3 m 10.0 m 15.8 m 6.2 m 0.9 m Measurement Plot 13.7 m 19.2 m A Measurement Plot 12.8 m Treatment Plot 14.6 m B

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30 Figure 2-3. Top view of firststop LiDAR point heights of a t ypical plot from each cultural intensity at each site. A) High culture at PPINES. B) Low culture at PPINES. C) High culture at IMPAC. D) Low culture at IMPA C. All units are in meters. Elevations represent relative heights above the ground. Variable point densities across the LiDAR data sets are primarily due to differences in scan angle and multiple flights overlap. 2.2 Ground Truth and ALSM Data Acquisitions Ground surveys were perfor med in February 2006 for both sites to reco rd the tree heights (HT) and the length of live crown (CL). The height to the base of the live crown was measured directly in the field and crown length was then interpreted as th e difference between total height and height to the base of the live crown. Th e ground surveys and high-resolution aerial imagery were used to verify the individua l tree segmentation results in Ch apter 4 and estimates of HT and CL in Chapter 5. The aerial imagery was acquire d simultaneously with the LiDAR data. Because C B A D

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31 the objective here is to explor e the degree to which informati on can be extracted from LiDAR data to segment trees, I only use the aerial im agery to aid in validati on and not in the actual segmentation. LiDAR data was collected as close in time to the ground surveys as possible. Collection of in situ and remotely sensed data at the same time is always the ideal, but we expect only negligible canopy differences if they are collected during the same year and season. However, one may generally expect considerable canopy changes if measurements are taken during the same season but in a different year, especially if the site has young fast-growing trees, or during different seasons, especially for deciduous trees. The LiDAR data used in Chapter 4 and 5 were acquired by the UF-ALSM system on March 09, 2006. Both the first and the last returns were recorded, and each laser return is the result of laser photons reflecting from the ground or foliage back up to the ALSM receiver optics. The first returns tend to reflect more from the top canopy, and the last returns reflect more from the understory and the ground. High laser point densities are generally required to robustly detect indi vidual tree crowns. Given that the maximum available laser pulse rate was 33 kHz for these acquisitions, the fli ght plans were configured for dense coverage. To achieve high point densities, the LiDAR data was acquired from a relatively low AGL altitude of 350 m with a reduced scanner angle range (10 maximum deviation from nadir) and a 45 Hz scan rate. The maximum allowable scan angle of the sensor is 20 but half that value was used to minimize the possibili ty of laser pulses passing through multiple trees. The average point densities over the study sites were 14.2 points/m2 for PPINES and 10.6 points/m2 for IMPAC, but the point density in ea ch plot varied from 12 to 18 points/m2 for PPINES and 8 to 20 points/m2 for IMPAC due to variations in overlap among the multiple flight lines and the particular scan angle.

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32 2.3 Preprocessing Most studies employing small-footprint laser al timetry to date have focused on surficial mapping. In those analyses, segmentation algorit hms are usually applied to estimate the bare surface elevations by filtering out returns from the vegetation using empirical thresholds on height variance or spatial connectedness of points (Weed et al., 2002; Haugerud et al., 2003; Zhang et al., 2003). An adaptive multisca le filter developed by Ka mpa and Slatton (2004) is employed to separate the laser returns corresponding to the ground from those corresponding to the above-ground biomass. The filter employs an information-theoretic hierarchical data segmentation scheme. First, the area is classified into heavily vegetated and minimally vegetated cells. Then, a Gaussian mixture model (GMM) is estimated from the vertical histogram of aggregated last return points. An asymmetric deci sion rule is applied to the GMM to ensure that the probability of missing a ground return is less than the probability of erroneously admitting a non-ground return in the bare surface estimate. This decision rule is used to capture small-scale surface features, such as scarps and stream banks This filter avoids empirical thresholding on the point distributions and retains the 3D point cloud data format. Figure 2-4 shows the ground laser points segmented by the filter and the re sulting estimated ground surface at the IMPAC site. Both study areas are relatively flat, so the terrain slope and height are not a factor for this work. However, to remove the contribution of the terrai n slope and heights for ar bitrary sites, the low order (slowly varying) terrain su rface is subtracted from the LiDAR points to level out the ground. The flattened laser point s are shown in Figure 2-5.

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33 Figure 2-4. Segmented ground laser points and the estimated ground elevation at the IMPAC site. A) Segmented ground laser points. B) Estimated ground elevation surface. All units in meters. Figure 2-5. Raw and flattened fi rst/last stop elevation points. A) Raw first stop elevation points. B) Raw last stop elevation points. C) Flattened first stop elevation points. D) Flattened last stop elevation points. A B B C D A

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34 CHAPTER 3 FIELD OF VIEW GEOMETRIC MAPPINGS 3.1 IPAR Estimation The amount of light intercepted by forest canopies plays a crucial role in forest primary production. However, the photosynthetically active pa rt of this intercepte d solar radiation (IPAR) is difficult to measure using tr aditional ground-based techniques. In situ measurement of IPAR requires labor-intensive field work, often resulting in limited datasets, especially when collected over extensive areas. Remote sensing methods ha ve been applied to the estimation of light interception in forests, but until recently have been restricted to two-dimensional (2D) image data. These approaches do not directly account for the three-dimensional (3D) structure of forested canopies, and therefore predicting IPAR for arbitrary sun positions is problematic. I utilized a 3D point cloud dataset acquired via an airborne laser ranging (LiDAR) system to predict in situ measured IPAR. This was achieved by defi ning a field of view (scope) function between observer points just abov e the forest floor and the sun, which relate IPAR to the LiDAR data over Southern pine experi mental plots containi ng a wide range of standing biomass. A conical scope function with an a ngular divergence from the cente rline of provided the best agreement with the in situ measurements. This scope functi on yielded remarkably consistent IPAR estimates for different pine species and growing conditions. IPAR for loblolly stands, which have diffuse canopy architectu re, was slightly underestimated. 3.1.1 Motivation Forest productivity is generall y a function of leaf area index (LAI), as is well documented for Southern pine forests (McCrady and Jokela, 1998; Jokela and Ma rtin, 2000; Martin and Jokela, 2004; Samuelson et al., 2004). Light attenuation throu gh the canopy depends strongly on the amount of foliage in the stand (Gholz et al., 1991; MacFarlane et al., 2003), and therefore it

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35 is not surprising that net forest productivity has been positively and linearl y related to the amount of photosynthetically active radi ation (PAR) that is absorbed or intercepted by canopies (Monteith, 1972; Dalla-Tea and Jokela, 1991; McCrady and Jokela, 1998). The quantity of PAR that is intercepted (IPAR) is largely determined by the amount of foliage in the canopy as well as its orientation (Colbert et al., 1990; McCrady and Jokela 1996; Landsberg and Gower, 1997; Kucharik et al., 1998). However, the ability of trees to support leaf area an d intercept light decreases with environmental stresses (Waring and Schlesinge r, 1985; Hebert and Jack, 1998), such as soil nutrition and water limitations. The relationship between leaf area and light interception may also be modified by stand de velopmental processes (M artin and Jokela, 2004). Leaf area and incident radiation have been succe ssfully used to regionally model loblolly pine productivity across the Southeast United Stat es (Sampson and Allen, 1999) and are the key drivers in process-based models of forest productivity (Wang and Jarvis, 1990; Cropper and Gholz, 1993; Battaglia and Sands, 1998; MacFarlane et al., 2003). However, IPAR estimates across the landscape are limited by a lack of available radiatio n measurements, which are the most sparsely measured of routine clim atologic data (Aber and Freuder, 2000). Traditional measurement of IPAR is time c onsuming, which is problematic given the changing light conditions throughout the day. The lig ht incident on a partic ular forest canopy is constantly changing in both direction and intensity (Gay et al., 1971). As a result, the proportion of intercepted radia tion may need to be corrected to a cons tant sun angle from zenith in order to facilitate repeated measurements through time (Will et al., 2005). Additionally, Southern pine foliage exhibits strong seasonal dynamics and rapid responses to altered nutrition (Gholz et al., 1991), thus requiring frequent measurement of IPAR As an alternative, remote sensing methods have been utilized to estimate canopy parameters, such as LAI, that are related to sunlight

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36 penetration through the canopy. However, since th e sun constantly changes position and forest canopies exhibit strong 3D struct ural variations, it is not suffi cient to estimate PAR from traditional 2D data, such as multi-spectral imagery (Butson et al., 2002) or polarimetric synthetic aperture radar (Saatchi et al., 1994). Explicit 3D structural in formation is needed to predict sunlight transmission for differe nt sun angles. While interferom etric synthetic aperture radar (InSAR) can provide some 3D information, it is generally of insufficient spatial resolution to adequately measure standlevel variations (Slatton et al., 2001). Airborne light detection and ranging (LiDAR) systems on the other hand can pr ovide both high spatia l resolution and canopy penetration in a 3D point cloud format. For exam ple, airborne LiDAR measurements have been reliably related to in situ measurements of individual tr ee and stand structure (Holmgren et al., 2003; Lim et al., 2003; Maltamo et al., 2004; Farid et al., 2006), and has also been used to successfully estimate IPAR for maiz e and sunflower crops (Holdcroft et al., 2005). For this investigation, I show that it is possible to directly exploit th e 3D nature of LiDAR data to estimate sunlight intercepted by the forest canopy while accounting for variations in sun angle. A few investigators have begun to analyze the 3D measurements of forest structure from small-footprint LiDAR (Eggleston et al., 2000; Todd et al., 2003). Todd et al. (2003) attempted to estimate indicator probabilities for different s urfaces representing different vertical strata in the canopy, such as overstory, middle canopy, and lower canopy. Their approach involved interpolation of point data into surfaces and the a priori assumption of a preferred geometric shape for local distributions of points in canopies. They used a small-footprint LiDAR operating at an altitude of 750 m above gr ound, with a laser pulse rate of 20 kHz and a scan angle range of which produced 400 m wide swaths with a stated density of 8662 laser pulses per hectare (0.87 pulses per square meter). In this work small-footprint LiDAR data was acquired on

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37 October 11,2005 by UF-ALSM system, flown at 450 m AGL with a laser pulse rate of 33 kHz, scan rate of 30 Hz, and a scan angle range of 18, resulting in a nominal laser shot density of 1.83 transmitted pulses per square meter on a single pass. Both first and last returns from each pulse are used to maximize sampling of the cano py. This configuration was used because I found that LiDAR sample densities on the order of a few per square meter we re required to reliably resolve the 3D distribu tion of forest canopy for accurate estimates of IPAR. This sub-meter sampling supports the direct representation of the canopy as a point cloud rather than as a set of interpolated surfaces. The overall objective of this work is to dem onstrate a simple procedure for the estimation of IPAR in loblolly and slash pine plantations at the IMPAC s ite using airborne LiDAR remote sensing measurements. Specifically, I determined th at a single parametric field of view (scope) function can be found that enables reasonable estimates of IPAR acr oss the set of widely varying canopy conditions studied in this trial. Figure 3-1. The spatial arrangement of the plot s in the IMPAC site. A) The spatial arrangement of the 24 plots in the IMPAC study (plot codes: L = Loblolly, S = Slash, H = complete understory vegetation control, and F = Fertilized). B) Color-coded elevation (above local ground) image derived from AL SM data (all units in meters). The 12 plots outlined in bold correspond to those used in this study (plots 2, 3, 4, 5, 6, 7, 9, 16, 17, 18, 19, and 22). A B

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38 3.1.2 Estimation of In-Situ IPAR In this work, the same 12 plots in the IMPAC s ite in Chapter 2 are used. The details of the spatial arrangement of the plots and the selected plots are show n in Figure 3-1. A summary of tree survival and solar angles at the time of measurement for each plot is provided in Table 3-1. sun position was defined in terms of two angles, (the angle from the eas terly direction to the nadir projection of the observer-sun v ector in the horizontal plane) and (the elevation angle of the sun above the horizon along the zenith), relative to the observation point at the origin of a translating (local) spherical coordinate frame (Figure 3-2). Table 3-1. Plot level inventory data detailing tree survival and solar angles at the time of the in situ PAR measurements. Data was collected in October 2005. A total of 40 trees were planted on each measurement plot in 1983. See Figure 3-2 for a visualization of sun angles, which are expressed in degrees. Species Fertilized Plot Survival (no. of trees) Sun Angles ( ) 2 38 (45, 55) 9 29 (49, 69) No 22 27 (51, 98) 7 25 (49, 67) 16 35 (41, 48) Loblolly Yes 19 28 (51, 95) 4 29 (44, 53) 6 30 (47, 63) No 18 29 (51, 92) 3 19 (43, 51) 5 27 (47, 61) Slash Yes 17 18 (51, 88) Multiple techniques have been used to estima te the amount of PAR intercepted by forest canopies. The most common method is to estimat e PAR incident at th e top of the canopy and relate it to PAR incident below the canopy unde r uniform conditions (clear-sky or overcast) centered on solar zenith (Messi er and Puttonen, 1995). Many t ypes of sensors have been

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39 employed to quantify the light environment under forest canopies, such as radiometers, photosensitive paper or chemicals, hemisphe rical canopy photographs, plant canopy analyzers, or visual estimators of canopy density (Leiffers et al., 1999). For the results reported here, in situ measurements of IPAR were made using a comb ination of a LiCor LI-190 Quantum PAR sensor (LI-COR inc., Lincoln, NE) and an integr ating PAR ceptometer (AccuPAR Linear Par Ceptometer, Model PAR-80, Pullman, WA). The AccuPAR is a battery-operated linear PAR ceptometer containing 80 independent photodiodes spaced 1 cm apart. The photodiodes measure PAR in the 400-700 nm spectral band in units of micromols per meter squared per second (mol m-2s-1). The hemispherical field of view (FOV) was directed upward. Figure 3-2. Solar angles ( ) defined relative to an observer point at the origin of a local spherical coordinate frame. The elevati on angle of the sun above the horizon along the zenith is defined as while the angle from the eas terly direction to the nadir projection of the observer-sun vector in the horizontal plane is defined as All angles are reported in degr ees. Local zenith is at ( ,90). Above canopy incident PAR (b ackground) was collected using the LiCor LI-190 Quantum sensor which was placed in an open area adjace nt to the study site. Concurrent below canopy PAR samples were collected over two measur ement periods on October 16, 2005, using the integrating PAR ceptometer during a period of 2 hours centered about local solar zenith. At regular intervals during the sampling period side by side estimates were made in the open (background) to ensure concurren ce between the two sensors. Ob servations were taken during E N

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40 clear sky conditions to minimize contributions due to diffuse s ky irradiance. The sun angle was noted during each in situ collection so that the correspondi ng sunlight penetration could be computed from the ALSM data. Ground measurem ents were collected from nine systematic transects spanning the width of each measurement plot (18.3 m) at a height of 1.5 2 m. Sixteen light readings were taken along each transe ct and averaged to generate a single in situ data point per plot for each of two measurement periods. In situ IPAR was computed using equation 3-1 with the average IPAR per plot computed from the average of the two readings (J = 2) J j situinj Background j Ceptometer J IPAR1)( )( 1 1 (3-1) where 1,0 situinIPAR since the intercepted sunlight fl ux is non-negative and the below canopy value does not exceed the open sky value. 3.1.3 Isolating the Vegetative Contribution to IPAR Spatial variations in the sun light flux through forest canopies are, in general, governed by local topography, latitude (sun a ngle), meteorological conditions (e.g. cloudiness, water vapor), and the amount and distribution of occluding vegetation. In this work, I am interested in capturing the contributing effects of vegetation, so a low-relief test site was chosen with a wide range of standing biomass. In order to rela te the distribution of vegetation to ALSM observations, I first separated laser light inte rception by the ground surface from that of the nonground objects by using the adaptive multiscale filte r in section 2.3. While it was possible that some vegetation returns near the ground may have been included in the segmented ground points, the probability was minimized in this in vestigation since the data collection was limited to the areas where the understory vegetation had been removed.

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41 To further reduce the probability of miscla ssifying ground points as non-ground points (i.e. vegetation), all points less than 1 m above the estimated ground surface were removed from consideration by assuming that the total error (system error + surface estimation error) was less than or equal to 1 m. This 1 m buffer is reasona ble since field validation revealed that the RootMean-Square (RMS) error in the estimated gr ound surface under the canopy was much less than 1 m near ALSM points. Since that error can be la rger (still less than 1 m) in small data voids where dense crowns prevent ALSM points from reaching the ground, the ALSM IPAR estimates are computed for an observation hei ght of 2 m to correspond to the in situ IPAR measurement height. 3.1.4 Optical Scope Functions Incident sunlight flux between the sun and a hypothetical observer under the forest canopy was determined by defining an optical field of vi ew (scope function) for the observer. The scope functions originated at the obs erver and extended thr ough the canopy in the dire ction of the sun. I examined a combination of cylindrical and coni cal geometries consisting of four unique scope functions: 1) a simple cylinder of 40 m in length, 2) a simple cone, 3) a cone weighted by the distance between the ALSM point and the observer, and 4) a cone weighted by both the distance between the ALSM point and the observer a nd the angular divergence from the conical centerline (Figure 3-3). Secondary to this, within each function, five uniqu e sizes were defined: diameters of 2 m, 3 m, 4 m, 5 m, and 6 m for the cylinder a nd 0, and angular divergences from centerline for each of the coni cal functions. The choice of cylinder length was dependent upon the dominant tree height and the sun angles represented in the study area at the time of the investigation. In order to minimize computations, the shortest length that included all ALSM laser points wa s chosen. Since the tree height in the study area was generally less than 30 m and the su n angle greater than 40o, a 40 m cylinder length was utilized.

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42 Figure 3-3. Different types of scope functions investigated. A) Cylinder scope function with diameter d. B) Cone scope function with angular divergence C) A weighted cone scope function, where is the distance from an ALSM point in the scope (blue dot) to the observer, is the angular deviation of that ALSM point from the center line, and I is a truncated Gaussian irradiance distribution across th e field of view. The weightings for the conical functions took two forms. In the first case, the occluding effect of a LiDAR point was weighted only by the distance between that point and the observer. I required the function, w decrease monotonically with It was also desirable to have a function with compact s upport to enforce upper and lower limits on the occluding effect. Maximum occlusion ( w =1) occurs when the LiDAR reflector is located at the observer point ( =0). Zero occlusion (w =0) occurs when the point in the scope is farther than vanishing from the observer. The function must also be nonlinear to accommodate the op tical property that an objects occluding effect becomes less sensitive to changes in its distance from the observer as that distance increases. A second order polynomia l is the simplest such function that gives a graceful decline in w as approaches vanishing by ensuring that derivatives up to 1st order remain continuous (Figure 3-4). The choice of vanishing =100 m is simply a conservative bound on the maximum expected path length from the obser ver to the canopy top give n that canopies at the A d 2 I B C

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43 study site were all less than 30 m tall and that sun elevation angles of less than 20 are generally not of interest for IPAR studies. Figure 3-4. The weighting functions for the c one scopes. A) The quadr atic occluding effect weighting function w with respect to distance from the observer. B) The truncated Gaussian weighting function w with respect to angle from the line of sight, where = 6 and the scale factor a = 13.5. In the second case, the occluding effect of an ALSM point relative to the observer was weighted by both its distance from the observer and its angular divergence from the cone centerline. I followed similar reasoning for the weighting as for the weighting. Namely, I wanted a function, w that monotonically and continuously decreased from a maximum value at the scope centerline as a function of to a minimum value at the cones edge. This occluding effect should be approach the cone edge in a smooth manner (continuous up to 1st order 2 vanishing 2 vanishing ) ( WA 20 1.0 20 2 exp 2 1.02 2 a W B

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44 derivative), but it should not strictly reach zero at the cone edge since there can still be some occluding effect as long as the obj ect is in the field of view. Th e function should be nonlinear to accommodate the optical property that an object s occluding effect becomes less sensitive to changes in its divergence angle as the divergence increases. A truncated Gaussian distribution was therefore used as a simple parameterizati on for the angular weighting of the sunlight intensity (relative irradiance). The Gaussi an was preferred over a quadratic for w because it corresponded more closely to observations of di rect solar irradiance ve rsus angle (Halthore et al ., 1996). The weighting has the following characteristics, as depicted in Figur es 3-3 and 3-4: (a) the effective intensity of the suns radiation I follows a Gaussian distribution from centerline up to and (b) the minimum intensity is reached at 20o and maintains a constant value of 0.1 for larger angles. The and weighting functions were applied to each ALSM point inside a given scope so that the maximum total weight was 1.0 and the minimum was 0. In the case here, the minimum total weight never reached 0 since the maximum scope lengthmax of 40 m was less thanvanishing 3.1.5 Estimation of IPAR from ALSM For each scope function, the point densities of non-ground laser returns inside the scope, originating 2 m above the ground surface, were computed. Since the type of scope function used was fixed for a given IPAR estimate over the stu dy area, and therefore the volume of the scope was fixed, LiDAR point densities were comput ed simply by counting th e number of non-ground laser returns inside the scope. Each scope functio n was given a constant orientation towards the position in the sky that the sun occupied during the corresponding in situ data collection. This procedure was iterated across each measurement plot in 1 m horizontal grid increments. The suns angular position was computed for each ALSM estimate using the latitude and longitude of

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45 the study site in combination with the date a nd time of the ground truth measurement (Giesen, 2005; Gronbeck, 2005). This allowed for a direct comparison between in situ measured IPAR, situinIPAR and ALSM estimated IPAR, ALSMIPAR Since ALSM point clouds consist of irregularly spaced samples, with each location in the imaged area having variable point densities, the IPAR estimates derived from ALSM data were normalized by the local point density. The variati on in point density in this study was small due to the fact that data from a single flight lin e was used. However, normalizing by point density would be crucial when working with LiDAR data sets composed of mosaics of multiple and partially overlapping flig ht lines. I utilized a simple norma lized functional mapping algorithm in order to estimate ALSMIPAR from the point density of LiDAR returns corresponding to the canopy at a specific observer point, denoted by i in equation 3-2: )1ln(max )1ln( )(,...,2,1 i Mi i ALSMiIPAR (3-2) where i is the number of the ALSM non-gr ound points inside the scope at the ith location where each points contribution has been wei ghted as described in section 3.1.4, and M is the total number of ALSMIPAR calculations over the entire study site. The number of ALSM points in the scope function can in general vary from zero to some finite but large number L, which is not known a priori ALSMIPAR was computed across the entire 370 m 300 m study area in order to thoroughly sample the local foliage densities for normalization purposes (i.e. the denomina tor in equation 3-2). The effective ALSMIPAR for each measurement plot was then computed as the average of all ALSM I PARi within that measurement plot.

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46 The simple nonlinear relationship in equation 3-2 was defined as a continuous-valued dimensionless measure bounded by 0 and 1, whic h could be used for comparisons with situinIPAR in equation 3-1. While a linear scaling, such as max could provide a linkage between 0, L and 1,0 ALSMIPAR the logarithm provided the desired property that small differences in would have significant impact on the calculation for small but little impact for large. Normalizing by the maximum value provides the unity upper bound. The arctangent could also have been used, which would have pr ovided somewhat similar results. However, in that case the upper bound would have been fixed (no longer dependent on L) and therefore not related to the distribution of foliage in the st udy area in the same way that situinIPAR was. The exact manner in which true IPAR increases as a function of foliage density is not generally known since it depends upon the pa rticular arrangement and sp ectral absorbance of occluding objects, such as stems, branches and clumps of foliage. The goal of this investigation was to derive a set of simple scope functions with minimal parameteri zation and empirical calibration, such that they could be employed across a wi de variety of forest types and conditions. 3.1.6 Results ALSMIPAR was calculated across the 12 plots using all combinations of the 4 scope functions and 5 dimension classe s, which resulted in 240 estimate d values. The most appropriate overall scope function and dimension was sele cted by comparing the residuals between the estimated ALSMIPAR and the in situ measured IPAR for each plot. Analysis of Variance (ANOVA) was performed on this dataset of residu als using SAS software (SAS Institute Inc., 2000). The best combination of scope function a nd dimension was select ed using the LSMEANS option in the PROC GLM procedure. The PROC REG procedure was used in SAS in order to

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47 quantify the strength of the rela tionship between observed and estimat ed values of IPAR. I tested for the need for different equations for the main effects of species and fertilization using the oneway fixed group model. Differences among the treatments for in situ and ALSM derived IPAR were tested using ANOVA via the PROC GLM pro cedure in SAS. Separation of means analysis was done using the LSMEANS procedure in SAS. 3.1.6.1 Selection of the Best Scope Function Analysis of variance indicated that there were large differences betw een scope functions in their ability to predict IPAR (p < 0.0001). The performance was dependent on the physical dimensions as well as the shape of the scope functions. In Figure 3-5, the average absolute error is plotted for each scope function. The smallest residuals for the cylindr ical function occurred when a radius of 2.5 m was used. Based on the average absolute difference values, I found that the conical scope functions have the advantage of yielding smaller maximum errors (no greater than 0.17) than the cylindrical sc ope function (0.33) for a wide ra nge of angles and weights. In the case of the conical scopes, I found the strong est dependence to be on the divergence angle An angle of =7 yielded the minimum mean squared error between ALSMIPAR and situinIPAR regardless of weighting by distance and/or angle Thus, relatively narrow conical scope functions performed best overall, and wi thin such scope func tions, the position of individual ALSM points had a re latively weak effect on the IPAR estimate. This angle, =7, produces a cone with a diameter of 6.2 m wher e it intersects the approximate middle of the canopy, given that the average tree height is 21.3 m and the average elevation sun angle was 45. Interestingly, this diameter is the same as the average crown length in the study site. Future investigation on other sites may fi nd a connection between the angle and the average crown length in the ROI.

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48 Figure 3-5. Residual analysis co mparing the two types of scope functions as dimensions change, where average absolute difference is simp ly the average absolu te value of ALSM IPAR estimates minus in situ IPAR measurements. A) Cylinder scope function performance with respect to diameter. B) Performance of three different cone scope functions with respect to angular diverg ence. The conical scope function with an angle of 7 yielded the best overall estimates. In terms of the sign of the erro r, I found that for the cylindrical functions, all radii less than 2.5 m resulted in underestimates of ALSMIPAR and radii greater than 2.5 m resulted in slight overestimates. For conical functions, small divergence angles ( 5) led to a slight underestimation of ALSMIPAR, while large divergence angles ( 10) led to an overestimation of ALSMIPAR. Although the underestimation of ALSMIPAR for small and overestimation for large were relatively small, the fact that thos e trends were consistent for all weighting schemes suggests that omitting indirect sky irradiance may have been the cause. 3.1.6.2 Variation in IPAR Analysis of variance for both ALSMIPAR and situinIPAR demonstrated a significant interaction between species and fertilization (p = 0.0276 and p = 0.0957 respectively) (Table 32). Fertilized loblolly pine inte rcepted the most light, while non-fert ilized loblolly intercepted the least (Table 3-3). Fertilizati on did not have a statistically significant influence on light A B

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49 interception in the slash plots, a lthough fertilized slash pine intercepted slightly less light than non-fertilized. I used the cone function with =7 and weighted by distan ce because, as can be seen in Figure 3-5, that gave the minimum average absolute error. Table 3-2. Analysis of Variance (ANOVA) table for in situ and estimated IPAR. p-values in bold are considered statistically significant at alpha less than or equal to 0.1. Degrees of freedom and mean squared residual are represented by df and MS respectively. Source of In situ ALSM Estimate Variation df MS p-value MS p-value Species (S) 1 0.000108 0.8113 0.001800 0.3864 Fertilization (F) 1 0.002945 0.2334 0.003924 0.2132 SF 1 0.012805 0.0276 0.007650 0.0957 Error 8 0.001772 0.002145 Table 3-3. Least Squares es timates of IPAR measured in situ and estimated from ALSM. Using Bonferronis Least Significant Diffe rence (LSD), differences between in situ and ALSM values in all four rows are not si gnificant at alpha equal to 0.05. The cone function with =7 and weighted by distance is used in this analysis. Species Fertilized In situ ALSM Loblolly Yes 0.735 0.705 Slash No 0.698 0.693 Slash Yes 0.664 0.679 Loblolly No 0.639 0.618 3.1.6.3 Residual Analysis Overall the strength of the relationship betw een observed and predic ted values of IPAR was strong, however, regression anal ysis determined that a bias in the prediction of remotely sensed estimates of IPAR existed between species. While there was no difference between the slopes of the equations between species (p = 0.4850), there was a sign ificant difference between

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50 intercepts (p = 0.0094). Using the cone function with =7 and weighted by distance, IPAR for loblolly pine was slightly unde restimated by the ALSM, however, slash pine was very close to the 1:1 line between observed a nd predicted (Figure 3-6). The relatively small residuals are considered encouraging given the minimal parameterization of these scope functions. Figure 3-6. Relationship between observed (in situ) and estimated IPAR (from ALSM) using the cone function with =7 and weighted by distance. Separate equations were developed for each species since analysis indi cated statistically different intercepts (p = 0.0094). There was no significant difference for slopes between the equations so a common slope was used (p = 0.4850). The light dotted lin e represents a hypothetical 1-to-1 ratio between observed and estimat ed. The equation for Slash pine is y = 0.9351x + 0.0493, r2 = 0.935, RMSE = 0.0133; and for Loblolly pine it is y = 0.944x + 0.0132, r2 = 0.913, RMSE = 0.0197. 3.1.7 Discussion 3.1.7.1 Factors Influencing in s itu IPAR In general, fertilization builds leaf area and creates a denser canopy with high light interception (Sampson and Allen, 19 98). This was the case in this study where fertilized loblolly pine had the greatest levels of light interception. The lack of differences in light interception between fertilized and non-fertiliz ed slash pine was not unexpected since it is less responsive to 0.55 0.60 0.65 0.70 0.75 0.80 0.60 0.65 0.70 0.75 0.80 In-situ IPARALSM Estimate Slash Loblolly

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51 fertilization than loblolly pine (Roth et al., 2007b). Individual tree mo rtality resulted in open gaps in this study area and co rresponding lower amounts of light interception in the fertilized slash pine treatment plots. However, this occurred only where mortality was the most recent, since with time the surrounding tree canopies expand to fill these gaps. 3.1.7.2 Potential Sources of Error One potential source of unexplained error in this investigation may be the relatively low sun elevations at the time of in situ PAR data acquisition (between 41 and 51). At these angles there was some contribution to PAR interception from trees in the surrounding gross treatment plot. A hypothetical case in which th e observer is in the center of the plot and the sun elevation angle is 45 is shown in Figure 37. Due to the plot size, trees out side the treatment plot can be seen to intercept the sunlight. While not quantified, it was assumed that tree attributes and mortality did not vary between the gross treatment and measurement portions of each plot. Another potential source of error is the contribution of di ffuse radiation. Laser light is phase-coherent and spectrally na rrow-band, while sunlight is broad-band and incoherent. Therefore, in order to simplify the analysis, c ontributions from diffuse sky irradiance were neglected by virtue of using scope functi ons with narrow fields of view, collecting in situ measurements during clear sky conditions, and adjusting for the angle of the sun during the in situ measurements. For small too little interception was ascribed to the LiDAR points via equation 3-2, implying an overestimation of sunli ght reaching the observer. This is likely caused by attributing too much of the measured light at the observer to direct so lar irradiance because the contribution of indirect sky irradiance was neglected. A logical refinement of this work in future investigations would be to employ two se parate scope functions to estimate IPAR, where one is tailored to capture the direct component of the total solar irradian ce and the other tailored for the indirect component. However, a rigorou s examination of those two components would

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52 also require independent in situ measurements of each, which were not available for this investigation. Figure 3-7. A side view of a plot with a hypothe tical position of the sun and a scope function. When the sun elevation angle is 45 and the observer point (location of a scope function) is at the center of the plot, trees outside of the treatment plot can affect the PAR values. Varying proportions of standing woody material to leaves is another potentia l source of error. Neither the exact reflectance nor orient ation was known for objects reflecting emitted laser light, such as leaves or branches. It was therefor e not possible to derive an explicit closed form relationship between the laser light reflection a nd sunlight interception, since the laser beam interacted with an unknown mi xture of reflectors inside each 15 cm diameter footprint. 3.1.7.3 Bias Between Species The slight, yet consistent, underestimation of IPAR for loblolly pine was unexpected and is thought to be due to structural differences in their canopy architect ure. Slash pine canopies are 5 m 10 m 25 m 20 m 15 m 28 m 5m 10m 15m 20 m 25m 28 m Inside treatment p lot Inside measurement p lot

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53 highly aggregated and clumped as opposed to loblolly pine, which is more diffused and continuous (Colbert et al., 1990). Since each laser return is th e result of laser photons reflecting from occluding surfaces, the surfaces must be dense enough to reflect a measurable signal back to the ALSM receiver optics. In the case of the underestimate for l oblolly pine, it is thought that the diffuse canopy allowed a greater number of laser photons to pass through for a given amount of foliage. Apparently, the clumped canopy propertie s of slash pine, which have made traditional measures of light intercep tion difficult to model (Gholz et al., 1991), are in effect beneficial with respect to the ALSM methodology. Figure 3-8. ALSMIPAR distribution for contrast ing sun angles at an observer elevation of 2 m, illustrating the spatial resolution of ALSMIPAR computed in equation 3-2. The conical scope function weighted by the distance be tween the ALSM point and the observer was used in this case. 3.1.7.4 Spatial Variations of IPARALSM The ability of ALSM to estimate the 3D spatia l variations in IPAR with superior spatial resolution is illustrated in Figure 3-8. The distribution of ALSMIPAR is computed using equation 3-2 assuming two different hypothe tical sun angles at a 2 m el evation of scope origin. The = 92, = 51; observer elevation = 2 m = 48, = 41; observer elevation = 2 m 1.0

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54 conical scope function weighted by the distance between the AL SM point and the observer was used in this case. Due to the conical nature of the scope, less spatial aggregating of the IPAR estimates is expected by using observer heights farther off of the ground since a raised conical scope will have a smaller radius when it inters ects the canopy points. Thus, raising the scope has the potential to reveal more detailed canopy structure. 3.2 Detecting Forest Trails There is a critical need to locat e trails and other optical gaps in forested terrain for locating optimal paths and for planning troop movement, locating sites for optimal ground-to-sky Radio Frequency (RF) communications, and mapping areas of likely detection from overhead sensors. In this chapter, visibility vectors between candida te foliage voids are defined to identify optical lines of sights over the terrain. Most probable trails are detected using these optical lines of sights with help of the detected stem locations and geometric constraints. 3.2.1 Introduction In forests with dense lower canopies and unders tories, walking trails can be regarded as narrow irregular paths in which there is an absenc e of understory biomass. Such trails that wind through densely forested terrain are difficult to detect by aerial photograp hy and radar methods because the crown layer occludes the understo ry. Long-wavelength microwave energy can penetrate foliage, but discriminati on of vertical structure requires more information than what a single radar backscatter im age provides. In principle, vertical structure of the terrain and foliage can be estimated from multiple interferometric radar observations, but these observations generally lack the spatial resolution to detect small-scale voids in the foliage arising from trails. ALSM technology that employs small footprints and two-stop detection can also penetrate dense canopy by illuminating the ground and understory through small gaps in the crown layer. While this leads to precisely located measurem ents under the canopy, the fraction of laser pulses

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55 reflected back from below the canopy is small. Th ese sparse measurements lead to a condition of undersampling. The layer of canopy just above the ground is the primary location of the biomass voids that correspond to trails. Yet, it is precisely the region that is most severely undersampled by ALSM sensors that record only first and last stops. Because of the sparseness of the ALSM da ta from the understory and ground, direct detection of trails based on dens ity variations in ALSM data poi nts is not reliable. Instead, I derive several features from the ALSM data and us e them to constrain the search space and infer the location of trails. First, the ground surface gz is estimated using the information-theoretic approach in section 2.3. Knowledge of the gr ound elevation constrains the search space and reduces the subsequent segmentation to a series of 2D problems. Then I use two characteristics of trails: (1) trail su rfaces yield lower standa rd deviations of hei ghts than does understory vegetation, and (2) the presence of a trail implies an empty volu me immediately above the trail surface. Locations exhibiting these features are then used as seed locations for computing radial visibility functions. The notion of visibility which is of much in terest in surveillance applications (Zacks, 1994) implies a linearly oriented volume of em pty space between two points. Each visibility vector is considered to be a lo cal trail segment. Many false candidate vectors remain due to the data sparseness. Because trees ra rely grow on trail su rfaces, all visibility vectors that pass too close to the estimated tree trunk locations are di scarded. Finally, additi onal features involving geometric consistency of visibility are used to further window the set of candidate trails segments. The primary trail is identified by choos ing the longest connected set of trail segments (winner take all strategy). The tr ail detection algorithm is demonstrated in a dense forest near Gainesville, Florida.

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56 3.2.2 Study Area and Data Acquisition The study site was imaged with UF-ALSM syst em from an above gr ound altitude of 600 m. The site was imaged with two flight lines, re sulting in an average of 2-2.5 returns per square meter. The majority returns correspond to the upper canopy, but some do manage to penetrate deep into the foliage through sma ll gaps. At meter scales (the scales at which trails must be resolved) these penetrating shots are quite sparse, with an average of 0.25 returns per square meter. The study area analyzed for this work is a mi xed coniferous and deciduous forest in Northcentral Florida, USA. The forest is a part of Hogtown Greenwa y in the city of Gainesville (Figure 3-9). The true location of the walking trail (red dots) was acquired during a kinematic survey with an Ashtech geodetic G PS receiver, yielding few meter rms. In the training site, the trail is generally stra ight and is roughly 3 m wide. An approach for identifying the trail was developed using this training site and then validated in the testing site, in which the trail is 2~3 m wide and curved at some points. 3.2.3 Data Segmentation The presence of a trail implies an empty sp ace above the trail surface where a person could walk. Trails form elongated and continuous voids in the vegetation while non-trail gaps exhibit irregular shapes. The trail in the training site is straight, so the empty space above the trail surface can be seen in the 3D point cloud (Fi gure 3-10). Most of the significant trail space resides between 1 m and 4 m above the ground. Selected last stop elevation points which penetrate through the canopy and reside in this space describe the gap distribution in this elevation level where the tra il exists. However, the undersam pling problem of ALSM in understory makes trail gaps and non-trail gaps indistinguishable based on these points alone (Figure 3-11).

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57 Figure 3-9. Shaded relief image and ground photos of the study area. The GPS trail is in red dots, training and testing sites photos are on each side. Axes labels in Universal Transverse Mercator (UTM) meters. Figure 3-10. Point cloud from the training si te. The empty space above the trail surface (red box) is the trail. Testin g Site Trainin g Site

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58 Figure 3-11. ALSM data points between 1 m a nd 4 m elevation (blue dot s), tree trunks (black double circles), smooth surface points (red small circles), and GPS trail (yellow circles). Units are in meters. Finding the connected gaps between two points on the trail is similar to computing the visibility between those points. Ther efore, the selected data points wi ll be considered as visibility blocks. However, it is still necessary to f ill up the unknown space where no penetration occurs due to the data sparseness. The estimated tr ee trunk locations serve th is purpose by adding the locations to the set of visibility blockers. An el aborate algorithm is introduced in Chapter 4 to detect and delineate individual tree crowns, but for the purpose of estimating of big dominant certain tree locations and avoid adopting falsely detected (or un certain) small tree locations, only the seed finding process in section 4.3.1 is empl oyed in this work. Adjacent trees are assumed to be at least 5 m apart (i.e. R = 5 m in the process of finding seed points). The selected peak points are added to the set of visibility blockers. It is computationally intensive to compute the visibility for all angles at all locations, and the blockers are still too sparse to uniquely or clearly show trail path s. Another feature of trails is therefore used to further constrain the problem. I e xploit the fact that height variances on the trail

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59 surface should be small relative to variances in the understory. Triplets of ground surface points are used to compute a height st andard deviation. A threshold is computed, assuming a single measurement over an ideal flat plane (equation 3-3). ([0,0,])0.058 std (3-3) where m1.0 The value of includes the ALSM system error and the estimated ground surface error. Standard deviations less than are considered smooth surfaces and are used as seeds for computing visibility vectors. The visibility blockers and smooth surface points are shown with the GPS trail in Figure 3-11. 3.2.4 Visibility Vectors and Geometric Constraints While visibility is often regarded as a ra y-tracing problem, in the foliage, we must recognize that meaningful visibil ity requires a reasonable (non-zero) solid angle. This constraint is enforced using a visibility cylinder, create d between each pair of sm ooth surface points. Tree trunks and any ALSM points in th is cylinder are considered as vi sibility blockers of the path between the two smooth surface points. The diameter of the cylinder is empi rically chosen to be 3 m. Too small a diameter will yield many false visibility vectors, and too large a diameter will fail to detect some trail gaps. A slightly bigger scope diameter than the size of the actual trail may miss the clear optical gaps on the trail, but it could detect easiest path s to traverse through the terrain even if there is no formal trail in th e area. It is assumed that more than three data points or a tree trunk inside this cylinder causes no visibility. A ll such visibility vectors are shown in Figure 3-12 (A). Note that false trails indicate potential lines-of-fire for tactical scenarios. Finally, geometric constraints of visibility vectors are used to remove vectors which are on non-trails. First, the visibility vectors on trails should have front-back co nnections (non-terminal

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60 points). A backside angle of 30 is allowed, and all visibili ty vectors which do not have connections in this angle are eliminated. This angle gives the freedom of handling non-straight trails. The ability to detect more curved tra ils (or simply paths of potential trafficability) increases as this angle tolerance is increased, but that could also potentially increase the confusion between the real front-b ack connection and the side visibi lity vectors. Secondly, most real trails exhibit some side visibility. These side visibility vectors in an angle range (30o~150o on both sides) are removed where fr ont-back connections exist. In this study area, there was only one trail. So, thirdly, the longe st trail is selected after summ ing the lengths of the connected paths to finalize the dete ction in a winner take all strate gy (Figure 3-12 (B)). Unlike the study site in this work, more than one trail could exis t in many cases. In those cases, instead of finding the only wining trail, we could find multiple paths by successively omitting the winning paths from consideration and picking the next best pa th. For the case where there is no formal trail but one desires to detect paths of least resist ance for route planning and soldier trafficability analysis, we could use all acquired visibility vectors that are found in Figure 3-12. Figure 3-12. All acquired visibili ty vectors and the winning trail candidate in the training site. A) Visibility vectors (green lines). B) The winning trail candidate in the training area (green lines). All units are in meters. A B

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61 3.2.5 Result on Test Sites The trail in the testing site is fairly straight overall, but is locally curved at several points and narrower than in the training site (2 m ~ 3 m). Using the same approach as in the training site, visibility blockers, tree trunks, and smooth surface points are acquired. GPS trail points are indicated with these segmented points in Figure 3-13 (A). The winning tr ail candidate is shown in Figure 3-13 (B) after using the same geometric constraints of visibility vectors as in the training site. The trail in the tes ting site is successfully detected. Note that the edges (north and south side) of the trail do not have visibil ity vectors because they do not have front-back connections. Figure 3-13. The winning trail candidate in the testing site. A) Segmen ted points and GPS trail (yellow circles) in the testing area. B) Th e winning trail candidate in the testing area (green lines). All units are in meters. A B

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62 CHAPTER 4 A CLUSTERING APPROACH TO I NDIVIDUAL TREE DETECTION 4.1 Introduction In Chapter 3, two important applications were presented that utilize field-of-view (scope) geometric mappings. Such structuring elements were appropriate fo r those point-to-point paradigms. Most civilian resear ch and management of forests, however, is more concerned with structural parameters that relate directly to individual trees because they bear directly on ecological health of the forest and the potential yield of forest stands in timber or paper pulp resources. More recently, it has be en suggested that the estimation of such parameters could also be used to arbitrate carbon sequestration and cap-and-trade practices to mitigate the buildup of greenhouse gasses (Binford et al., 2006). Locating and delineating full tree crowns can enable estimates of tree counts, tree species, crown area, canopy closure, gap analysis a nd volume and biomass estimation (Gougeon and Leckie, 2003; Reurebuch et al., 2005). For the detection of singl e trees from LiDAR data, most previous work has focused on segmentation of raster ized or interpolated tree height images (i.e. 2D digital images in which the pixel value equa tes to height, also ca lled Digital Surface Model (DSM)) using standard image processing methods (Hyypp et al., 2001; Persson et al., 2002; Holmgren and Persson, 2004; Chen et al., 2006; Koch et al., 2006). However, airborne LiDAR data is acquired as a discrete set of point locatio ns (a so-called point cl oud), and collapsing the point cloud down into an image unnecessarily dis cards much useful information. Recent work has been reported that employs direct processing on the original LiDAR point data rather than rasterized image data (Andersen et al., 2002; Pyysalo and Hyypp, 2002; Morsdorf et al., 2003; Wack et al., 2003) to avoid this loss of information.

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63 There is strong interest in the integration of laser scanning and aerial imagery because laser data provide accurate height information and 3D crown shape (at high point densities), whereas optical imagery provides better planform geometry and color (spectra l) information (Hyypp et al., 2004). Leckie et al. (2003), Popescu et al. (2003), Popescu et al. (2004), and Popescu and Wynne (2004) used laser scanning and aerial im agery data on the problem of single tree isolation. However, the focus here is to develop an improved method to segment trees based solely on LiDAR measurements, with the understanding that the proposed method could subsequently be used in conjunction with imagery to further improve segmentation. Even with high resolution LiDAR data, such as that described herein individual trees can be hard to separate because more than one tree can occupy a given volume above a surface patch, e.g. interlocked canopies and leanin g trees (Figure 4-1 (B) and (C)). Th is results in clusters in the tree segmentation process that can have severe ov erlap. In addition to the overlapped canopies, some other characteristics of trees, such as very irregular shapes and the different sizes of tree canopies as shown in Figure 4-1 (A) make the use of simple de tection techniques problematic. Figure 4-1. Aerial photos illustrating the va riation of canopy morphology even within managed pine forests. A) An aerial photo showing i rregular shapes and di fferent sizes of tree canopies. B) A ground photo showing interlocked canopies. C) A ground photo showing leaning trees. A B C

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64 The most common approach to segmenting tr ees in LiDAR data is to employ a region growing algorithm instantiated with seed points on each tree. Finding the seeds (i.e. treetops) is a crucial step in the process of detecting i ndividual trees since subsequent steps are heavily dependent on the number of seeds and the locatio ns of seeds. Most current approaches are moderately successful, provided that the filt er size and image smoothing parameters are appropriate for the particular tree size and image resolu tion (Gougeon and Leckie, 2003). Finding an appropriate size of filter (or search ra dius when point data is used) to detect the treetops is not a trivial problem because different filter sizes should be ap plied to different areas for optimal detection accuracy. Schardt et al. (2002) and Brandtberg et al. (2003) tried to solve this problem using linear scal e-space method (Lindeberg, 1996) that was based on Gaussian smoothing of the rasterized image data at multiple scales. Results from this approach remain sensitive to determining the a ppropriate scale parameter, and the step of convolving the image with a Gaussian kernel could be problematic because individu al canopies may exhibit diverse asymmetric shapes. A detailed explanation of the scale-space method and its implementation on the study sites are presented in section 4.2. In this work, I address the issue of the size of the search radius, R and propose an approach that automatically grow s locally optimal canopy clusters, or regions, (equivalent to an adaptive search radius) to segmen t individual trees. All steps in the process work directly on the 3D cloud of LiDAR points. I first separate th e laser returns correspond ing to the ground from those corresponding to the above-ground biomass usi ng an adaptive multiscale filter (Kampa and Slatton, 2004) presented in sec tion 2.3. In the process, the lo w order (slowly varying) terrain surface is subtracted from the LiDAR points to level out the ground. The subsequent tree segmentation operates only on the above-ground point s and is divided into three main stages: (1)

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65 finding all possible seed points for each tree using a minimum search radius minR, (2) region growing instantiated at those s eed points, (3) merging partia l tree detections (incomplete clusters) using an agglomerative hierarchical structure. 4.2 Scale-Space Method It is well known that measurements of many natural proces ses or objects often exhibit structure over a wide range of s cales (Turcotte, 1997). In the part icular case of tree segmentation in aerial data (be it from LiDAR or some other modality, such as multispectral imagery or radar), one finds that trees in locali zed stands may exhibit similar canopy shapes and sizes, but over larger areas or multiple areas the canopy shapes and sizes can vary widely. Thus, for a tree segmentation algorithm to be truly successful, it must accommodate this variation automatically without requiring a high degree of empirical tuning for each site. The scale-space method represents one of the most successful previ ous methods for addressing tree segmentation in LiDAR data, and is thus explored here for th e purpose of providing context to the new method proposed in this work. In image processing, extracting meaningful st ructure that exists over a certain range of scales, sometimes referred to as multi-scale st ructure (Lindeberg, 1993) is often handled by creating a scale-space representation of the image data. The idea of scale in signals and scalespace filtering of 1D signals were introduced by Witkin (1983) and Koenderink (1984). A scalespace representation of a given image (,) f xy is a family of derived signals (,;) Lxyt defined by convolution of the image with Gaussi an kernels of different variances (,;) gxyt with the scale parameter 2t (equation 4-1). (,;)(,;)(,) Lxytgxytfxy (4-1) The 2D Gaussian kernel at scale level t is given in equation 4-2.

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66 221() (,;)exp 22 x y gxyt tt (4-2) The Gaussian kernel belongs to a class of ke rnels that guarantees a monotonic smoothing of the original image (Babaud et al., 1986) meaning that Gaussian smoothing does not produce new extrema when increasing the scale parameter. As a preliminary step, for the detection of i ndividual trees, the 3D poi nt data are converted into a 2D digital height image by selecting the ma ximum height laser point within each grid cell. The pixels with empty values are replaced with the mean of non-zero ne ighbor pixels, and this process is repeated until no empty values ex ist in the image by gradually employing more neighbor pixels (Figure 4-2). Often times, laser point outliers from a lightly Gaussian smoothed 2D height surface are remove d to produce a smooth and consistent canopy surface. Figure 4-2. Creation of 2D he ight image from 3D LiDAR po int clouds. A) First-stop 3D elevation points in a plot with low culture at PPINES. Units are in meters. B) Interpolated image of the 3D laser points with a 25 cm pixel size. Thus, the imaged area is roughly 27 m by 22 m. A scale-space representation of the image in Figure 4-2 (B) using equa tion 4-1 is shown in Figure 4-3. Since an appropriate scale interval is not known in advance, in practice, a user defines a range of scales with a constant scale in crement. In this example, a large interval is A B

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67 chosen (here, = [0.5, 6]) with an increment of 0.5 to see the changes in a wide range. Each layer in the scale-space stack (Figure 4-3 (B)) represents con volution at a scale showing the evolution of the original image through scale. Individual images have been successively smoothed by convolution with a Gaussian kernel of increasing scale. Figure 4-3. An example of a scale-space represen tation. A) A scale-space representation of the image in Figure 4-2 (B) with ranging from 0.5 to 6.0 in increments of 0.5 (beginning from the top left to the bottom right). B) An illustration of the scale-space stack. The smallest resides on the bottom of the stack and the largest on the top. Although the scale-space method well represents image structures at multiple scales, it does not address the problem of selecting locally a ppropriate scales to dete ct wanted objects. A general methodology for feature detection with au tomatic scale selection has been proposed by Lindeberg (1993). This method is based on local extrema over scales of different combinations of normalized derivatives. Lindeberg (1993) showed that a Gaussian blo b with characteristic radius 0t assumes a maximum of its s cale-space signature at a scale 0t. The scale-space signature of a blob is given by the no rmalized Laplacian (equation 4-3) 2(,;)norm xxyyLxyttLL (4-3) A B

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68 where x xL and yyL are the 2nd order derivatives along x-axis and y-axis respectively. The normalization factor, t allows the blobs to be compared at different scale-levels. These derivatives are computed at the spatial maximum of the blob, which is found by locating the maximum value in a moving window of pre-defined size. The detected blobs and strength of their scale-space signatures at each scale is shown in Figure 4-4. Note that the scale-space signature becomes stronger and th e number of blobs reduces as the scale parameter increases. Figure 4-4. The detected blobs and strength of their scale-space signatures at each scale. The scale, = [0.5:0.5:6], starts from the top left to the bottom right. The dominant scale-level in the image is rev ealed by the mean blob signature (Figure 4-5). The mean blob signature typically has a maximum at a certain scale, and an appropriate scale interval is usually defined from this mean blob signature graph in orde r to capture blobs of notably smaller and larger sizes. Figure 4-5 indica tes that the size of the dominant blobs for this

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69 example is around at = 3 (i.e. 3 pixels = 0.75 cm in radi us), which roughly corresponds to the significant width of dominant tr ee crowns in this plot when doubled for crown diameter. Figure 4-5. The mean blob signature. The ma ximum occurred at a sc ale corresponding to = 3. All detected blobs from the scale-space interval are now sorted in descending order according to their blob strength. The strongest blobs are marked in the image in this order until the distance between the current blob and other marked blobs are far enough (here, 4 pixels = 1 m is chosen for the threshold to yield best re sults). The identified single blobs represent individual trees, and the result in the selected area is shown in Figure 4-6. Several false positives are found in the measurement plot. Figure 4-6. The result of indi vidual tree detection by the scalespace method. The detected trees are shown by black circles.

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70 4.3 Proposed Algorithm 4.3.1 Finding Seed Locations Finding the seed points (i.e. tr eetops) for canopies in the LiDAR point cloud is a crucial step since it serves as the initial condition for subsequent steps. The search radius R (or, when rasterized image data are used, the window size of the local-maximum filter) determines the minimum allowable canopy radius, and the seed poi nt should be the highest LiDAR point for a particular tree canopy. In this sect ion, an algorithm is developed to find the seed locations using the raw laser point data assuming that R is known for the region of in terest (ROI). In general, the appropriate size of R is not known, and this case will be explored in section 4.3.4. The elevations of the first-stop LiDAR points are used for this step since these points better express the overall top canopies than do th e last-stop elevation points. To identify the seed points, it st arts by finding the highest point 1h in the LiDAR data set, denoted by A which is taken to be the first seed point 1s. The subset A is then formed by removing points proximal to 1s from the set A Proximal points are defined to be those points in the full data set A inside a circular search region (with the radius R ) centered at a seed point. The highest point 2h is then located within A If 2h is higher than the set of points proximal to 2h in set A (Figure 4-7 (A)), it is identified as a second seed point 2s and a reduced subset A is defined. If 2h is not higher than the points proximal to it (Figure 4-7 (b )), the next highest point 3h in A is identified. The process is repeated to identify additional seed points in progressively smaller subsets AAA while using the entire data set A to search for proximal points. This process terminates when all such seed points are found. The seed points are then indexed to represent individual trees. The algorithm is summarized by a pseudo code in Table 4-1.

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71 Figure 4-7. Identifying the seed points in two different cases. A) The case of the highest point in set A, 2h, being above all points w ithin the search region (2 R ), so that 22sh B) The case of the highest point in A 2h, not being above all points within the search region (2 R ), so 23sh. Table 4-1. Algorithm of finding seed points. Initialization: 1 i, R }{F Set ROIinpoints LiDARall A The set of seed points: } {S Define neighbor points: RhpdistphNR ),(:)( AA)0(, i j jR isNAA1 )()( for 1i while }{)1(FAi FAahi i )1(max )( maxiRhNaf if fhi iihs, }{F, 1 ii, iSSS else if fhi ihFF end if end while 4.3.2 The Effect of R on Finding Seed Points Most previous algorithms for finding seed point s either assume that the search radius R (or size of the movi ng window) is known a priori or they empirically test different sizes to find the best one for a particular s ite. However, it is not optimal to define a single measure of canopy z x A h1 s1 h2 s2 2 R s1 s2 2 R A s2 x z A h1 s1 A h2 s1 h3 s2 2 R 2 R 2 R A B

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72 size due to their irregular shap es and different morphologies acr oss various tree species, ages, and management treatments. As one would expect, tree detection results are very sensitive to the size of R If R is too large, small trees are missed, ye t elongate branches (o r small clusters of branches) are mistakenly segmented as trees if R is too small (Figure 4-8). Therefore, there is a need for a systematic approach to find an optimal size of R that adaptively react s to the nature of the canopies locally in the given ROI. Figure 4-8. Sensitivity of the detection result to the search region R If a single R value is used that is too big, elongated bran ches are not detected as trees, which is good, but some small trees are missed, which is not good. The converse occurs if a single value for R is used that is too small. As an example, a small area (14 m14 m) in th e IMPAC site is select ed (Figure 4-9 (A)). The Figure 4-9 (B) shows the changes in the number of detected seeds when different sizes of R (from 10 m to 1 m in intervals of 0.1 m) are used over the area. Figure 4-10 shows the locations of detected trees with different sizes of R Note that using smaller intervals than 0.1 m or R values smaller than 1 m would not provide any reliable improvement since the LiDAR data have approximately decimeter point spacing. Using th e algorithm described in section 4.3.1, we see that more trees are detected as R decreases, but we also get more falsely detected trees. There = detected seeds Rbig Rbig Rsmall

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73 are 9 trees in this example area, and the number of detected seed points is very close to the ground truth when R = 1.3 m, but it never found the correct number of trees. The implication is that a single value of R is not sufficient to detect all diffe rent sizes of trees in general. To overcome this problem, an agglomerative cluste ring approach is developed and described in section 4.3.4. Through the local agglomeration of sm all clusters, the effect of a spatially-adaptive R is realized while assuring every point is uniqu ely associated with a particular tree cluster. Figure 4-9. The number of detected seeds depending on R in a small selected area. A) The ground truth of a small selected area (14 m m). The known tree locations are circled in the area. B) The number of de tected seeds for the area depending on the size of R The number of real trees in the plot, which is 9, is indicated by the dashed line. Figure 4-10. The changes in detected seed points that occur by changing the size of R from 10 m to 1 m (from top left to bottom right). All units in meters. A B

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74 4.3.3 Region Growing Process After finding the seed locations, the remaini ng LiDAR points associat ed with individual tree canopies need to be delineated. It is challenging to extract the exact boundaries between trees because some tree canopies are intermingled (overlapping in 3D) and tree canopy boundaries are not always distin ct. The well known watershed se gmentation algorithm (Beucher and Lantuejoul, 1979) has been the most popular method to delin eate the tree crown boundaries in 2D (image) data. By conceptually pouring wate r onto the elevation imag e starting at the seed locations, the approximate tree boun daries are detected as connect ed paths. In this study, I develop a new method that is similar in concept to the watershed segmenta tion but applicable to the raw LiDAR 3D point data To find the boundary of each tree, the first-stop elevation points are used. First, the seed points are found using R = 1 m and then indexed. Starting fr om the highest point that is not already indexed, the nearest indexe d point that is above the current considered point is found. If the horizontal distance between th e current point and that neares t indexed neighbor is smaller than an interval T the current point is assigned the sa me index number as that neighbor. Otherwise, it is not labeled. The interval T starts from 0.1 m. Once al l the points in the ROI are considered, T is increased by 0.1 m, and the process is repeated. This incremented labeling progressively grows the clusters of LiDAR points associated with each seed point until we form a collectively exhaustive and mutually exclusive collection of sets representing the initial tree canopies. The purpose of restricting the labeling to a neighborhood, set by T and adopting the label of the nearest indexed poi nt within that neighborhood regard less of whether it is a seed point or just a previous ly indexed point is to reduce the ch ance of erroneously associating a considered point on a large canopy with a smalle r tree (seed) that happens to be closer. An illustration of this case is shown in Figure 4-11. In the figure, assigning labels using Euclidian

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75 distance would result in 1: sxLi (i.e. Tree 1) because of 21dd even though we see that xi should be associated with 2s (i.e. Tree 2). By following the incremental labeling by growing regions with T as described herein, we can correctly a ssociate points with larger canopies even if they are closer to smaller trees This is critical since we have instances of canopies touching or overlapping. The LiDAR point spacing dictates the range of reasonable starti ng values and step sizes for T which are roughly 1 to 2 times the nomi nal LiDAR point spacing. The algorithm of region growing process is illustrated in Table 4-2, and an example of a region growing result is shown in Figure 4-12. In it, th e seed points were found using R = 1 m, and the regions were subsequently grown by incrementing T from 0.1 m in steps of 0.1 m until all points were labeled. Figure 4-11. An illustration of a case where T is necessary. The point ix can be correctly associated with Tree 2 by following the in cremental labeling by growing regions with T 1s and 2s represent the treetops (i.e. se ed points) of Tree 1 and Tree 2 respectively. d1 d2 Tree 1 Tree 2 1s ix 2s

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76 Table 4-2. Region growing algorithm. Initialization: T stepT Set ROIinpoints LiDARallA The set of seed points: } ,,,{21lsssS The set of unlabeled points: } ,,,{21npppSAP The set of labeled points: } ,,,{21mbbbB Set SB Sort P (high low) while } {P for i = 1: number of points in P Find the nearest point from ip : minb if TbpdistiXY ),(min } {ipBB } {ipPP end if end for stepTTT )( Psizen end while Figure 4-12. An example of the regi on growing result with incrementing T from 0.1 m in steps of 0.1 m until all points are labeled. The seed points are found using R = 1 m. This is a downward looking view of the area in Figure 4-9 (A). Each color indicates a segmented cluster of LiDAR points representi ng a detected tree in the region growing process. Each cluster is numbered from 1 to 13. Over segmentation can be seen in some cases.

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77 4.3.4 Agglomerative Hierarchical Clustering Even with the incremented labeling described in section 4.3.3, we expect the initial results to be over segmented in some instances (Figure 4-12) since R was chosen small so as not to miss trees. An agglomerative hierarchical cluste ring approach is therefore employed to overcome this over segmentation. To show the inherent hier archical structure of this problem, in Figure 413, a hierarchical tree is crea ted by merging the clusters create d by the region grow ing process in section 4.3.3 based on the specific values of R that was found in section 4.3.2. The must merging clusters, eight small clusters should be merged as four trees, are shown with red branches. As shown in the hier archical tree, one value of Rcannot guarantee successful segmentation. Agglomerative hierarchical methods genera lly begin with each observation being considered as a separate cluster and then pro ceed to combine clusters until all observations belong to one cluster or some st opping criterion is satisfied. E ach LiDAR point could represent an individual observation (i.e. singl eton) in the lowest level of th e hierarchical clustering data structure, but it would not be ve ry meaningful or computationa lly efficient to use individual LiDAR points to initiate the clustering. Since the size of R dictates the size of tree canopy clusters that can be detected, I specify a minimum value for Rto be 1 m because no trees smaller than that are present in the study sites. Note however, that the minimum value of Rcould be chosen to be smaller if needed.

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78 Figure 4-13. An example of hi erarchical tree and merged clusters at specific levels ofR. A) An example of hierarchical tree over the small area in Figure 4-9. Each number represents a cluster at the lowest level, and the red branches in the hierarchical tree are the cases where the following clusters s hould be merged. B) Merged clusters at specific levels of R. All units are in meters. < R = 3.2m > < R = 4.3m > < R = 7.2m > < R = 9.9m > < R = 10.0m > < R = 1m > < R = 1.1m > < R = 1.3m > < R = 1.5m > < R = 1.6m > B 1.0m 1.3m 3.2m 1.6m 1.1m 4.3m 7.2m 9.9m 10.0m < R > 1.5m (1) (4) (5) (7) (10) (8) (9) (3) (2) (6) (11) (12) (13) A

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79 The region growing process in section 4.3.3 provi des the set of clusters at the lowest level (i.e. the leaf level) of the hier archical clustering tree. From that point on, clusters are merged solely using agglomeration and not region growing. Small cluste rs representing partial canopies are merged with their nearest neighbor cl uster in space as determined by the distance ,drs between cluster centroids (also known as th e centroid linkage me thod). Essentially, mindis used to establish which clusters are nearest neighbors. In equation 4-4, (,) drs is the horizontal 2l-norm (Euclidean distance) between cluster centroids, rn, sn are the number of LiDAR points in cluster r and s respectively, and irx is the ith point in cluster r 11 211 (,)s r iin n rs ii rsdrsxx nn (4-4) In most agglomerative methods, the decision to merge clusters require s a threshold test on a similarity measure. For tree segmentation, when attempting to select a threshold value based solely on 2D measures of horizontal point simila rity, it is generally not possible to find a value that provides good separation among all trees an d yet does not over segment individual tree canopies that exhibit large elonga ted branches (i.e. partial-tree clusters), which may appear similar to small, yet complete tree clusters. Th us, I exploit the canopy penetration of the LiDAR to find a threshold based upon vertical point adjacen cy within a cluster. A value for each cluster is assigned to be the standard deviation of z values (above-ground eleva tions of both first and last returns), z It was suspected that high values of z would occur for complete trees and lower values of z would occur for elongated branches becau se of the larger vertical distribution of biomass in complete trees. All clusters satisfying z are merged with their nearest cluster neighbors by the centroid linkage technique, where the threshold is determined via supervised

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80 learning. This process is repeated at the next level in the cluste ring tree until no clusters remain with z Through this process, we realize the effect of a spatially adaptive R Table 4-3 outlines the agglomerative clustering algorith m that is developed in this section. Table 4-3. Agglomerativ e clustering algorithm. Initialization: minR, T stepT Set level index 1 L Do seed finding process at L (section 4.3.1) Do region growing process ( T stepT ) (section 4.3.3) while any cluster satisfies z at L for i = 1: number of clusters at L Compute z for cluster i ; ) (izc Compare ) (izc with if )(izc Leave ic as is else if )(izc Find the nearest cluster, jc by centroid linkage Merge ic with jc : ijjccc end if end for 1 LL end while To determine the threshold, a Bayesian approach was used with 120 training sample points randomly selected from each class (partial tree clusters 1w and complete tree clusters 2w) at the PPINES site. The probability density function (pdf) for each class, (i.e. the likelihood of iw with respect to x ), is estimated using a Par zen windowing approach (Duda et al., 2001), and shown in Figure 4-14. The likelihood ()i p xwshows the probability of obtaining a particular feature value x (here, zx ) given that it belongs to class iw. The optimal (Bayesian) decision boundary between the two classes, *x, is selected by minimizing the probability of error (equation 4-5) under the assumption of equal prior probabilities (i.e. )()(2 1wPwP). Basically,

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81 the probability of error is mi nimized by choosing the maximum a posteriori probability. That is, by deciding 1w if )|()|(2 1xwPxwP and by deciding 2w otherwise for a given x From 100 different subsets of training sample s, I observed that the value of *x was not very sensitive to the particular training samples. I obta ined a mean value of 0.62 m for *x, with a standard deviation of 0.04 m, which is at the noise floor of the LiDAR data (5 ~ 10 cm). The value of 0.62 m was subsequently adopted for and used on all plots in the PPINE S. This value would have to be trained on each forest among differe nt pine plantation forests to be optimal, but the same value of is used in the IMPAC st udy site in this work to observe the robustness of by testing it on data from a plantation that is diffe rent from the one used to train 2211min() where()()(|)()(|)x x xxArgPerror PerrorPwpxwdxPwpxwdx (4-5) Figure 4-14. Probability density functions of the two classes (1w: partial tree clusters, 2w: complete tree clusters) estimated by th e Parzen windowing method. The Bayesian (optimal) decision boundary, *x and the resulting probability of error (shaded area) are shown. Here, the random variable x represents the standard deviation (in meters) of heights in the cluster points, z *x )|(iwxp x 1w 2w

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82 The segmentation result over the small area is pr esented in Figure 4-15. In this example, the algorithm successfully segments nine actual tree canopies, thus revealing the overall efficacy of this approach. Block diagram of the pr oposed algorithm is shown in Figure 4-16. Figure 4-15. The segmentation result over the small area. A) The ground truth showing known locations of nine actual trees with circles. Actual sizes and shapes of the tree canopies are different from those of the circles. B) The segmentation result. A uniform color is used to indicate the set of LiDAR points that are segmented as a given tree. The seed points are marked as crosses, and the maxi mal boundary of each tree is indicated by convex hulls (closed black curves). Nine ac tual trees are succe ssfully identified. 4.4 Results and Comparison The results of the tree segmentations are tabulat ed in Table 4-4. As shown in Figure 2-3, the canopy distributions differ according to the cultu ral treatments and the age of plots, and we expect the segmentation results to be dependent on these distributions. The numbers of all trees detected by the algorithm are recorded in the column of Detected in Table 4-4. Correct is the number of trees that are correc tly detected among all detected tr ees, and their per centages are in the parentheses. Wrong is the number of trees detected by the al gorithm that do no t exist in the ground truth (partial canopies labele d as whole trees), and Missed is the number of trees that the algorithm could not detect (whole trees labeled as partial ca nopies and subsequently merged A B

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83 into nearest complete trees). The evaluation of the tree detection was based on the measurement plots even though the algorithm dete cts all the trees inside the tr eatment plots. The areas on all sides in the treatment plots but not in the measurement plots comprise a buffer zone that mitigates edge effects in the spatial analysis. Figure 4-16. Methodology overvie w of the proposed algorithm. The overall detection accuracy was 970/1020 = 95.1% with no significant bias (i.e. the number of false positives (57 trees) is similar to the number of false negatives (50 trees)). As expected, the detection accuracy was higher at PP INES since the horizontal distribution of trees was more regular because of the young age of th e trees and the square spacing between trees. The plots at the PPINES with low culture show ed the best result (98.6%) without significant First and last stop elevation points Merge Clusters (centroid linkage) Classification (tree vs. partial-tree) Result First stop elevation points Data input Algorithm First and last stop elevation points Find Seeds (for min R ) Filter out Ground Points Level out the Ground Region Growing

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84 bias. In the high culture plots, th e trees grew bigger, resulting in more overlap and complexity in the canopy distributions. This caused more occu rrences of Wrong and Missed, but the percentage of correctly detected trees (96.9%) was still close to that of the low culture plots. The detection results at the IMPAC pl ots with high culture were as good as the high culture results at PPINES since fertilization made the older trees at IMPAC bigger and distinct from their neighbors. Also contributing to th is high detection accuracy was th e fact that fe rtilization over the long duration of the IMPAC plots eventually resulted in instances of competitive tree mortality (Table 4-4), which increased some of the gaps between trees. The lowest detection accuracy occurred for the case of the low culture plots at IMPAC (84.0%). Unlike at PPINES, the IMPAC plots with low culture had less tree mortality (more closely packed trees) and more irregularity in canopy size and shape. Several di fficult cases were also observed in these plots where small trees were leaning towards nearby taller trees and parts of their canopies were underneath or inside neighboring trees. Table 4-4. Results of indivi dual tree segmentation. Here, H = High culture, L = Low culture. High cultural intensity attempts to maximize growth and health of the trees through fertilization and control of understory vegetation. Low cultural intensity does not. Result Site Plot Type Number of Plots Number of Planted Trees Number of Living Trees Detected Correct Wrong Missed H 8 384 351 367 340 (96.9%) 27 11 PPINES L 8 384 354 356 349 (98.6%) 7 5 H 6 240 134 150 129 (96.3%) 21 5 IMPAC L 6 240 181 154 152 (84.0%) 2 29 Total -28 1248 1020 1027 970 (95.1%) 57 50 A segmentation result on a plot at the PPINES with high culture is shown in Figure 4-17. Odd-shaped tree canopies are successfully detected because no assumptions are made on

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85 horizontal canopy morphology. The treetop, tree boundary, and LiDAR points of each tree are shown in the figure. Two false positives and one false negative are found in the measurement plot. Figure 4-17. An example of the segmentation resu lts (a plot with high culture at PPINES). A) Known tree locations are manually circled on top of the first-stop elevation points where the ground points are filtered out. Actu al sizes and shapes of the tree canopies are different from those of the circles. B) The segmentation result. A uniform color is used to indicate the set of LiDAR points that are segmented as a given tree inside the measurement plot. The seed points are mark ed as crosses, and the maximal boundary of each tree is indicated by convex hulls (close d black curves). Detected trees that lie outside the measurement plot are sh own with grey crosses and lines. The same study sites are tested by the scale-sp ace method mentioned in section 4.2 (Table 4-5), and the detection result is compared with the result by the propos ed method (Figure 4-18). There is no big difference between the two methods in detection accuracy at PPINES because of relatively less complex of the spatial distribution of trees and closer to Ga ussian distribution of the tree crowns. However, the accuracy by scal e-space method drops more rapidly than the accuracy by the proposed method as the test s ite becomes complicated. The accuracy by the scale-space method drops more than 10% at IM PAC compared to the a ccuracy by the proposed method. In addition, the scale-space method produ ces more false positives (92 trees) and false negatives (85 trees) overall. B A

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86 Table 4-5. Results of indivi dual tree segmentation by the scal e-space method. Here, H = High culture, L = Low culture. Result Site Plot Type Number of Plots Number of Planted Trees Number of Living Trees Detected Correct Wrong Missed H 8 384 351 378 343 (97.7%) 35 8 PPINES L 8 384 354 366 348 (98.3%) 18 6 H 6 240 134 142 115 (85.8%) 27 19 IMPAC L 6 240 181 141 129 (71.3%) 12 52 Total -28 1248 1020 1027 935 (91.7%) 92 85 Figure 4-18. Performance comparison between the proposed method (blue) and the scale-space method (red) based on Tables 4-4 and 4-5. Pl ot codes: PL = low culture at PPINES, PH = high culture at PPINES, IH = high cult ure at IMPAC, and IL = low culture at IMPAC. 4.5 Discussion Using the proposed approach, I obtained overall tree detection accuracies in excess of 95% over the two test sites (Table 4-4). The only exce ption was the set of low culture treatment plots at IMPAC, where a fairly good detection accuracy of 84% was still achieved. As mentioned in the previous section, those plots exhibited co nsiderable intermingling among adjacent canopies

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87 and greater variation in canopy size and shape than the other plots. The detection accuracy in the set of high culture treatment plots at IMPAC was high and close to that for the plots at PPINES even though was trained on PPINES, providing evidence of the robustness of In general, lower detection accuracy at a testing site (site at which was not trained) coul d be attributed to either greater structural complexity at the testing site or simply the fact that was not trained at the testing site. But here, we see good performance at IMPAC with high culture similar to that at PPINES. Thus, it appears that th e detection accuracy was mainly affected by the complexity of the tree canopies in the low culture IMPAC site. The small standard deviation in x across multiple randomized samplings of the training da ta suggests that the parameterization in the clustering step is robust and could be applied to other managed sites of different tree ages, stem spacings, or species using only modest amounts of training data. This is an important observation because the availability of high resolution remote sensing data sets, (in particular LiDAR data sets) over sites with ample ground-truth is often limited. As a result, one cannot generally run a large number of inter-comparisons of estimation pe rformance across different sites, as is often done in other estimation or patt ern recognition studies in which data is not so limited. Even though the scale-space method shows high accuracy at PPINES where the trees are well apart and the crown shapes are close to Gaussi an distribution, there are some caveats in this method: (1) The scale-space method needs a prepro cessing to convert 3D poi nt clouds into a 2D smooth image by giving up more detail informati on of LiDAR points. More over, a reverse step is needed, after segmenting indi vidual tree crowns, to recover the individual tree LiDAR points which are necessary to estimate tree parameters such as tree heights and crown lengths. (2) Another drawback of scale-space method is findi ng the local extrema at each level. This is a chicken-and-egg problem since it is similar to the problem of finding the right size of R

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88 mentioned in section 4.3.2. (3) As seen in the Figu re 4-3, the local maxima drift as scale changes. This drifting phenomenon becomes severe as the s cale parameter gets larger, and the blobs in the bigger scales generally have high scale-space signature. The algorithm chooses the strong blobs rather than following weaker blobs which have more accurate locations. (4) Besides the drifting phenomenon, it is not a trivial problem to deci de if the current blob is overlapped with previously chosen blobs since an other search region should be determined for this task. Flying multiple times over a particular ROI is generally necessary to obtain high densities of laser points (10 20 points/m2) given the current constrai nts on minimum flight speed, minimum allowable flying altitude, maximum lase r pulse rate, and maximum scanner frequency. Although, increasingly high laser pulse rates of new LiDAR systems can reduce somewhat the need for multiple flight lines (Slatton et al ., 2007). Unlike the fli ghts over IMPAC, only horizontal (East-West) flights were acquired ov er PPINES. As shown in Figure 4-19, this resulted in narrow vertical (Nor th-South) gaps that are visible in the point clouds between scan lines. While the overall tree detec tion accuracy was high in spite of this phenomenon, in general such gaps can cause difficulty in detecting trees if a tree happens to be separated into a multiple clusters by a gap. The worst case scenario woul d be when the scan lines from multiple flights overlap almost exactly rather than one flight filling in the gaps from another. Therefore, when researchers have input on the design of the flight plan, ort hogonal flight lines should be requested to get better coverage over the ROI.

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89 Figure 4-19. A top view of the low culture PPINES plot shown in Figure 2-3. The aircraft was flying East-West (right-left in the figure) over the site. Narrow gaps roughly 1m or less in width are visible (marked with a rectangle) in the point data between scan lines even though partially-overlappi ng flight lines were acquired. A subset of the detection result is shown inside the small box to th e left. While such gaps do not seem to strongly affect the correct dete ction of the trees, they can affect the estimated shapes of the detected canopies and estimates of HT and CL in cases where the highest points on the trees are missed. Orthogonal flight lines could mitigate such gaps.

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90 CHAPTER 5 FOREST PARAMETER ESTIMATION 5.1 Introduction Once individual trees are detected, the possibi lity is opened up to estimate important parameters such as the number density of trees, tree height, crown length, and crown area directly from the segmented points. From these parameters, other forest parameters, such as diameter at breast height (DBH), basal area, an d leaf area index (LAI) c ould be estimated from allometric equations (Amaro et al ., 2003; Song, 2007). The focus on this chapter is estimations of two parameters for which I had in situ measured values from a ground survey, tree height (HT) and crown length (CL). 5.2 Estimation of Tree Height and Crown Length 5.2.1 Tree Height (HT) The highest point among the segmented points fo r each tree is considered as the treetop, and the distance to the treetop from the ground is rega rded as the height of that tree (Figure 5-1). The accuracy of this depends primarily on the density of LiDAR points since the laser beam divergence is very narrow, the height error fr om UF-ALSM measurements is at the decimeter scale (Shrestha et al ., 1999), and the error in the estimation of bare-surface ground elevation (Cho and Slatton, 2007) rarely exc eeds two or three decimeters. If the point density is very low, it is likely that the system will miss the actual treetop thereby resu lting in underestimation of the true maximum height. 5.2.2 Crown Length (CL) In the field work, foresters are interested in effective crown length. A whorl is a common feature of pine trees and is defi ned as a cluster of branches that radially come from the main trunk at roughly the same height. The base of th e live crown can be defined as the lowest whorl

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91 with 50% or more of the branch es containing live green needles. As a tree ages, the older (lower) whorls become shaded by the newer whorls on th at tree. This trend is emphasized in managed forests where all trees are at the same stage, so shading on older whorls by neighboring trees of similar heights increases with tim e. As the whorls age and lose sun exposure, they die and over time the base of the live crown moves up as the tree height increases (Long et al ., 2004). Crown length can be computed simply by subtracting th e height to the base of the live crown (HTLC) from HT (Figure 5-1). Figure 5-1. An illustration of estimates of HT, HTLC, and CL on segmented LiDAR points. An estimate of the vertical projection of ma ximal crown area for a segmented tree is circumscribed by a convex hull (closed red curves), and the estimated location of a tree stem is indicated by a brown bar. The base of the live crown is usually difficult to estimate since the lower limit of the canopy is not always obvious because LiDAR points can hit the stems (trunks) and dead branches. In this work, owing to absence of understory vegetation, a simple method is developed. By smoothing the vertical distribution of non-ground LiDAR points (both firs t and last returns), HTLC CL HT

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92 the height where a significant number of points firs t appear in a given tree cluster can be found. A 2 m long sliding window was incremented up from the ground in 1 m intervals at each tree cluster, and the number of points in the window is counted. When the number of points in the window first exceeds more than 1% of the total nu mber of points in that cluster, the median height of the LiDAR points in the window is recorded as the H TLC of that tree. 5.3 Results and Discussion From the IMPAC site, I was able to use all trees in the 12 plots to estimate HT and CL because the ground truth survey included all trees. It was thus possible to examine two cases for IMPAC. In the first case (Case 1), only correctly detected trees are used, that is, falsely detected trees and missed trees are not counted. In the second case (Case 2), all trees segmented by the algorithm are used for the experiment. Case 2 is more general since it is not always known beforehand if a segmented tree is classified corr ectly or not. Unfortunately, at PPINES only 25% of the trees in each plot (except 2 plots) were selected to measure the parameters during the ground survey. So at PPINES, I used all correctly detected trees (83 trees) in two plots and a random sampling of 140 correctly detected trees from the remaining 14 plots. As a result, wrongly detected trees and missed trees could not be included in the PPINES results. The differences between estimates and ground truth va lues for HT and CL are summarized in Table 5-1. 5.3.1 Tree Height For the PPINES site, the mean of all ground trut h tree heights was 7.95 m, and the mean of all estimated tree heights was 7.71 m. The mean of absolute height differences between the ground truths and the estimates wa s 0.34 m (percentage of error = 4.22%) and the standard deviation was 0.29 m.

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93 Table 5-1. The mean differences between the ground truth values and the estimates of HT and CL. The standard deviations are given in parentheses. Because the ground survey at IMPAC was exhaustive, two different cases could be studied: (1) Case 1: only correctly detected trees are used, and (2) Case 2: all tr ees segmented by the algorithm are used. Only Case 1 could be studie d at PPINES because the ground survey was based on randomized sampling rather than exhaustive. Tree Height (HT) Crown Length (CL) Case 2 Case 2 Case 1 Whole Each plot Case 1 Whole Each plot PPINES 0.34m (0.29m) --0.84m (0.58m) --IMPAC 0.78m (0.63m) 0.58m 0.60m (0.44m) 1.40m (0.97m) 0.39m 0.81m (0.69m) For all correctly detected trees in IMPAC (i.e. Case 1), the mean of all ground truth tree heights was 22.00 m, and the mean of all esti mated tree heights was 21.85 m. The mean of absolute height differences was 0.78 m (percentage of error = 3.55%) and the standard deviation of them was 0.63 m. For Case 2, over the whole (all 12 plots), the mean of all ground truth heights was 21.34 m and mean of all estimated heights was 21.92 m. Interestingly, this difference (0.58 m) was smaller than the differen ce achieved in the first case. This shows that there is a good agreement between the mean of all ground truth and the mean of all estimates (from all detected trees) at this site even though the algorithm misses some trees and detects some false trees. To look at a smaller size of ROI, the same experiment was executed for individual plots (0.027 ha), and the result still shows good agreement but s lightly larger errors; the mean of difference between ground truth a nd estimates of each of the 12 plots was 0.60 m and the standard deviation was 0.44 m. While it is possible in general for large errors to occur locally, these results imply that one could r easonably expect good av erage agreement with ground truth even over small plots, such as these.

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94 5.3.2 Crown Length For the PPINES site, the mean of all ground trut h crown lengths was 5.51 m, and the mean of all estimated crown lengths was 5.04 m. The mean of absolute CL differences between the ground truths and the estimates was 0.84 m and the standard deviation was 0.58 m. For IMPAC, in Case 1, the mean of all ground truth crown lengths was 6.39 m, and the mean of all estimated crown lengths was 6.01 m. The mean of absolute CL differences was 1.40 m and the standard deviation was 0.97 m. In Case 2, the mean of all ground truths was 6.18 m and mean of all estimates was 5.79 m. As seen th e trend in HT estimation, this difference (0.39 m) is smaller than the difference in Case 1 s howing that there is a good agreement between the mean of all ground truths and the mean of a ll estimates over the test area. Based on the individual plots for a smaller size of ROI, the mean of diffe rence between ground truths and estimates of each of the 12 plots was 0.81 m and the standard deviation was 0.69 m. 5.3.3 Underestimation of the Parameters In the subsequent parameter estimation, I al so obtained agreement between estimates and ground truth to within several d ecimeters. The average tree height was underestimated by 0.24 m and 0.15 m over PPINES and IMPAC, respectively. Much of this residual is likely caused by instances where the LiDAR did not happen to hit the top most point of some crowns. There was more chance of missing the treetops over PPINES because the peaks of the crowns tended to be sharper over PPINES than over IMPAC resulting in larger underestimation for HT over PPINES. The average crown lengths were underesti mated by 0.47 m and 0.38 m over PPINES and IMPAC, respectively. The slightly larger estimation error for CL is not surprising since CL estimates depend on both the estimated HT and how well the lower canopy is sampled. The occluding effect of the upper canopy implies that the lower canopy is not sampled as densely as the upper canopy. The underestimate of CL at PPINES was slightly larger than at IMPAC. The

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95 most likely reason for this is that the younger tr ee canopies in PPINES are shorter and thicker resulting in less penetration of the LiDAR. Furtherm ore, there is always some uncertainty in the field measurements themselves because of irregularities in the terrain surface and measurement errors. In these study sites, the terrain is quite flat, so any errors that may be present in the ground surveys are most likely due to random measurement errors by field personnel. 5.3.4 Impact of LiDAR Point Density Over the range of LiDAR point densiti es examined here (10 20 points/m2), the RMS errors in the estimates decreased with increasing density for both th e tree heights and crown lengths (roughly 0.5 m to 0.1 m for HT and 1.1 m to 0.3 m for CL for 10 to 20 points/m2, respectively). This suggests that high LiDAR point densities are important for accurate estimation of individual tree parameters. In partic ular, as mentioned in the previous section, higher point densities increase the chances of a Li DAR return from the highest point in each tree canopy, thus reducing underestimation of tree he ight. It would be potentially interesting to determine minimal LiDAR point densities that could still yield useful estimates in order to acquire LiDAR data most effi ciently. However, general statements along those lines are problematic because the degree to which lower LiDAR point densities would be useful would depend on the flight pattern (presence of orthogonal flight lines), forest type, parameters being estimated, and the tolerance for uncertainty for the particular application. 5.4 Other Parameters 5.4.1 Crown Area Based on the segmented LiDAR points, estimate s of the vertical projection of maximal crown area for each segmented tree could be obt ained using the circumscribing convex hulls computed for each crown cluster (Figure 5-1). Similarly, the 3D shape of the upper crown surface of each tree could be estimated since the LiDAR points provide height information

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96 along with horizontal positions. However, I do not present formal estimates of crown area or shape here since they were not indepe ndently measured in the ground survey. 5.4.2 Diameter at Breast Height (DBH) The diameter at breast height (DBH) is one of the most important parameters in forest inventories. Usually the tree hei ght correlates strongly with stem diameter and height can be assessed accurately with a laser s canner as shown in section 5.3. A simple empirical DBH model for loblolly and slash pines using the regression formula in equation 51 could be developed on the basis of field measurements of tree height and crown diameter (CD). CD HT DBH (5-1) where coefficients ,, and can be calibrated using lo cal field inventory data. 5.4.3 2-Dimensional Open Gaps There are many ways of quantifying the 2-dim gaps over a forested area. The simplest method is computing the ratio of non-vegetation area to the whole area. This is a straight forward computation since the non-vegetatio n area is the complement of the area of the detected trees in Chapter 4. Simply, it would be max(gap)=1 in the case of no vegetation in the area, and min(gap)=0 when vegetation covers the whole area. However, the area ratio method described above fails to coun t the canopy density. Although it is very difficult to have accurate can opy density from LiDAR da ta due to lack of LiDAR penetration in understory in thick forest we can still use some information from LiDAR data which shows some difference between dens e canopy and sparse canopy; we have less nonground LiDAR points on sparse canopy because mo re points penetrate the canopy and reach the ground. Therefore, instead of considering the ve getation area uniformly, we can compute 2D pdf of ALSM points in the area by using a non-parametric approach such as Parzen window method.

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97 It would be a good supplement to compute lacu narity as an overall parameter for the interest area since area ratio or D pdf does not inform of the distribution of the gaps. Mandelbrot (1982) introdu ced the concept of lacunarity as a quantitative measure of the distribution of gap sizes, and is also used in texture analysis (Dobson et al ., 1997; Limas Serafim, 1997; Du and Yeo, 2002) Lacunarity was developed to cover the case of fractals that have different appearances even though they are constructed with identic al fractal dimensions. Large lacunarity implies large gap and clumping of points, and small lacunarity implies a more uniform distribution of gap sizes. The range of lacunarity is between 0 and infinity. 5.4.4 3-Dimensional Open Gaps Three dimensional gaps can be more pr ecisely defined if we know the full canopy structure. Since ALSM describes the upperstory canopy structure very well, open gap towards zenith sky that is related to GPS (L-band) mi crowave attenuation and pe rsonnel detectability from the sky can be computed. Figure 5-2 shows an example of using 3D gap to compute the maximum possible open angles at locations on the ground. The open angle is calculated at 90% confidence level assuming that the observer is at 2 m above ground level, moving inside the measurement plot at 1 m interval s. The ALSM points that cover th e circle area of the cone scope are used to compute the confid ence level. That is, the angle is increased until the ALSM point coverage on the circle area of the cone scope reac hes 10% of the circle area. A weight was given to the point inside the cone sc ope depending on the height of the point since lower points inside the cone scope contribute more towards blocking the visibility than highe r points. In Figure 5-2 (c), we clearly see the high open angle wher e big open gaps (no tr ee near around) exist.

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98 Figure 5-2. An example of the maximum possibl e open angles at locations on the ground. A) Illustration of upward open gap from an obser ver. B) A plot in the IMPAC site. C) Maximum possible open angle at the 90% c onfidence (observer level = 2 m from the ground). Observe r A B C

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99 CHAPTER 6 SPIN IMAGES OF DIFFUSE TARGETS 6.1 Motivation Geometric structures of individual trees are one of the most interests to forest researchers, but it is usually difficult to have them from overhead image sensors. However, due to some penetration through canopies of ALSM points an d their precisely locat ed 3D measurements, there will be some ways of showing vertical (side-view) differences between different canopy classes. In this chapter, spin images are com puted to see the possible discrimination between the different geometric structures of the segmented clusters. Spin images developed by Johnson and Herbert (Johnson, 1997; Johnson and Hebert, 1999) are a 3D point matching method based on shape characterist ics only. Spin images have some attractive characteristics, such as invariance to rigid transformations (rotation, scale, and pose), limited sensitivity to variations of pos ition of mesh vertices, flexibility (since no hypotheses are made on the surface representation), and ease of co mputation. This method has been successfully applied to shape matching (Johnson and Hebert, 1998; Johnson, 2000) and 3D object retrieval (Assfalg et al ., 2004), and textured spin images were recently introduced to include texture information (Brusco et al ., 2005). It is a new attempt to use spin images on diffu se targets such as tree canopies described in this study, and there are a couple of advantages of using spin im ages for this application: (1) ALSM points are not evenly distributed on the ca nopies because the spot dispersal created by the oscillating mirror creates a saw-toothed pattern on the ground, and because of the combining of multiple flight lines. Also, trees that are viewed near the edges of the ALSM imaging swath are partially occluded (i.e. the opposite side of the canopy from the laser dire ction has very sparse point density at high scan angles). Therefore, instead of using the raw point distribution,

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100 spinning around the tree stem mitigates these ir regularities. (2) Tree canopies are inherently irregular targets, so we desire many realizations to characteri ze the canopies. Spin images are expected to reduce overall sensitivity to these irregularities and increase the discrimination between profiles of different ca nopy structures. Therefore, for example, comparing spin images of the segmented clusters in Chapter 4 could be another way of classi fying small tree canopies from partial-tree clusters at the expense of more complexity and computational cost (but more detail vertical structures). 6.2 Spin Images Creation of a spin image begins from an orient ed point that is a 3D point associated with a direction. Usually, an oriented point is defined at a surface mesh vertex using the 3D position of the vertex and surface normal at the vertex. An oriented point defines a partial, objectcentered, coordinate system. Two cylindrical coordinates are define d with respect to an oriented point: the radial coordinate defined as the perpendicular distance to a line along the surface normal vector n, and the elevation coordinate defined as the signed perpendicular distance to the tangent plane defined by vertex normal and position (Figure 6-1). In Figure 6-1, p is a point on the surface of the object and n is the normal of the tangent plane in p For an oriented point, npO, a spin map is defined by mapping any point x in the 3-D space onto a 2-D space according to the equation 6-1, where the se t of spin image pixel values is denoted by OS such that 23RRSO )(,))(( ,)(2 2pxnpxnpx xSO (6-1) In other words, the oriented point defines a fam ily of cylindrical coordi nate systems, with the origin in p and with the axis along n The spin map projection of x retains the radial distance

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101 ( ) and the elevation ( ), while it discards the polar angle. This projection ensures that, for any given oriented point, a unique spin map exists. The projected coordinates and of each mesh vertex are used to construct the spin images. Figure 6-1. The object centered 3-D coordinate system to create a spin image. The ) ,( coordinates provide a 2D index of a surface point x relative to the oriented point p 6.3 Creating Spin Images from ALSM Points The process in this application could be so mewhat different from the process that was originally developed since the oriented points ca n be defined as just th e treetop points of each cluster. By defining them, it greatly reduces the amount of computation n eeded in the original algorithm such as computing the surface mesh vert ices, computing surface normal at each vertex, and considering each surface mesh vertex as an or iented point. Another big difference is that the sizes of the spin images can be fixed since initial canopy clusters are already segmented. Choosing the size of spin image is an issue in many other applications si nce it strongly affects the result a lot. In this work, I fixed the size of the spin images ) ( as 4 m 10 m with the grid size of 0.5 m resulting in 8 pixel 20 pi xel images (Figure 6-2). However, there is a Object Surface Tangent Plane n x p

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102 problem with fixing the size of images since th e sizes of canopies of the segmented clusters varies a lot. This may not be a problem if many samples (i.e. clusters) from each class can be created, but creating many traini ng samples is not easy for this application. Furthermore, the shape of the crown is more important than the size of the canopy for characterizing different tree crowns. This problem is easily solved by scaling the range of the ALSM poi nts in the cluster to fit in the spin image range, [0 m, 4 m]. By doing this, th e size of canopies is no longer an issue. For the -axis of the spin image, I limited the range to be [ H H -10 m] where H is the height of the treetop points. In this way, ALSM points that are lower than 10 m from the treetop are not considered. This allows us to take most of th e main canopy points into account, and remove the contribution of understory objects. Figure 6-2. Selection of the size of spin image. The size of spin image is fixed as 80 with grid size of 0.5 m. The -axis is the horizontal axis, and the -axis is the vertical axis. Spin Image (1, 1) Max( H ) Max( H )-10 m 0 m Treetop ALSM point 0.5 m Spin Image (20, 8)

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103 One of the disadvantages of the standard spin images algorithm is that the density of the data points must be uniform across the surfaces being compared (Dinh and Kropac, 2006). This issue occurs in the application here because there are different numbers of ALSM points in each cluster. The local point density varies a lot, a nd the size difference of canopies creates different number of points in each cluster. Again, this may not present a big problem if we could create many spin images for many cases with different number of points, but that would require an unrealistic number of training examples. Therefore, to make fair comparisons between spin images, the number of points in each cluster is normalized. Figure 6-3 shows an example of a spin image of a full tree cluster. Figure 6-3 (A) shows just the points that are spun and mapped onto 2D. The spin-map of the clus ter (Figure 6-3 (B)) is created by using the image size th at is defined above, and the co rresponding spin image is shown in Figure 6-3 (C). The idea of accumulating the poi nts of the spin-map into discrete bins is equivalent to a linear smoothing of the spin-map with an impulse response of value one over the bin and zero elsewhere. In the spin image, the gr ay values are associated to the counts of points in the spin-map falling in each discrete bin (w hite color = zero points, darker color = more points). Unlike the application of spin image to arbitrary 3D object recognition from any vantage point, the application here is c onsidered as a special case for three reasons: (1) There is no full description of the model (no expected closed -form geometric shape). The query points (or cluster), and model as well, are always from the partial view (i.e. dow nward-looking from the sky). This partial view makes it harder to distin guish the objects, but it makes the spin image computation easier. (2) Whole tree canopies or portions of tree canopies are segmented via the adaptive region growing algorithm in Chapter 4 befo re the spin image computation. This greatly

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104 reduces the computation load since a single spin image is needed per cluster by centering the spin image at the seed point of the cluster. T hus, computing a spin image at each and every point is not necessary. (3) The LiDAR data can be e xploited much more fully by using both first and last stops and other features including intensity values. By these extra features, the standard spin images can be extended to better characterize diffuse objects. Figure 6-3. An example of a spin image of a full tree cluster. A) The raw points are spun with respect to the oriented point. Units are in meters. B) The spin-map. Units are in halfmeters. C) The spin image of the cluster. Units are in half-meters. 6.4 Spin Images of Canopy Clusters The spin images of 12 initial clusters in the small test area at the IM PAC site (Figure 4-12) are created and shown in Figure 6-4. Cluster #1, 2, 3, and 6 are tree clusters, and the other clusters are partial-tree cl usters. The maximum pixel value in the whole spin image set occurred in cluster #9. The numbers of point s in each pixel are normalized by this maximum A B C

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105 value. In the spin images of the tree clusters, we see that the points are spread diagonally from the upper left to the lower righ t portions of the image. Cluste r #5, 9, and 10 are partial-tree clusters representing small portions of the tree canopies, and the spin images are quite different from the general spin images of tree clusters. Many points are located on the top portion of the images and the pixel values are spiky suggestin g that good separation between the complete trees and partial trees could be achieved. Clusters #4, 7, 8, 12, and 13 are partial-tree clusters representing large portions of the tree canopies and present spin images that exhibit intermediate values between the two cases of full tree clusters and small canopy portion clusters. As another example, in Figure 6-5, two spin images are created from each three different classes; PPINES with low culture treatment ( PPINES-L), PPINES with high culture treatment (PPINES-H), and IMPAC. To take the differences of actual canopy sizes into consideration, the range of -axis is not scaled here. Most of the point s in the cluster at PPINES-L, as shown in Figure 6-5 (A), are located righ t near the stem showing very narrow cone shape of the tree crown. The spin images of the clusters at IMPA C, Figure 6-5 (C), show that the distribution of the pixels is smoother unlike the spiky distribution of the clusters at PPINES-L. We also see wider cone shapes with more voids inside the cr owns. The spin image shapes of the clusters at PPINES-H are intermediate between the two other cl asses, but closer to the spin images of the clusters at PPINES-L.

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106 Figure 6-4. Spin images of each cluster in Figure 4-12. A) Clusters #1, 2, 3, and 6 are tree clusters. B) Clusters #4, 7, 8, 12, and 13 are non-tree clusters, but they correspond to large fractions of the tree canopies. C) Clusters #5, 9, and 10 are also non-tree clusters, and they correspond to small frac tions of the tree canopies. (The cluster number on each cluster is shown in Figur e 4-12.) All units are in half-meters. A B C

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107 Figure 6-5. Spin images of tree clusters from three different classes. A) A cluster at PPINES with low culture treatment. B) A cluster at PPI NES with high culture treatment. C) A cluster at IMPAC. It is promising that, in many cases, sp in images provide good separation between different tree structures. For the training processe s, in the future, the spin image of each sample from each set of clusters could be computed and stored in the model library. To classify a given cluster, the spin image of the given cluster is generated and compared to all the stored spin images to find the most highly correlated image us ing a template matching scheme. The standard A B C

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108 way of computing linearly related images is the normalized linear correlation coefficient. Given two images P and Q with N bins each, the linear correlation coefficient ) ,( QPR is shown in equation 6-2 (Johnson 1997). ))( )()( ( ),(2 2 2 2 i i i i ii iiqqNppN qpqpN QPR (6-2) R ranging between -1 (anti-correlation) and +1 (completely correlated), measures the normalized error using the distance between the data and the best least squares fit line to the data. The images are similar when R is high and not similar when R is low. The correlation coefficient imposes an ordering on point corresp ondences, so the spin image that gives the highest value of R is selected. It should be noted that over modest sized areas, such as IMPAC and PPINES, this correlation comparison could be don e between the considered spin image and every training spin image, as suggested above. For larger areas, ho wever, it would be more efficient to estimate an expected spin image for the various training cases and simply compare the considered spin image to that small library of expected (mean or maximum likelihood) spin images. As an example, the expected spin image fo r each class in Figure 6-4 is computed by averaging the spin images in each class. Each spin image is then compared to the expected spin images by using the linear correlation coefficient in equation 6-2. The mean of the correlation coefficients for each case is shown in Table 6-1. From Table6-1, we see that the spin images in the class of large fractional tree canopies appear to be more correlated to the expected spin image of the complete tree class than the expected sp in image of the class of small fractional tree canopies. Very weak correlation between the cla ss of complete tree and the class of small

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109 fractional tree canopies suggests reasonable separa bility between these two classes, which could be helpful in tree detection. Another example for the case of different tree classes, such as PPINES-L, PPINES-H, and IMPAC, is shown in Figure 6-5. Five spin im ages are created for each class to compute the expected spin image, and the mean value of the co rrelation coefficients for each case is listed in Table 6-2. It shows a very weak correlation be tween the spin images in PPINES (both PPINES-L and PPINES-H) and the expected spin image in IM PAC, indicating that the spin image features offer good separability between plantations. Th e age difference (here, between PPINES and IMPAC) is well captured by the spin images wh ile the cultural difference (here, between PPPINES-L and PPINES-H) is not. The results in Tables 6-1 and 6-2 are regarded as preliminary findings primarily because a small number of spin images were used. They do provide evidence, however, that spin images have the potential to separate full tree clusters from partial tree clusters and trees of one age from trees of another age. Thus, it is speculated that spin images could be used to revisit tree clusters that are suspected of erroneously grouping two trees into one clus ter or over segmenting one tree into two clusters. Based on spin image results, old seed points could be deleted or new seed points could be instantiated and the clustering al gorithm re-run for that small area to improve the tree detection accuracy. Table 6-1. The mean value of the correlation coe fficients for each case in Figure 6-4. Here, CT = complete tree clusters, LPT = large fraction of the tree canopies, and SPT = small fraction of the tree canopies. CT LPT SPT CT 0.808 0.517 0.087 LPT 0.438 0.799 0.327 SPT 0.088 0.271 0.684

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110 Table 6-2. The mean value of the correlation coe fficients for each case in Figure 6-5. Five spin images are used to compute the e xpected spin image for each class. PPINES-L PPINES-H IMPAC PPINES-L 0.815 0.673 0.263 PPINES-H 0.687 0.842 0.380 IMPAC 0.265 0.367 0.813 6.5 Reducing Computational Complexity 6.5.1 Number of Bins Each pixel in the spin image is considered as a feature, so a high dimensional feature space is usually created. As a result, basic template matching is sometimes inefficient because: (1) each spin image comparison requires a correlation of two spin images, an operation on order of the relatively large number of bins (e.g. 160 bins in se ction 6.3) in a spin image; and (2) when a spin image is matched to the model library, its correlati on with all of the spin images from all of the models should be computed. Therefore, it would be desirable to transform the spin image pixels into a low dimensional space via Principle Component Analysis (PCA), and then take a small number of features that capture most of th e variance of the spin image. PCA is a common technique for image compression in object recognition (Murase and Nayar, 1995). By computing the eigenvectors of the covariance matrix of th e set of vectors, PCA determines an orthogonal basis, called the eigenspace, in which to describe the vectors. PCA has become popular for efficient comparison of images because it is optimal in the correlation sense (Fukunaga, 1990). 6.5.2 Number of Points on an Object There are some cases where the whole (or part ) of the object can be pre-segmented before computing spin images. These cases resolve some issues of standard spin images and reduce the computational cost tremendously. Deciding on the size of spin image bins (resolution) and the

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111 size of spin image (local region of interest) is no t trivial, and it is important to have uniform mesh resolution over the entire model for spin image matching. These issues are much less problematic in the cluster-based spin images de scribed here. Furthermore, the required costly search over all n spin images of the object to find the point that corresponds to a given spin image on an object of n points is greatly reduced by the initial segmentation. 6.5.3 Number of Spin Images As we have seen in this study, there are cases where objects ha ve irregular shapes. In these cases, many spin images should be created from each class and stored in the model library because of non-fixed shapes of the objects. This results in high computational cost during numerous spin image comparisons to the library even though great redu ction is achieved by the initial segmentation. Instead of st oring all the spin images for each class, one global pdf could be computed since the spin images from the same class would be similar. This global pdf can be less sensitive to noisy sampling on diffuse and no n-regular object shapes. By considering each spin image as a 2D histogram, a non-parametric method such as Parzen window estimation can be used to compute individual 2D pdf. These 2D pdfs will be combined to create the global pdf for each class. Then, a simple way of comparing two spin images is measuring the KullbackLeibler (KL) divergence between their two pdfs.

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112 CHAPTER 7 CONCLUSIONS AND FUTURE WORK 7.1 Conclusions Small footprint LiDAR technology can provide spatially dense coverage over forest canopies and penetrates the canopy by illuminating the ground and understory through small gaps in the crown layer. These advantages, relative to other remote sensing modalities, such as passive optical and radar, allow the identificatio n of individual trees and the estimation of their heights and crown lengths from LiDAR data Determining the optimal window sizes to accurately find treetops has been the most im portant and difficult part in the process of delineating single trees to date. An adaptive re gion growing method was developed by using an agglomerative hierarchical clustering structur e to merge the partialtree clusters that are segmented by the region growing process. The entire process of the proposed approach was developed directly on the raw point cloud data to avoid loss of 3D information from inte rpolating the point data into height images. Working on point data with high point density re quires more computational time and/or memory than working with images, but this can be alle viated by dividing the ROI into smaller areas to suit the memory resources of a particular comput ational platform (i.e. the divide-and-conquer strategy). It was shown that the proposed algorithm performs ve ry well overall for two managed pine plantation forests of different ages and sp ecies. The lowest detect ion accuracy occurred for the IMPAC plots with low culture because the canopies in these plots are more interlocked and variable in sizes than in other plots. However, the performan ce was more than 10% better at IMPAC than that of the scale-space method. The estimates of tree heights and crown lengths were slightly underestimated, but agreed with ground truth to within several decimeters.

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113 Geometric mappings with field of view functio ns inside forests were developed to find optical gaps. The most probable walking trails in heavily vegetated areas were detected by computing optical lines of sight based on a set of visibility blockers and geometric constraints. I also found that it is possible to define relatively simple paramete rizations of light interception by forested canopies that allow for the prediction of IPAR from ALSM data. I employed optical scope functions that constraine d the field of view from the ground through the canopy towards the sun in order to estimate IPAR from a 3D point cloud of ALSM data. Several scope functions were investigated, and a simple cone functi on with a divergence angl e of and distance weighting was found to produce very good agreement with in situ IPAR measurements across species and treatment classes. Estimates of IPAR using ALSM data and a calib rated scope function are likely to be more statistically reliable across wide areas than in situ estimates of IPAR derived from a limited sample population. This is because estimates of IPAR obtained from ALSM data are spatially dense due to the fact that the scope function can be translated in small spatial increments. Because ALSM provides us with meter-scale 3D stru cture rather than simply vertical structure, we can easily compute the number of laser re turns, which corresponds to the number of occlusions, from a hypothetical observer in the fore st to any location in the sky. Furthermore, by knowing the site latitude and l ongitude and the suns position on arbitrary dates and times, one could predict clear-sky IPAR for a variety of times of the year or times of the day using a couple of seasonally representative ALSM data sets (e .g. ALSM acquired during periods of peak and minimum leaf areas). Such predictions through tim e could be useful inputs for ecological process models.

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114 7.2 Future Work 7.2.1 Extension to Different Forest Types In the proposed tree detection algorithm, th e stopping criterion on the agglomeration was determined by minimizing the Bayes error over the training data, resulting in a threshold Additional features could, in principle, be incorporated for the estimation of but that would likely make the results more sensitive to the sp ecific training data set. Strictly speaking, the optimal value of for a given location will depend on characteristics of the ROI, such as the tree species, crown density, spacing between trees, and age of the trees. However, the small standard deviation in values obtained from repeated randomized sampling in this study suggests that conditioning the a gglomeration on the standard devi ation of point elevations is robust and that modest amounts of tr aining data will suffice to estimate To achieve optimal results over sites other than thos e examined here (particularly if those sites contain tree species other than Loblolly and Slash pi ne), one should train the algor ithm using local ground truth data. It would be interesting to test the robustness of on natural forests and determine how much the detection rate is degraded. In the estimation of IPAR, a lthough testing over different fore st types was not possible due to a lack of additional ground truth data, I expect that the proposed a pproach may perform well over other forests with minimal empirical calibra tion since I used scope functions described by a minimal set of parameters. In the case of the conical scope, I found the strongest dependence to be on a single parameter, the divergence angle This implies that the adjustment of one parameter may be sufficient to achieve reason able agreement with ground-based measurement over differing forests. That performance would depend, however, on the nature of the understory. ALSM data obtains fewer returns from the understory than from the upper canopy. Thus, interception by the lower canopy and understory ma y be understated using the current approach.

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115 This limitation of the ALSM measurement c ould be mitigated however by limiting observer points to be higher than some specified elevation above the ground, or by estimating 3D volumes for the detected trees (for example, by assumi ng a uniform biomass distribution inside a 3D convex hull of ALSM points on a tr ee). It should also be noted that if one were to use high observer elevations, the distance from the observer to the LiDAR points may then take on greater importance than it did in this study. This hypothesis re quires further verification through future testing over other manage d and natural forests as the ALSM and ground truth data become available. 7.2.2 Line-of-Sight Visibility Two of the most critical f actors governing estimating of optical flux through the canopy are topography and landcover. InSA R has been used to map topography at spatial resolutions of a few meters to tens of meters. However, in st eep terrain, distortions in the topography caused by radar foreshortening lead to signi ficant errors in the resulting Digital Elevation Models (DEMs). ALSM, on the other hand, can provide very high resolution 3D positions of millions of laser pulses that intercept th e ground or landcover. By coupling 3D landcover density estimates with underlying topographic information, there are many applications that can be addressed, as extensions of the ideas of line-of-sight visibilities and optical scope functions in Chapters 3, such as: (1) optimal path planning thr ough forested terrain to minimize traversal times, (2) reducing the vulnerability of personnel that occurs when forward progress is slowed due to impediments (dense vegetation), (3) detecti ng or avoiding detection of pe rsonnel by thermal InfraRed (IR) sensors, and (4) improving satellite-ground RF communications (including GPS reception) in forested terrain by locating and avoiding areas of high canopy density.

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116 7.2.3 Multi-feature Spin Images Spin images have been successfully us ed in shape matching by deriving a viewindependent description of both database and query objects. Often, when range data are used to measure 3D structure, the targets are opaque to the laser. Thus, there is no penetration of the target by the laser and one obtains measurements of a true surface. In such cases, only surface information (surface shape) is accounted for in the spin image calculation. However, there are other instances where not only the surface shape is acquired but also some internal information due to penetration into the obj ect, such as medical imaging, ranging sensor over rough loose material (or, an object with discontinuous surfaces), radar imag ing of vegetated terrain, and LiDAR sensing over forests. These internal points can potentially provide more information, but these points could also cause problems in the cal culation and matching of standard spin images. Consequently, an extension of spin images, tentatively called multi-feature spin images, could be suggested to account for partial penetrat ion of diffuse targets. This new approach is targeted to some special applica tions, but this could be looked at as a more general way of using spin images. Multi-feature spin images create more features than using th e raw value of the point location in standard spin images or spin image in Brusco et al (2005) that characterize texture values such as R, G, B, and luminance. This leads to potentially many scalar-valued spin images (one for each feature) at each loca l part of the object. The features could consist of statistics that are extracted from the neighborhood of points inside a predefined region from the local origin, and appropriate features could be extracted depending on the applications. Since ALSM gives partial penetration over fore st with intensity and last stop points, multi-feature spin images should allow better discrimination between different structures than standard spin images. Also, it is expected that this new appr oach could give better recognition fo r clusters that are in between tree clusters and partial-tree clusters in sta ndard spin images as shown in Figure 6-4.

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117 Feature-based spin images suggested here w ould promise better performance, but this method implies potentially high computational cost as the number of selected features grows. Therefore, reducing the number of features is very important to speed up the process, but in many cases, the best features are not known in advance so that many possible features need to be examined to see which features tend to give best separation between classes via spin images. One way to address this problem is computing mutual information (MI) over training data to select only those features that are most predictive of class separabil ity. Optimal feature reduction for LiDAR data using MI was developed in (Luzum et al. 2005). That method could be extended for this work such that simple PCA is still used to control the computational complexity of comparing scalar-valued spin images to the model lib rary, and MI is used to select the subset of transformed spin image features that best predicts the class. 7.2.4 New ALSM Technology Modern ALSM systems, such as the Optech Gemini system, have made it possible to map large areas much more efficiently than before by employing laser puls e rates in excess of 150 kHz. This laser pulse rate is five times faster than the Optech 1233 system that is used in this study. In addition, the Gemini system records f our returns (instead of two returns with the 1233 system) and provides the choice of angle beam divergence (wide and narrow). Denser spatial coverage by this system can reduce the need for multiple flight lines and reduce the visible gaps in the point clouds between scan lines shown in Figure 4-19. Th e finer representations of tree canopies by this denser spatial a nd vertical resolution are expect ed to yield better accuracy in individual tree detection and tr ee parameter estimations. Moreove r, it is anticipated to better observe understory vegetation, which will help to estimate line-of-sight visibilities in natural forests.

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127 BIOGRAPHICAL SKETCH Heezin Lee was born in Kwang-Yang, South Ko rea. He received his B.S. degree in electrical engineering from Sung-Kyun-Kwan University, Sout h Korea in 1995 and his M.S. degree in electrical engineering and computer science from Syracuse University, Syracuse, New York in 1999. Since 2000, he has been worki ng toward his Ph.D. degr ee in electrical and computer engineering at the University of Flor ida. He began working under the supervision of Dr. K. Clint Slatton in 2003. His research inte rests broadly include remote sensing, pattern recognition, image processing, and digital signal processing.