Citation
Photogrammetry and Lidar from the Unmanned Aerial Platform for Measuring the Physical Structure of Forests

Material Information

Title:
Photogrammetry and Lidar from the Unmanned Aerial Platform for Measuring the Physical Structure of Forests
Creator:
Lassiter, Howard A
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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Language:
english
Physical Description:
1 online resource (138 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Forest Resources and Conservation
Committee Chair:
WILKINSON,BENJAMIN E
Committee Co-Chair:
BARNES,GRENVILLE
Committee Members:
ABD-ELRAHMAN,AMR H
VOGEL,JASON
IFJU,PETER G

Subjects

Subjects / Keywords:
lidar -- photogrammetry -- uas -- uav
Forest Resources and Conservation -- Dissertations, Academic -- UF
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Forest Resources and Conservation thesis, Ph.D.

Notes

Abstract:
Accompanying the emergence of unmanned aerial systems (UAS) mapping in research and industry has been the development of lightweight sensor formats that, until recently, could only be deployed on larger, manned aircraft. The release of lightweight laser scanners, specifically the Velodyne VLP-16, has brought UAS-borne laser scanning (lidar) to the forefront. The first study simulates and analyzes the VLP-16's peculiar scan pattern at various configurations of flying height, forward speed, and other mission parameters, to ultimately produce guidelines, equations, and software to aid in planning a successful aerial mapping mission with the VLP-16. Alongside lidar, UAS photogrammetry continues to flourish, particularly in forestry and forest ecology, as UAS platforms and data processing software become easier to use and more affordable. However, the use of UAS photogrammetry has outpaced the development of best practices for mission planning. In most cases, UAS photogrammetry missions resemble conventional aerial photogrammetry missions, despite the photographic and geometric differences between the two cases. Mission planning for UAS photogrammetry stands to benefit from being treated as a case of dynamic, close-range photogrammetry, as opposed to low-altitude aerial photogrammetry. The second study explores the photographic and geometric differences between conventional aerial and UAS photogrammetry, from which it derives best practices for UAS photogrammetry over forested scenes. In the final study, an application of UAS-derived point cloud data is presented. UAS mapping for via lidar and photogrammetry can provide dense, three-dimensional reconstructions of a forested scene; as the technologies and workflows have developed over the past decade, UAS-augmented forest cruises have begun to rival conventional timber cruises in both efficiency and accuracy. A host of algorithms is presented in the final chapter that automatically detect tree stems in point clouds created from UAS lidar and photogrammetric data, and estimate their locations, diameter at breast height (DBH), and heights. The algorithms' performances are assessed against field survey measurements, with the goal of demonstrating the advantages and shortcomings of estimating pine morphology from point clouds created from the low-altitude aerial pose. ( en )
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, 2018.
Local:
Adviser: WILKINSON,BENJAMIN E.
Local:
Co-adviser: BARNES,GRENVILLE.
Statement of Responsibility:
by Howard A Lassiter.

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UFRGP
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Applicable rights reserved.
Classification:
LD1780 2018 ( lcc )

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PHOTOGRAMMETRY AND LIDAR FROM THE UNMANNED AERIAL PLATFORM FOR MEASURING THE PHYSICAL STRUCTURE OF FORESTS By H. ANDREW LASSITER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULF ILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2018

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2018 H. Andrew Lassiter

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To Faraday

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4 ACKNOWLEDGMENTS My journey to this highest of academic achievement h as been anything but a solitary one. I am especially grateful for the support of my family, especially my grandmother, Wilma, my father, Jeff, and my brother, Adam. I do not take on this pursuit, much less make it to Gainesville, without their unwavering s upport. This journey may not be taken alone, but the feelings of isolation and uncertainty still find host in academic minds. The camaraderie and companionship of my friends, many of whom are fellow graduate students, helped me find my footing and stay ded icated to taking care, both of myself and in my work, in those times when I doubted myself. I cannot believe how fortunate I am to say the following: there are too many of you to name here. I am grateful to work alongside collegial and supportive fellow re searchers, especially John Roberts, Ruoyu Wang, Travis Whitley, Luiz Felipe Ramalho de Oliveira, and Ivn Raigosa Garca. Your candor and cooperation these past four years has made my time at the University fulfilling and enriching. I am a better scholar a nd colleague for working alongside you. This dissertation is 34 pages longer and at least 22% better because of you. We have done great work together, and I would be so lucky as to encounter colleagues of your caliber in my next chapter. I have heard so ma ny nightmare stories from my fellow graduate students about collecting data; these stories are so rampant that they are a sort of currency among researchers. I am happy to say that, in this sense, I am quite poor. Collecting data for my research has always been, dare I say it, easy. Thank you to Ordway Swisher Biological Station and Austin Cary Memorial Forest for providing access to so many trees. The UFUAS Research Program has provided me am amazing opportunity to learn so much about the UAS platform whil e working alongside supportive and knowledgeable people. Thank you to Matthew Burgess, Ray Carthy, Ben Wilkinson, Peter Ifju, Scot Smith, Travis

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5 Whitley, Chad Tripp, and Andrew Ortega Working with you all the past two years has been a pleasure. The suppor t I have received in all matters from the School of Forest Resources and Conservation is incomparable. In my years studying at the University, I have always had access to opportunities and assistance thanks to SFRC faculty and staff I have encountered an openness and willingness to help here that I hope to find again in my future endeavors. A special thanks to my committee members Grenville Barnes, Amr Abd Elrahman, Jason Vogel, and Peter Ifju Your commitment to my scholarship is evident in our interactio ns, from examining my research and brainstorming new avenues of inquiry to working alongside you in the field. I should have asked you all a thousand more questions during my time here; curse my habit of working in solitude. To my advisor, Ben Wilkinson, I owe a tremendous debt of gratitude. In the past few months I have rifled through data and prose spanning my time as a graduate student, and I could hardly recognize the previous version of my researching self. I have grown so much as a scholar under your too common ailment among those who take to this journey. Through all that I have learned and through all the opportunities you have presented to me, I can say today that I no longer feel this way. I am ready to take this next step in my career in research and education. Thank you for everything.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF FIGURES ................................ ................................ ................................ ....................... 10 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 13 ABSTRACT ................................ ................................ ................................ ................................ ... 15 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 17 UAS Lidar ................................ ................................ ................................ ............................... 17 UAS Lidar Payload Development ................................ ................................ ................... 18 El Sheimy Georeferencing Equation ................................ ................................ ............... 19 Cubic Spline Interpolation of Navigation Data ................................ ............................... 19 UAS Photogrammetry ................................ ................................ ................................ ............ 21 Forest Mensuration f rom Point Clouds ................................ ................................ ................... 22 2 MISSION PLANNING FOR LOW ALTITUDE AIRBORNE LASER SCANNING WITH THE VELODYNE VLP 16 ................................ ................................ ........................ 27 VLP 16 Configuration ................................ ................................ ................................ ............ 28 Analytical Characterization of VLP 16 Scan Pattern ................................ ............................. 29 Point Density Function ................................ ................................ ................................ .... 29 Optimal Separation of Flight Lines ................................ ................................ ................. 30 Gap Equation ................................ ................................ ................................ ................... 30 Simulation of the VLP 16 Scan Pattern ................................ ................................ .................. 31 Input and Output ................................ ................................ ................................ .............. 31 Spatial and Error Analysis of Simulated Data ................................ ................................ 32 Results and Discuss ion ................................ ................................ ................................ ........... 34 Single Strip ................................ ................................ ................................ ...................... 34 Overlapping Strips ................................ ................................ ................................ ........... 35 Rotation Rate and Gaps ................................ ................................ ................................ ... 36 Yaw ................................ ................................ ................................ ................................ .. 36 Spatial and Error Analysis ................................ ................................ ............................... 37 3 OBLIQUE UAS PHOTOGRAMMET RY IN FORESTED SCENES ................................ ... 53 Introduction ................................ ................................ ................................ ............................. 53 Automated 3D Reconstruction of the Forested Scene ................................ ..................... 53 Feature Matching in a Forested Scene ................................ ................................ ............. 54 Dynamic, Close range Photogrammetry ................................ ................................ ......... 55 Methods ................................ ................................ ................................ ................................ .. 57

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7 Study Areas ................................ ................................ ................................ ..................... 57 Mission Simulation ................................ ................................ ................................ .......... 58 Mission Planning ................................ ................................ ................................ ............. 60 Reconstruction Analysis ................................ ................................ ................................ .. 62 Results ................................ ................................ ................................ ................................ ..... 63 Mission Simulation and Planning ................................ ................................ .................... 63 Quantitative Checkpoint Analysis ................................ ................................ ................... 64 Qualitative CHM Analysis ................................ ................................ .............................. 64 Application: Individ ual Tree Detection (ITD) ................................ ................................ ........ 65 Methods ................................ ................................ ................................ ........................... 65 Results ................................ ................................ ................................ ............................. 66 4 A STEM BASED AP PROACH TO SEMI AUTOMATED ESTIMATION OF PINE MORPHOLOGY FROM LOW ALTITUDE 3D MAPPING ................................ ................ 79 Introduction ................................ ................................ ................................ ............................. 79 Aerial Photogrammetry in Fo restry ................................ ................................ ................. 79 Automated Forest Mensuration from Point Clouds ................................ ......................... 81 Canopy Based Versus Stem Based Individual Tree Detection ................................ ....... 83 Methods ................................ ................................ ................................ ................................ .. 83 Data Collection and Processing ................................ ................................ ....................... 83 Stem Detection Algorithm ................................ ................................ ............................... 86 Diameter at Breast Height Estimation Algorithm ................................ ........................... 87 Height Estimation Algorithm ................................ ................................ .......................... 89 Equivalence Testing ................................ ................................ ................................ ........ 89 Results ................................ ................................ ................................ ................................ ..... 90 Terrestrial Data, Preliminary Study ................................ ................................ ................. 90 Dense Matching, ACMF Site ................................ ................................ .......................... 91 Lidar, Flatwoods Site ................................ ................................ ................................ ....... 92 5 CONCLUSION ................................ ................................ ................................ ..................... 105 Recommendations for UAS 3D Remote Sensing ................................ ................................ 105 Forest Mensuration from UAS borne Point Clouds ................................ ............................. 106 Current State of the Art ................................ ................................ ................................ ......... 108 APPENDIX A VLP 16 CHARACTERIZATION EQUATIONS ................................ ................................ 110 Point Density Probability Density Function ................................ ................................ ......... 110 Optimal Separation of Parallel Flight Lines ................................ ................................ ......... 112 Possible Positions of Coverage Gaps ................................ ................................ ................... 113 Generalizing the Equations for Yaw ................................ ................................ ..................... 114 Point density probability function ................................ ................................ ................. 114 Optimal separation of flight lines ................................ ................................ .................. 115 Gap equation ................................ ................................ ................................ .................. 115

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8 B VLP 16 SIMULATION SOFTWARE ................................ ................................ ................. 117 Line Plane Intersection ................................ ................................ ................................ ......... 117 Assumptions ................................ ................................ ................................ ......................... 118 Optimization ................................ ................................ ................................ ......................... 118 Azimuth bounds ................................ ................................ ................................ ............. 119 Time Bounds ................................ ................................ ................................ ................. 1 19 C DERIVATION OF OBLIQUE UAS PHOTOGRAMMETRY EQUATIONS .................... 124 Air Bas e and Air Width ................................ ................................ ................................ ........ 124 Ground Sample Distance ................................ ................................ ................................ ...... 125 D SIMULATING IMAGES IN MATLAB ................................ ................................ .............. 127 E CONVERSION OF ROTATION DATA BETWEEN ENU AND NED FRAMES ............ 129 Rotation Matrix from Yaw Pitch Roll, Xsens Definition ................................ .................... 130 Rotation from Yaw Pitch Roll, Aviation Convention ................................ .......................... 131 LIST OF REFERENCES ................................ ................................ ................................ ............. 133 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 138

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9 LIST OF TABLES Table page 2 1 Gap equation results, rotation rate 5 Hz ................................ ................................ ............. 51 2 2 Gap equation results, rotation rate 10 Hz ................................ ................................ ........... 51 2 3 Gap equation results, rotation rate 20 Hz ................................ ................................ ........... 52 3 1 PhotoScan processing details ................................ ................................ ............................. 74 3 2 Processing specifications ................................ ................................ ................................ ... 74 3 3 Checkpoint error results ................................ ................................ ................................ ..... 74 3 4 Checkpoint analysis, F test resul ts ................................ ................................ .................... 75 3 5 t test results ................................ ................................ ....... 75 3 6 Summary statistics for the canopy height models ................................ .............................. 75 3 7 Individual tree detection results from lidar CHM ................................ .............................. 76 3 8 Individual tree detection results from nadir CHM ................................ ............................. 77 3 9 Individual tree detection results from oblique CHM ................................ ......................... 78 4 1 Stem detection summary ................................ ................................ ................................ .. 104 4 2 DBH estima tion summary ................................ ................................ ................................ 104 4 3 Height estimation summary ................................ ................................ ............................. 104

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10 LIST OF FIGURES Figure page 1 1 Mul timodal corner cube target ................................ ................................ ........................... 24 1 2 Flowchart of lidar data collection and processing ................................ ............................. 25 1 3 Incorrectly georeferenced lidar data du e to nave rotational interpolation ........................ 26 2 1 Optimal orientation of the VLP 16 scanner aboard a UAS ................................ ............... 39 2 2 Comparison of scan patter ns ................................ ................................ .............................. 39 2 3 Gaps in the VLP 16 scan pattern ................................ ................................ ....................... 40 2 4 Statistical analysis of the VLP 16 scan pattern ................................ ................................ .. 41 2 5 Point density function relationship to flying height ................................ ........................... 42 2 6 Point density function relationship to forward velocity ................................ ..................... 43 2 7 Plot of gap equation results ................................ ................................ ................................ 44 2 8 Plot of gap equation results with missing gap results ................................ ........................ 44 2 9 Plo t of overlapping flight lines ................................ ................................ .......................... 45 2 10 Effect of rotation rate on scan pattern and gap bands ................................ ........................ 46 2 11 Ground truth of a flight line with nonzero yaw ................................ ................................ 47 2 12 Effects of yaw on point density and gap locations ................................ ............................ 48 2 12 Average scan angle ................................ ................................ ................................ ............ 49 2 13 Mission planning for artificially limited maximum range ................................ ................. 50 3 1 Artifacts in dense matching point clouds ................................ ................................ ........... 67 3 2 Geometry of exposure stations ................................ ................................ ........................... 67 3 3 Jonesville Park study site with mission plans ................................ ................................ .... 68 3 4 University of Fl orida Agricultural Experimental Station with mission plans ................... 68 3 5 Oblique mission simulation ................................ ................................ ............................... 69 3 6 Simulated bundle adjustment re sults ................................ ................................ ................. 70

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11 3 7 Ground sample distance along format as a function of tilt ................................ ................ 70 3 8 Canopy height models, Millhopper study site ................................ ................................ ... 71 3 9 Differenced canopy height models, Millhopper study site ................................ ................ 72 3 10 Histograms of canopy height models ................................ ................................ ................. 72 3 11 Histograms of differenced canopy height models ................................ ............................. 73 3 12 Distortion in dense matching reconstruction of the scene ................................ ................. 73 4 1 Baseline study site at Ordway Swisher Biological Station near Gainesville, F L .............. 94 4 2 Locations and orientations of exposure stations for terrestrial dense matching ................ 95 4 3 Oblique view of ACMF dense matching point cloud ................................ ........................ 95 4 4 Longleaf Flatwoods Reserve study site ................................ ................................ ............. 96 4 5 GatorEye Unmanned Flying Laboratory (UFL) ................................ ................................ 96 4 6 Moving window search strategy ................................ ................................ ........................ 97 4 7 Circl e recognition by Hough transform ................................ ................................ ............. 97 4 8 Flowchart of the stem detection method ................................ ................................ ............ 98 4 9 RANSAC cylinder fitting ................................ ................................ ................................ .. 99 4 10 Steam detection results, TLS data, OSBS study site ................................ ......................... 99 4 11 Outlier ratio trials for RANSAC DBH cylinder fitting for DBH estimation ................... 100 4 12 Stem detection results, dense matching cloud, ACMF study plot ................................ ... 100 4 13 DBH estimation results, dense matching cloud, ACMF study plot ................................ 101 4 14 Height estimation results, dense matching cloud, ACMF study plot .............................. 101 4 15 Stem detection results, lidar cloud, Flatwoods s ite ................................ .......................... 102 4 16 DBH estimation results, lidar cloud, Flatwoods study plots ................................ ............ 103 4 17 Height estimation results, lidar cloud, Flatwoods study plots ................................ ......... 103 A 1 Nominal configuration of VLP 16 in relation to ground ................................ ................. 116 B 1 Solving for the representative profile ................................ ................................ .............. 123

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12 C 1 Air base ................................ ................................ ................................ ............................ 126 C 2 Ground sample distance in the direction of tilt ................................ ................................ 126

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13 LIST OF ABBREVIATIONS 2D Tw o dimensional 3D Three dimensional ACMF Austin Cary Memorial Forest AGL Above ground level ALS Airborne laser scanner/scanning AT Aerotriangulation BS/LA Boresight/leverarm CCW Counterclockwise CDF Cumulative distribution function CHM Canopy heigh t model COTS Commercial, off the shelf CW Clockwise DEM Digital elevation model DBH Diameter at breast height DSLR Digital single lens reflex ENU Easting Northing Up EOP Exterior orientation parameter FN False negative FP False positive FWS Fixed window size GCP Ground control point GNSS Global navigational satellite system GSD Ground sample distance GPS Global Positioning System

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14 IE Inertial Explorer IMU Inertial measurement unit INS Inertial navigation system ITD Individual tree detection lidar P ortmanteau LTP Local tangential plane MEMS Microelectromechanical systems NED Northing Easting Down OLS Ordinary least squares OSBS Ordway Swisher Biological Station PDF Probability density function RANSA C Random sample consensus RGB Red green blue RMSE Root mean square error RTK Real time kinematic sUAS Small unmanned aerial systems SWS Smoothing window size SfM Structure from motion TLS Terrestrial laser scanner/scanning TOST Two one sided t test TP True positive UAS Unmanned aerial systems UFUAS University of Florida Unmanned Airborne Systems (Research Program) VTOL Vertical takeoff and landing

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15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PHOTOGRAMMETRY AND LIDAR FROM THE UNMANNED AERIAL PLATFORM FOR MEASURING THE PHYSICAL STRUCTURE OF FORESTS By H. Andrew Lassiter August 2018 Chair: Benjamin E. Wilk inson Major: Forest Resources and Conservation Accompanying the emergence of unmanned aerial systems (UAS) mapping in research and industry has been the development of lightweight sensor formats that, until recently, could only be deployed on larger, mann ed aircraft. The release of lightweight laser scanners, specifically the Velodyne VLP 16, has brought UAS borne laser scanning (lidar) to the forefront. The first study simulates and analyzes th e VLP peculiar scan pattern at various configurations of flying height, forward speed, and other mission parameters, to ultimately produce guidelines, equations, a nd software to aid in planning a successful aerial mapping mission with the VLP 16. Alongside lidar, UAS photogrammetry continues to flourish, partic ularly in forestry and forest ecology, as UAS platforms and data processing software become easier to use and more affordable However, the use of UAS photogrammetry has outpaced the development of best practices for mission planning. In most cases, UAS ph otogrammetry missions resemble conventional aerial photogrammetry missions, despite the photographic and geometric differences between the two cases. Mission planning for UAS photogrammetry stands to benefit from being treated as a case of dynamic, close r ange photogrammetry as opposed to low altitude aerial photogrammetry Th e second study explores the photographic and geometric differences

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16 between conventional aerial and UAS photogrammetry, from which it derives best practices for UAS photogrammetry over forested scenes. In the final study, an application of UAS derived point cloud data is presented. UAS mapping via lidar and photogrammetry can provide dense, three dimensional reconstruction s of a forest ed scene ; a s the technologies and workflows have dev eloped over the past decade, UAS augmented forest cruises have begun to rival conventional timber cruises in both efficiency and accuracy. A host of algorithms is presented in the final chapter that automatically detect tree stems in point clouds created f rom UAS lidar and photogrammetric data, and estimate their locations, diameter at breast height (DBH), and heights T are assessed against field survey measurements with the goal of demonstrat ing the advantages and shortcomings of estimat ing pine morphology from point clouds created from the low altitude aerial pose

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17 CHAPTER 1 INTRODUCTION At the confluence of Moore's law and the rise of unmanned aerial systems (UAS) lies a unique opportunity for researchers and commercial use workflow, from data collection to processing and analysis. Such an endeavor, once undertaken only by those with access to costly aircraft, equipment, and software, has never been more accessible. This democratized a pproach to mapping opens new doors in forestry, silviculture, and ecology, advancing toward the semi automated study of the forest at the level of individual trees. What satellites and manned aircraft offer in area of coverage, UAS offer in resolution, all owing users to explore the forest at an ever finer spatial (and temporal) scale in the 3D point clouds derived from laser scanning and photogrammetry. Virtual forest mensuration from 3D mapping products, from manual measurements to automated model fitting and feature extraction, may soon mature from research to practice. UAS Lidar The first study altitude airborne laser scanning with the Velodyne VLP 16 laser scanner. This lightweight sensor, originally developed for self driving automobiles, has found success in UAS mapping. Velodyne's unique "fan" laser configuration is unlike any laser configuration before it, and so it follows that its scan pattern more precisely, t he pattern of laser pulses incident along some scanned surface is rather unique as well. The success of the VLP 16 has influenced newer scanners to mimic this configuration, and thus a number of popular sensors exhibit this peculiar pattern of "pointillate d affine hyperbolas ." This pattern can lead to long strips of poor coverage, thus warranting the study.

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18 One of the reasons for examining the VLP studies conducted by the University of Florida Unmanned Airborne Systems Research Program (hereafter referred to as UFUAS) required the use of relatively small targets to be placed in the study areas for the purposes of strip adjustment, boresight/leverarm verification, and absolute accuracy assessment. These custom ma de multimodal targets are corner cube pyramids measuring 1.1 m along the base, which is the diagonal of the three cube faces across which the cube is bisected (Figure 1 1). The planar faces of a pyramid can be used to align overlapping strips of lidar dat a, and the tip of the pyramid can be used as a ground control point (GCP) for absolute accuracy assessment. In practice, this process compared field survey data gathered via RTK GNSS with coordinates derived from the point cloud data. The top of the pyrami d in the point cloud was found by fitting three planes to the three detected planes of the pyramid; the intersection of the three planes was held as the GCP as detected in the point cloud. UAS Lidar Payload Development The lidar payload and data processing pipeline was developed by UFUAS. The payload consists of the following components: 1. Velodyne VLP 16 PUCK LITE laser scanner, a lightweight version of the VLP 16 PUCK (590 g vs. 830 g) with VLP 16 Interface Box 2. OEM components of the NovAtel SPAN IGM S1 GNSS /INS navigation system (STIM300 MEMS IMU OEM615 GNSS receiver, MEMS Interface Card) 3. ODROID single board computer with 1 TB flash storage for logging raw data from both the VLP 16 and the NovAtel SPAN IGM S1 4. NovAtel GPS 70 2 GG Pinwheel GPS antenna (dedicat ed to NovAtel SPAN IGM S1; used for positioning data) 5. Garmin GPS18x antenna (dedicated to the VLP 16 for timestamping lidar data)

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19 The data is then processed according to the flowchart presented in Figure 1 2. Aside from the processing of the navigation dat a by NovAtel Inertial Explorer (IE) software, all data processing is performed by custom software written by Dr. Ben Wilkinson in the Python language. El Sheimy Georeferencing Equation One function in the software suite is an implementation of el lidar georeferencing equation (el Sheimy, 2009) which considers the lidar sensor (S frame), an integrated GNSS/INS system (b frame), and the mapping datum (m frame): (1 1) The p osition vector represents the position of a point in the S Cartesian coordinate system. The v ector of interpolated coordinates of the GNSS/ INS in the m frame at time and the r otation of the b fram e into the m frame are both outputs of the processed navigational data The c onstant vector is the position of the sensor in the b frame, and the r otation between the S frame and the INS b frame Together, these are the boresight/leverarm ( BS/LA) calibration between the S frame (laser sensor center) and the center the b frame which is physically measured after the construction of the payload Cubic S pline I nterpolation of Navigation Data The six exterior orientation parameters provided by the GNSS/INS system at regular time intervals are position and angular orientation The lidar sensor and GNSS/INS system collect their data at different rates. The VLP 16 collects up to 600,000 returns per second (dual returns at 300,000 pulses per second), each re turn with a unique epoch The GNSS/INS collects positional data once per second and inertial data 125 times per second. After processing these data in IE, there exists navigational data at a rate of 125 Hz for epochs Direct georeferencing requ ires each point in the S frame to have unique navigational data, thus

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20 requiring an interpolation of the navigational data. By treating each of the six exterior orientation parameters (EOPs) in the navigational data as independent, a one dimensional cubic s pline interpolation can be applied to each parameter (as a function of the lidar epochs ) Rotational i nterpolation. Cubic spline interpolation of rotational data will fail if implemented directly onto the values of the rotational angles because the range of angles is multiply defined ; i.e., their ranges are or some translation thereof and any value outside of this range can be defined also as a value inside the range If the value of some rotational angle changes such that its value jumps from one extrema of the range to the other between epochs and all interpolated values between these two epochs will be nonsensical, resulting in failed georeferencing (Figure 1 3). Thus, rotational values must undergo rotational interpolation. Because the sine and cosine functions are continuous functi ons, they can be exploite d for smooth interpolation. Any angle can be expressed by its sine, and cosine, The series of sine and cosine values for multiple angles can then undergo interpolation. The interpolated values for angles at any interpolated epoch can then be found using full circle inverse tangent: (1 2) A properly implemented full circle inverse tangent function will output angles between Example. Apply a linear interpolation between the angles and using both nave interpolation and the rotational method l isted above to find the value of The correct answer can be found intuitively if at time the angle is o bserved, and at time the angle is observed, the best estimate for the value of at time is In this special case, the interpolated epoch is the midpoint between two

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21 epochs. T he nave linear interpolation for this simple case c an be solved by taking the mean of the two given values: which is obviously incorrect. Rotational interpolation, however, will yield the following: The lin ear interpolation between and by the nave method is 0.0087 and between and is 0. 9996 Thus : UAS Photogrammetry of conducting low altitude UAS photogrammetric missions as scaled down versions of their high altitude counterparts, where images are collected from a conventional aircraft. With the drastically decreased altitude comes new considerations of the geometric relationship between exposure stations the location and angular attitude of the camera when an image is taken and the scene being imaged. This study compares the convention d ownward looking, or nadir, imagery to ti lted, or oblique, imagery (Figure 1 4) a configuration that has been used with great success in urban settings. This study, along with the one presented before, have in common the aim of presenting best practices for planning UAS data collection missions with these two sensors, the miniature laser scanner and the commercial, off the shelf digital camera. The study utilizes both quantitative and qualitative comparisons of the data collected from the two aerial camera poses. For the quantitative study, both nadir and oblique datasets were georeferenced using the same control points, and an accuracy assessment was conducted using twenty checkpoints in the scene. The multimodal corner cube targets (Figure 1 1) served as

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22 the checkpoints. For the qualitative stud y, canopy height models (CHMs) were generated over a plot of planted pines from lidar, nadir imagery, and oblique imagery. Using the lidar CHM as control, the data from the two aerial poses are assessed. Forest Mensuration from Point Clouds The final chapt automated estimation of pine morphology from low altitude 3D virtual forest mensuration. The study presents a suite of algorithms that operate on the 3D point clo ud data derived from these sensors in an effort to demonstrate the capabilities (and limitations) of estimating key forest parameters at the single tree level of precision. geometric advantage of low altitude provides lower ground sample distances (GSDs) for images and a much higher point density of lidar data. However, the lightweight sensors required for UAS data collection collect lower quality data when compared to larger sensors used aboard conventional aircraft. In the balance betwe disadvantages lies the scope of their current abilities to deliver data capable of forest mensuration at the single tree level. The latest developments in UAS mapping have remarkable implications for the future of forest inventory and mensuration, but they by no means supplant established methods and technologies. The complexity of the form of trees, from the snarled sand live oak to the straight and simple slash pine, eludes full expression in even the finest reso lution point cloud. Th is complexity, however, has not deterred this researcher from pondering their form and struggling to understand and express them in prose, tables, graphs, images, and animations, a series of endeavors that has carried nascent ideas in to completed studies May the work presented herein be found to be worthy of the standard of doctoral research at the University of Florida, and that

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23 the algorithms and software developed, results obtained, and questions posed will benefit the communities and industries under the canopy of the School of Forest Resources & Conservation.

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24 Figure 1 1. Multimodal corner cube target. Photo courtesy of author.

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25 Figure 1 2. Flowchart of lidar data collection and processing. GPS time GPS antenna VLP 16 VLP 16 Interface B ox Scan data MEMS Interface Card GNSS receiver IMU GPS antenna GPS time and position Inertia Onboard computer parse to ASCII Flash storage ASCII lidar data ASCII nav data Parse ASCII data packets Polar to Cartesian conversion Add timing seq uence offsets Process nav data (IE) Cubic spline interpolation Cartesian lidar data, S frame Processed nav data, m frame Direct georeferencing Strip adjustment Final 3D point cloud = data = software = hardware

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26 Figure 1 3. Incorrectly geo referenced lidar data due to nave rotational interpolation The data are colored by the interpolated value of kappa. As the value of kappa switched between the two extrema of the domain, nave interpolation failed. Data collected from a mobile terrestrial test near Ben Hill Griffin Stadium, Gainesville, FL. Figure 1 4. Vertical (nadir) and oblique camera poses.

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27 CHAPTER 2 MISSION PLANNING FOR LOW ALTITUDE AIRBORNE LASER SCANNING WITH THE VELODYNE VLP 16 Airborne laser scanning (or lidar) from small, un manned aerial systems (sUAS) is gaining the reputation as a viable mapping tool for both academic researchers and commercial users within the past decade (Pilarska et al. 2016; Starek and Jung, 2015; Lin et al. 2011). Accompanying the release of the ligh tweight Velodyne VLP 16 in 2014 has been the emergence of highly accurate, lightweight navigational sensors (for example, the NovaTel SPAN IGM S1 GNSS/INS). These two core components form a payload that is functionally similar to the airborne lidar payload s aboard manned aircraft, but at a fraction of the weight and cost. Commercial outfits (such as YellowScan and Phoenix Aerial Systems) have offered turnkey sUAS lidar systems which utilize the VLP 16 since at least 2015 (Starek and Jung, 2015). Put another way: From an accessible platform the sUAS users can now collect an established, familiar data product the lidar point cloud that is compatible with existing data processing workflows. The adaptation of low altitude airborne lidar, specifically with the V LP 16, presents new issues. The configuration of the scanner head results in a scan pattern quite unlike a conventional line scanning airborne laser scanner. The VLP 16 emits lasers from sixteen channels oriented in resulting in a 30 vertical field of view. Th of lasers rotate s configuration of lasers is functionally similar to the VLP 64, which was d esigned for self driving automobiles (Glennie & Lichti, 2010). To ensure maximum coverage along a flight line when using the VLP 16 in the aerial pose, the most sensible way to allel with the direction of travel ( Figure 2 1). The resulting scan pattern is a series of hyperbolas visually distinct from

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28 the scan pattern of conventional line scanners ( Figure 2 2). However, the resulting scan pattern does not produce a uniform distri bution of laser returns (or points), and in some cases, can produce relatively large gaps in coverage (Figure 2 3). These gaps in coverage are not a function of point density, but rather point clustering, where many laser pulses are striking the target wit hin very close proximity to each other. This stands in contrast to point dispersion, where the laser pulses produce a more evenly spaced pattern across the target. This concept of point clustering, and what causes this phenomenon in the scan pattern, is in vestigated below. Proper mission planning is therefore vital to the success of airborne lidar data collection with the VLP 16. In addition to knowing the capabilities of the aircraft and the direct georeferencing payload, practitioners must also be aware o maximum range, angular resolution, and beam divergence, to name a few in order to plan a mission that will yield useable data for the task at hand. A new fold to consider in mission planning with the VLP 16 is its unique scan p attern. This study presents the development of VLP 16 simulation software that allows for the examination scan pattern of the VLP 16 both qualitatively i.e., manually examining simulated point clouds and quantitatively, via spatial statistics. Characteriza tion equations for the VLP lines, and possible gaps in coverage are also presented. VLP 16 Configuration The VLP 16 emits lasers from sixteen channels oriented between 15 and +15 in 2 intervals from the plane, or xy plane, resulting in a 30 vertical field of view. The vertical angle of each channel is fixed and is defined as the counterclockwise angle of the channel with respect to the scanner xy plane. The channels fully rotate vertical axis, or z axis for a 360 horizontal field of view The lasers are fired one at a time according to a precise timing sequence in which one laser is fired every 2.304 ; after all

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29 sixteen lasers have fired, there is a recharg e period of 18.43 (Velodyne, 2014) Therefore, each laser firing has a unique time, and because the scanner head is in constant rotation, each laser firing has a unique angle of rotation about the z axis, or azimuth Note that azimuth is defined as t he clockwise angle of rotation about the +z axis, where the +y axis is set to zero (Velodyne, 2014). Assuming the configuration described above, over flat terrain, the resulting scan lines from the VLP 16 are affine hyperbola s ; as the scanner travels forwa rd parallel to the terrain, these overlapping sets of skewed hyperbola s result in areas of varying point dispersion (Figure 2 3). L aser pulses are emitted at a constant angular interval (or, put more precisely, emitted at a constant time interval while rot ating at a constant angular velocity) along the Under the presented configuration with the VLP 16 turned on its side, point density along a nominally flat surface is a function of linear distance across the scanning prof ile (Figure 2 4) The point density, along with the point clustering, are the primary considerations for planning a UAS data collection mission with the VLP 16. Analytical Characterization of VLP 16 Scan Pattern Point D ensity F unction The point density of the laser return pattern of the VLP 16, as a function of lateral distance from the flight line can be closely approximated by the point density function (2 1) where is the height above ground, is th e pulse frequency of the scanner (approximately 300,000 pulses per second), and axis assuming the z axis is parallel to the target plane (see Appendix A) This equation is simplified under the assumpti on that the laser pulses are emitted at a uniform rate, although in practice, this is not the case. Each of the sixteen channels emits a pulse once per 2.304 followed by a recharge period

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30 of 18.43 This simplification, however, has a negligible ef fect on the results, as demonstrated Example. The plot of this example function is found in Figure 2 5 The maximum point density nadir to the scanner can be found at : Optimal S eparation of F light L ines T o assure a minimum density of laser returns along the profile of the laser return pattern of a mission with parallel flight lines, the maximum flight line separation can be expressed as (2 2) where the minimum desired return density is expressed as points/m 2 This equation is a further derivation of the point density function, as shown in Appendix A Inspection of the plot of should be used to inform a sensible choice for a value of Exam ple. Gap E quation The bands of gaps present in the laser return pattern occur at certain lateral distan ces from the flight line and can possibly occur at the distances found using the equation (2 3)

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31 where is the rotation rate of the scanner head (typically 5 20 Hz), is the angular sepa ration between adjacent channels (2 for the VLP 16); and is an integer, indicating the gap outward from the flight line at For smaller values of the term for which the arccosine is taken can be which yields a complex value of Example results from the gap equation for various flying height and forward speeds can be found in Tables 2 1 :3 Simulation of the VLP 16 Scan Pattern To test the VLP 16 scan pattern in a controlled environment, software was created in the MATLAB pro gramming language to simulate the laser return pattern of the scanner in the aerial pose. The scanner is modeled as a point at a user specified height above a horizontal plane, traveling a constant speed (also specified by the user) along a vector parallel to the plane. The emitted lasers are modeled as lines passing through the scanner point toward the target plane. the lasers, or azimuths, are determined by the each set of sixteen laser pulses emitted at epoch the simulation passes the line parameters to a solver, w hich finds the intersections of the lines with the target plane. The coordinates of those intersections a simulated point cloud are recorded and saved in a text file. Further explanation of the simulation software can be found in Appendix B Input and Outp ut The software takes as input key mission parameters with regards to the orientation and operation of the scanner: height above ground, forward speed, scanner head rotation rate, and axis and the direction of travel). The output is a point cloud that is a sample of the laser pulse return that could be expected from a mission flown over

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32 flat ground under these mission parameters The point cloud output is a comma delimited text file, where each row represents on e return, or point. For each point, the following attributes are attached: the mapping frame coordinates, ; the azimuth of the scanner head when the pulse was fired, ; the vertical angle, or channel, from which the laser was fired, ; the time at which the laser was fired, ; the range of the laser return (i.e., how far the laser traveled before i ntersecting the ground), ; and the direction in the mapping frame that the laser was fired, ( Definitions of azimuth and vertical angle can be found in the previous section.) Visual inspection of the simulated point clouds generated at various heights and speeds reveal a mesmerizing pattern ( Figure 2 3). Most notable about this pattern are the bands of point of a lowe r point density, but rather point clustering The scan pattern analysis and gap equation seek to detect and predict the location of these bands as a function of the mission parameters of flying height, flying speed, and the rotation rate of the scanner hea d (which can be adjusted anywhere from 5 Hz to 20 Hz). Predicting where these bands of high clustering occur as a function of mission parameters will lead to recommendations for optimal values for the parameters mentioned above, as well as side lap (i.e., the overlap of adjacent strips). Spatial and Error Analysis of Simulated Data The scan pattern, for all of its peculiarities, is in fact a repeating pattern. This allows for the extraction of a narrow across track profile which can be used for statistical analysis. The apparent clustering and dispersion of the points along the profile is analyzed by binning the profile of the simulated point cloud and calculating the nearest neighbor index for each bin. The nearest neighbor index is a measure applied to po int patterns that indicates whether the pattern is

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33 clustered, random, or dispersed. First, for each simulated return (point) in the bin its nearest neighbor and the distance between the two ( ) is found. This is accomplished by calculating a distance matrix (of dimensions ) for points in the bin, and for each column in the matrix, the lowest off diagonal value is retained. The mean of those nearest neighbor distances is the observed nearest neighbor distance, or : (2 4) Next, the expected nearest neighbor distance is calculated, which is a function of the area of the bin: (2 5) Next, the z score for each bin is found: (2 6) where The z score provides a normalized measure of the point dispersion or cl ustering in the bin. For example, a z score of (with its corresponding p value of ), indicates with 95% or greater likelihood that the point pattern is clustered, while a z score of ( ) indicates a 95% or greater likelihood that the pattern is dispersed, i.e. approaching interpretation of the z score presented is reflective of the source material, but is not appropriate for analyzing data of this n ature; see Discussion.) The analysis of the scan pattern extends beyond its geometric pattern. The point cloud simulation software records other attributes of each simulated return, such as the position of the scanner, range from scanner, time, and directi on of the simulated laser pulse. These attributes can

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34 provide a simulation of not only of point density and dispersion, but also the expected absolute accuracy of the points. The information that can be gleaned from these attributes e.g., range and inciden ce angle are key components of the lidar error budget (Baltsavias, 1999). Error ensor data) is essential to understanding the reliability of the resulting point cloud. For this study, the simulated returns within each bin are analyzed according to attributes unique to each return. Within each bin, histograms can be generated to show t he distribution of the number of returns as a function of average range and average incidence angle for each bin. These two measures are directly a laser pu that pulse must travel to reach the target. An analog to the accuracy of the points within a given scanned area can be visualized by finding the distribution of rang es and scan angles across the scan profile Results and Discussion Single Strip As shown in the point density function equation, the point density of the scan pattern is inversely proportional both to the flying height and forward velocity of the scanner. These relationships are shown in Figure 2 5 and 2 6 respectively. The simulations are in agreeance with the point density equation and, in most cases, the gap equation. There are, however, t hree limitations of the gap equation made evident through simulat ion: 1. Any gaps present at or near nadir to the flight line (i.e., gaps at some low value of ) are not always reported by the gap equation. 2. The severity of the gaps at some lateral distance is not reflected in the results of the gap equation. The equation only reports the possibility of gaps occurring at some lateral distance.

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35 3. At hig her forward velocities, some significant bands of gaps may not be reported by the gap equation. An example of these limitations is shown in Figure s 2 7 and 2 8 In conjunction with the gap equation results, inspe cting the point density histo gram s for each bin s z score (Equation 2 6) reve als flaws in interpreting the z score as a means of detecting gaps. This is d iscussed more in the Spatial and Error Analysis section below. As observed through simulation, in the areas of the greatest degree of point clustering, the gaps in the scan pattern tend to present as either near rhombuses, narrow and elongated perpendicular to the direction of flight. As the lateral distance from the flight line increases, the gaps will sometimes present as somewhat linear clusters of points, which have a less deleterious effect on the coverage of the area. Gaps near nadir to the flight line are elongated to the point of presenting similarly to a widely spa ced linear scan pattern, especially as the flying height increases (and the eccentricity of the hyperbolas decrease). Overlapping Strips With the exception of one way mission plans along some corridor, such as a utility easement or transportation corridor, most lidar data collection missions using UAS will likely feature parallel, overlapping strips of data. These overlapping strips not only provide common targets in each strip which can be used for strip adjustment and accuracy assessment, but also can be used to the V LP 16 scan pattern. Using the optimal flight line separation equation, it is possible to plan a mission in which a desired minimum point density is achieved across the mission area most efficiently. Figure 2 9 sho ws the resulting point density and point dispersion of a mission flown at 45 m flying height 9 m/s forward velocity with parallel flight lines spaced at 50, 68, and 88 m. These flight line spacings are the result of the flight line separation equation fo r values of 180, 150, and 120 points/m 2 respectively.

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36 Rotation Rate and Gaps The results in Tables 2 1:3 are initially misleading As the rotation rate increases, the number of predicted possible locations of gaps increases proportionally. In fact as the rotation rate doubles, so too does the number of predicted gaps. The predicted gap locations are somewhat linear, occurring every meters along the profile at some rotation rate ; at rotation rate the distance between gaps becomes roughly But the severity of those gaps is not reflected in the equation. In fact, as the rotation rate increases, the severity of the gaps decreases notably, and shown in Figure 2 10. This study does not comment on the potential benefits of lowering the rot ation rate of the scanner head, but the results do show that a lower rotation rate, especially when coupled with a higher forward velocity, can have detrimental effects on the quality of the resulting coverage. Yaw Adding yaw, or crabbing, the scanner with respect to the direction of flight leads to the coverage gaps becoming narrower along track and elongated across track, with respect to the gaps that would occur under similar conditions without crabbing. This is shown in Figure 2 11. The primary deleteri ous effect of the coverage gaps increasing the odds of missing small areas of interest, e.g. linear features such as sidewalks or power lines, or small areas of interest such as targets is negated with the addition of only a small amount of yaw. This has a minimal effect on the width of a single strip, as its width is a function of the cosine of the yaw angle. For example, even a yaw angle of 30 would only yield a reduction in the width of that strip. The analytical equations presented above can be further generalized to include yaw angle, as demonstrated in the derivations in the final section of Appendix A. Thus, intentionally

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37 crabbing the scanner can be worked into the mission planning. The point density function (Equation 2 1) generalizes to (2 7) The flight line separation equation (Equation 2 2) generalizes to (2 8) The gap equation (Equation 2 3) generalizes to (2 9) The effect of adding yaw to the scanner, and the results of the generalized analytical characterization equations are shown in Figure 2 12. Spatial and Error A nalysis The question remains of which (if any) z score threshold is indicative of point clustering resulting in undesirable gaps in coverage. The z score interpretation presented above is based on the distribution of expected nearest neighbor distances in a theoretically random distribution; the z score then indicates the probability that a distribution of points in a given area is clustered, random, or dispersed. The points in the VLP The p values associate d with nearest neighbor z scores are not useful information; thus, the probabilistic interpretation of the z score is not necessarily applicable. In fact, the z scores appear to be fully relative, only useful for comparison within a given flight configurat ion. Inspection of Figure 2 10 shows that both the 20 Hz and 5 Hz flight have comparable peak minimum z scores of 18 and 21, respectively. This belies the severity of the gap problem in the 5 Hz flight (or, conversely, overstates the gap issue in the 20 Hz flight, which is all but negligible).

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38 One final consideration for mission planning is optimizing the scan angles. Figure 2 1 3 shows the average absolute values of scan angles of each return within 1 m bins across the profile. Wider spacing of flight lin es may lead to fewer flight lines needed to cover an area, but as the scan angle (and range) of the returns increases, so too will their error. Another thought is to simply exclude returns beyond a certain range for the sake of a higher accuracy across the resultant point cloud. Figure 2 1 4 shows an example scan profile where the maximum range has been limited to 60 m. The profile width decreases drastically, but depending on the desired accuracy of the data, this may be advantageous. Note that the optimal flight line separation equation cannot be used if the maximum range is limited in this manner.

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39 Figure 2 1. Optimal orientation of the VLP 16 scanner aboard a UAS. This figure is a modified version of one found in the VLP 16 User Manual (Velodyne, 201 4). Figure 2 2. Comparison of scan patterns. The linear scan pattern of a conventional ALS line scanner (top) is apparent over nearly flat terrain. The scan pattern of a single pass of the VLP of 30 m (below) reveals a much different pattern. Each laser traces a path of a hyperbola across the plane, and the forward motion of the scanner adds a slight affine distortion to each hyperbola. Direction of flight shown in red.

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40 Figure 2 3. Gaps in the VLP 16 scan pattern. A simulated point cloud of the VLP 16 flying 30 m above a target plane at a speed of 10 m/s. The detail shows an example of the gaps in the point coverage that result from the unique scan pattern. The above diamond shaped gaps are roughly 1 m 2 m each. The points are colored by time of (simulated) return (blue > green > yellow > red).

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41 Figure 2 4. Statistical analysis of the VLP 16 scan pattern. Because the VLP 16 scan pattern is repeating, a representative cross track profil e of the scan pattern can be extracted to use for spatial statistical analysis. The black stripe above depicts a 5 m wide profile in the direction of flight. The histogram depicts the location and width of the bins. Each bin is colored by its clustering z score

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42 Figure 2 5. Point density function relationship to flying height. From top to bottom, point density function (black line) and simulation results (histogram) for flying heights of 30 m, 45 m, and 60 m. Forward velocity held at 9 m/s

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43 Figure 2 6. Point density function relationship to forward velocity. From top to bottom, point density function (black line) and simulation results (histogram) for forward speeds of 4, 9, and 15 m/s. Flying height is held at 45 m. The y axis is truncated for th e 4 m/s flight for sake of comparison to the other profiles.

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44 Figure 2 7. Plot of gap equation results. Flying height 45 m, forward velocity 4 m/s. TOP: Gap locations reported by the equation are marked with blue asterisks. BOTTOM: Return pattern of the same flight, exaggerated in the y direction to show detail. Figure 2 8 Plot of gap equation results with missing gap results Flying height 60 m, forward velocity 15 m/s.

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45 Figure 2 9. Plot of overlapping flight lines. Flying height 45 m 9 m/s forward velocity with parallel flight lines spaced at (top to bottom) 50, 68, and 88 m. These flight line spacings are the result of the flight line separation equation for values of 180, 150, and 120 points/m 2 respectively. Point density function of a single strip shown (black line).

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46 Figure 2 10. Effect of rotation rate on scan pattern and gap bands. Though the number of predicted gaps decreases as the rotation rate of the scanner head decreases, the severity of the gaps becomes notably greater. TOP: Flying height 45 m, forward velocity 9 m/s, rotation rate 20 Hz. BOTTOM: Rotation rate 5 Hz.

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47 Figure 2 11 Ground truth of a flight line with nonzero yaw. This figure depicts the results of a test flight (middle) that was flown with approximately 10 of yaw, versus the simulated point cloud (bottom) of that same mission. Both the histogram (top) and simulation verify the point density, and the dark bars in the histogr am correctly indicate the presence of point clustering.

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48 Figure 2 12. Effects of yaw on point density and gap locations. The results of the original PDF and gap equation are plotted in black and blue, respectively. The results from the generalize d PDF and gap equations are plotted in red.

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49 Figure 2 12. Average scan angle. Flying height 45 m 9 m/s forward velocity with parallel flight lines spaced at (top to bottom) 50, 68, and 88 m.

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50 Figure 2 13. Mission planning for artificially lim ited maximum range. The most noted effect of limiting the maximum range is the drastically decreased profile width. TOP: single flight lines, flying height 45 m, forward speed 9 m/s, max range 60 m. MIDDLE: Overlapping flight lines, 30 m spacing, colored b y nearest neighbor z score. BOTTOM: Overlapping flight lines colored by average scan angle

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51 Table 2 1. Gap equation results, rotation rate 5 Hz. Lateral distance [m] at integer i h [m] v z [m/s] 1 2 3 4 5 30 4 cplx 34.6 61.8 86.6 30 9 41.9 98.6 30 15 80.5 45 4 cplx 8.6 51.9 79.8 45 9 25.1 92.8 45 15 73.2 60 4 cplx cplx 33.5 69.3 97.6 60 9 cplx 83.8 60 15 61.5 Note: Gap values greater than 100 m have been excluded from these results. Complex results are Table 2 2. Gap equation results, rotation rate 10 Hz. Lateral distance [m] at integer i h v z 1 2 3 4 5 6 7 8 9 10 30 4 cplx cplx 1 6.8 34.6 48.8 61.8 74.4 86.6 98.6 30 9 cplx 41.9 71.3 98.6 30 15 30.7 80.5 45 4 cplx cplx cplx 8.6 35.4 51.9 66.4 79.8 92.8 45 9 cplx 25.1 62.9 92.8 45 15 cplx 73.2 60 4 cplx cplx cplx cplx cplx 33.5 53.2 69.3 83.8 97.6 60 9 cplx cplx 48.8 83.8 60 15 cplx 61.5

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52 Table 2 3. Gap equation results, rotation rate 20 Hz. Lateral distance [m] at integer i h v z 1 2 3 4 5 6 7 8 9 10 30 4 cplx cplx cplx cplx cplx 16.8 26.6 34.6 41.9 48.8 30 9 cplx cplx 24.4 41.9 57.0 71.3 85.1 98.6 30 15 cplx 30.7 57.0 80.5 45 4 cplx cplx cplx cplx cplx C plx cplx 8.6 25.1 35.4 45 9 cpl x cplx cplx 25.1 46.1 62.9 78.2 92.8 45 15 cplx cplx 46.1 73.2 97.5 60 4 cplx cplx cplx cplx cplx C plx cplx cplx cplx cplx 60 9 cplx cplx cplx cplx 23.5 48.8 67.4 83.8 99.3 60 15 cplx cplx 61.5 89.1 Table 2 3. Continued. Lateral distance [m] at integer i h v z 11 12 13 14 15 16 17 18 19 20 30 4 55.4 61.8 68.1 74.4 80.5 86.6 92.6 98.6 30 9 30 15 45 4 44.1 51.9 59.3 66.4 73.2 79.8 86.3 92.8 99.1 45 9 45 15 60 4 19.2 33.5 44.1 53.2 61.5 69.3 76.7 83.8 90.8 97.6 60 9 60 15

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53 CHAPTER 3 OBLIQUE UAS PHOTOGRAMMETRY IN FORESTED SCENES Introduction Photointerpretation and photogrammetry have been used for forest inventory dating back to at least 1929, when aerial timber cruises were conducted in Canada (Spurr, 1948). Stereo photography for forestry applications has been in use since at least 1958 (Avery, 1958). In fact, at least as early as 1967 photogrammetric me thods of forest sampling utilizing cameras mounted to a helicopter had been shown to produce results that were not statistically different from conventional ground based methods. Tree species, tree height, and crown width were determined from the photos, p arameters which were then used to develop equations for single tree volume and diameter at breast height, or DBH (Lyons, 1967). In the 1990s the advent of digital photogrammetry led to further applications in forest inventory, e.g. determining canopy heigh t (Gagnon et al., 1993). Even as the process for gathering 3D data from stereo photography shifted to the digital realm, the spatial resolution of that data was still limited. The collection of data points, i.e. the 3D locations of physical features, was p erformed manually by an operator. This manual process prohibited the dense 3D reconstruction of the forest. The operator, limited by time, could only select a handful of points of interest to estimate forest metrics. Automated 3D Reconstruction of the Fore sted Scene A powerful tool in digital photogrammetry today is structure from motion (SfM), method of generating accurate, high resolution topographic datasets from nonmetric photographs (Westoby et al. 2012). Though similar in many ways to conventional pho togrammetry, SfM offers a lower capital cost and more automated processing than conventional photogrammetric workflows. SfM, using low cost, commercial, off the shelf (COTS) cameras, can be used to

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54 produce a high resolution 3D reconstruction (often referre d to as a point cloud) of the photographed area. The ability to use common digital photos to obtain the 3D structure of objects has led to increased interest in 3D mapping in many fields, particularly forestry and forest ecology. Digital cameras are lightw eight, inexpensive, and simple to deploy, and the SfM methods used to process the photos have been shown to be comparable to light detection and ranging (lidar) in producing topographic datasets (Westoby et al., 2012; Fonstad et al., 2013). Photogrammetry from an unmanned aerial system (UAS) platform allows for not only a high spatial resolution, but also a high temporal resolution. UAS are much easier to deploy than a conventional aircraft, which allows for more frequent data collection. This high temporal resolution can be greatly beneficial for applications such as stress monitoring or plant phenotyping for forest tree breeding (Dhondt et al., 2013). Feature Matching in a Forested Scene Previous studies have demonstrated the successes of SfM reconstructi on of open, non vegetated areas of various terrains, as cited above. In a mission with a low base to height ratio i.e., the average distance between exposure stations is small when compared to the range of the target from the cameras a particular feature m ay be visible in five or more photos. Solving for the 3D location of the feature becomes more robust, assuming the errors in the location of said feature in each photo are random. By contrast, the heterogeneous structure of forests, with its sharp gradient s in height, varying textures, and irregular shapes, presents a challenge to the SfM workflow, particularly the feature matching process. A particular feature may appear in the lead to a large

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55 altitude nadir photography ( Figure 3 1). (Too few feature matches in certain areas is also the likely cause for false negatives, or missing information in the 3D point cloud where photo coverage exists.) Some error in the stereo parallax the change in apparent position of a feature from one stereo ima ge to the next will lead to a miscalculation of its range from the cameras. Further evidence to support this supposition is the orientation of clusters of false positive points. Usually they are longer than they are wide in the direction of the optical axe s of the cameras; as implied in Figure 3 2, these inaccuracies would likely take on such a shape. Further inaccuracies in the reconstruction of the scene may be caused by this poor geometry between exposure stations, but may not be easily spotted by inspec ting the point cloud. Dynamic, Close range Photogrammetry The geometry of the photos used to reconstruct a scene plays a central role in the accuracy of the scene. Current methods resemble a scaled down version of a conventional aerial photogrammetry miss ion flown from high altitude (typically >1000 m) with a manned aircraft. Such a conventional mission uses nadir looking photography. The crucial difference between a conventional mission and a UAS mission is the ratio of target height to flying height. A c onventional mission flown from 1000 m over an area where the average height of the targets (buildings, for example) is 20 m has a target to flying height ratio of 1:50, while a UAS mission flown at 75 m over a forested scene with an average of 15 m tall tr ees has a target to flying height ratio of 1:5. In other words, the targets are much closer to the camera; small changes in camera position during photography can lead to a greater change in apparent position of a feature from one photo to the next. Two ke y elements of photogrammetry are at play in this scenario: the high apparent change in position (or parallax) between the features may lead to decreased error in the computed positions of the feature, but the increased relief displacement between two key

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56 f eatures say, the top and bottom of a tree stem adds an element of distortion to each photo (Wolf et al. 2014). In cases presenting a high target to flying height ratio, a UAS photogrammetry mission should not be treated as low altitude aerial photogrammetr y, but rather as dynamic, close range photogrammetry. The most stated difference between conventional aerial and close range photogrammetry is the geometry of the cameras (herein referred to as exposure stations). The converging optical axes of the exposu re stations provides a stronger geometry for both the bundle adjustment and 3D reconstruction of the scene. The demand for aerial oblique imagery in commercial applications appears to be growing as well, as indicated by recent patents filed by Google (Reec e 2014) and Pictometry International (Schultz et al., 2010; Schultz et al., 2011) pertaining to the imagery, collected from manned aircraft at higher altitudes, have been quite impressive, as evidenced by the dense and accurate 3D reconstruction of buildings and vegetation (in some cases, individual trees!) in the urban areas where oblique images have been collected. A number of studies using low altitude and/or UAS o blique imagery has been noticed in the literature, mostly focused on reconstruction of structures or for monitoring geological (Aicardi et al., 2016, study of the sort explored the reconstruction and mensuration of a forested scene using low altitude oblique images collected via UAS, demonstrating moderate success in reconstructing and mensurating the tree stems (Fritz et al., 2013). This study explores the process of p lanning UAS photogrammetric missions in forested scenes to more closely align with the principles of close range photogrammetry with the goal of achieving a more accurate 3D reconstruction of the forested scene, particularly the forest canopy

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57 First, a qua ntitative analysis is presented comparing nadir and oblique imagery over a relatively flat and open (unforested) scene in which the errors of 20 checkpoints are assessed This analysis serves as a baseline for expected reconstruction differences between na dir and oblique imagery and comparing the reprojection. Next, a qualitative analysis is conducted using the canopy a set of three canopy height models (CHMs) of a planted pine stand generated from nadir imagery, oblique imagery, and lidar, all from the UAS platform. An application analysis is also presented in which canopy based individual tree detection (ITD) is conducted on the three CHMs and the results are compared with the a complete timber cruise, with the goal of assessing the utility of the CHMs for a forestry application. T ogether, these analyses are designed to test the notion that oblique imagery will lead to a more accurate 3D reconstruction of a heterogeneous, forested scene than will nadir imagery. Methods Study Area s Quantitative study Jonesv ille RGB images from both the nadir and oblique poses were collected 15 June 2018 at Jonesville Park north of Gainesville, Florida (Figure 3 3 ). The site is an open grass field, roughly 100 by 70 m. The images were collected from the DJI S1 000 vertical takeoff & landing (VTOL) UAS, equipped with a gimbal mount that allows for orienting th e payload at a predefined tilt angle of 30 (The process by which this angle was chosen is detailed below.) The camera used is a Canon EOS Rebel SL1, a com mercial, off the shelf (COTS) DSLR camera, with a 24 mm lens. Airborne control (position and attitude) was acquired via the Xsens Mti G 700 GNSS/INS. Five ground control points ( GCPs ) and 20 checkpoints were placed in the scene and their coordinates were measured via RTK GNSS. The data collected at this study site w ere used to perform a quantitative analysis on the reported error

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58 of the checkpoints, to determine if either camera configuration results in a significantly more accurate reconstruction of the s cene. Qualitative and application stud ies Millhopper RGB images were collected from both the nadir and oblique poses on 14 March 2018 at the University of Florida Agricultural Experimental Station in the Millhopper neighborhood just north of Gainesville Florida (Figure 3 4 ) The specific study site is a 160 by 160 meter plot of pines planted in 2010. The UAS platform and payload were the same as described above. Five GCPs were also placed in the scene, and their coor dinates were measured via RTK GNSS. UAS lidar data was also collected over this site on the same day from a second DJI S1000 equipped with the lidar payload described in Chapter 1 These three data sets were used to generate three canopy height models (CHMs ) which are compared amongst each other, holding the lidar CHM as control Specific information on the PhotoScan processing of the three flights can be found in Table s 3 1 and 3 2 Mission Simulation Battery life is a concern with VTOL UAS missions, especi ally with the generally narrower flight line spacing required for taking images with a DSLR camera. To maximize the efficiency of image data collection, mission planning equations and simulation software were developed for this study. These tools were used to calculate stereo overlapping coverage of photos in the direction of flight (end lap) and in adjacent flight lines (side lap ) as well as ground sample distance (GSD) conduct trials for optimal flying heights, and det ermine at which angle from nadir the camera should be tilted to achieve the hypothesized result of more accurate 3D reconstruction of the scene. This mission simulation also served to verify results The mission simulation software was written in the MATLAB programmin g language. The overall goal was to simulate images taken of a scene at various angles of tilt and to use

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59 those simulated images to perform a bundle adjustment at various angles of tilt. The bundle adjustment provides statistics on the precision and accur acy of the adjustment, allowing for comparison among the bundle adjustments. End lap and side lap. The MATLAB simulation software accepts as input the following mission parameters: (1) end lap, (2) side lap, (3) flying height, and ( 4) tilt. The standard methods for calculating the distance between exposure stations (i.e. air base, a function of end lap) and the distance between adjacent flight lines (i.e. air width, a function of side lap) assumes vertical (nadir) photography; theref ore, new equations needed to be derived for calculating these parameters. The air base for oblique images can be found by (3 1) where is the flying height, is the angle of tilt, is the field of vi ew of the camera in the direction of flight, and is the desired end lap expressed as a percentage The air width can be expressed as (3 2) where d is the desired side lap expressed as a percentage The derivations for Equations 3 1 and 3 2 can be found in Appendix C Camera simulation. The simulation software also requires two variables about the camera to be defined : fo cal length and format size. The parameters for the simulation of the camera are those of the Canon EOS Rebel SL1, which is the camera used for data collection. The software simulates the collection of three parallel strips of four images each, given the fo ur mission parameters listed above. These simulated images are, to be more precise, arrays of 2D

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60 points which are themselves back projections of a array of 3D points onto planes at the positions and angular orientations specified by the mission param eters ( Figure 3 5 ). For this simulation, the camera was assumed to be an ideal pinhole camera; no elements of lens distortion were added. Random noise of 0.5 pixel is added to each back projection in both the x and y axes in image space to simulate the ra ndom error in the detected location of some feature in an image Adding this noise turns out to be a crucial step in simulating a bundle adjustment, however; without the addition of this random noise, the residuals of the bundle adjustment would be zero, l eading to an error variance of zero. Further explanation of how the images are simulated can be found in Appendix D. Mission Planning For both study site s t wo missions were flown over the scene mission collecting nadir photos, and (2 ) a mission collecting oblique photos, with the camera inclined at some tilt angle from nadir. The tilt angle of 30 was determined after considering both the simulated accuracy assessments and the changes in the length of flight lines caused by covering a study area with an oblique, as opposed to nadir, camera. (Further discussion of these considerations can be found in the Results section below.) Both nadir and oblique missions were controlled with respect to percent end lap, percent side lap, and average range to target. The shutter of the camera aboard the UAS is fired on a timer at a regular interval so to control for end lap, the forward speed of the camera was manipulated Knowing the necessary air base for the required end lap as described above, the forward speed is determined by Controlling for side lap was d one by adjusting the flig ht pattern such that adjacent flight lines are the appropriate distance apart. Average

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61 range to target can be defined approximately as the distance between the camera and the target surface, and is a function of the flying height and tilt of the camera t : Another consideration with oblique photos is the ground sample distance (GSD) of each pixel of a photo and how it relates both to the desired resolution of the photos rarely an issue at low altitudes and the shutter speed of the camera. With a camera in motion, best practice is to ensure that the camera travels no farther than the length of 1 GSD while the shutter is open. Thus, the maximum forward speed of the camera is limi ted by (1) GSD in the direction of flight a function of flying height and pixel size and (2) shutter speed. With vertical photography, the GSD is constant, and can be found by multiplying the photo scale by the pixel size. The GSD is variable in oblique ph otography, growing larger in the direction of tilt. The GSD in the direction of flight that corresponds to a column of pixels of the photo is expressed by (3 3) where is the angle formed between the optical axis of the camera and the ray from the perspective center of the camera to the pixel in column with being the number of columns of pixels in the format. The derivation of Equation 3 3 can be found in Appendix C. Both nadir and oblique (Figure s 3 3, 4 ) For t he oblique photo mission, this flight pattern lends converging photos (or, more precisely, the converging of the optical axes of the camera exposure stations) co nverging, parallel optical axes To ensure full coverage of the study site, however, the flight lines for the oblique mission must be lengthened. This extra length is a function of the tangent of the til t angle, or

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62 Also, for both study site s the missions utilize the same GNSS/INS payload for airborne control and the same ground control points. Reconstruction Analysis For the qualitative analysis of the Millhopper data, two CHMs were created, one fr om each camera configuration. Agisoft PhotoScan was used to create the point cloud from which the CHMs were created. The workflow in PhotoScan to create the 3D reconstruction of the scene s i.e., dense matching point clou ds is based on the process presented by the USGS National UAS Project Office (2017) : 1. Align photos (high accuracy, 4,000 key point limit, no tie point limit) 2. Optimize camera s (focal length principal point offsets radial distortion coefficients and decentering distortion coefficients ) 3. Selectively remove tie points with greatest reconstruction uncertainty, optimizing the cameras after eac h set of points is removed 4. Dense point cloud reconstruction (medium quality depth filtering disabled ) 5. itself as false negatives below the ground 6. Export dense cloud without low noise After the point clouds are created, the CHMs were made using LAStools (Isenburg, 2012) using the process presented by Khosravipour et al. (2014) : 1. Normalize the height of the point cloud the z coordinate of all points is replaced by height above ground 2. Create a digital elevation model (DEM) of the area 3. Thin the point cloud one half of the cell size of the desired CHM in this case, 0.16667 m thinning step size for a CHM with cell size 0.33 333 m 4. From the thinned point cloud, create CHMs with all points above 0 m, 2 m, 5 m, 10 m, and 15 m (all heights above ground) 5. Merge the temporary CHMs into a single CHM, keeping for each cell the highest value

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63 This process was followed for both the nadir and oblique point clouds as well as the lidar point cloud, resulting in the three CHMs to be used for the qualitative analysis. Using MATLAB, t he CHMs were then subtracted from each other in three configurations: 1. Nadir CHM minus lidar CHM 2. Oblique CHM minus lidar CHM 3. Nadir CHM minus oblique CHM For the quantitative analysis of the Jonesville data, only the first four steps of the PhotoScan workflow shown above were used except that for the fourth step, a lower quality dense cloud was created. The dense cl oud was used to identify in the scene the locations of the checkpoints. Once identified in the scene, the approximate locations of the checkpoints were back projected into each image in which they appeared. The locations of the checkpoints were then manual ly adjusted in each photo. The reprojected error for each control point was reported by PhotoScan and used for the subsequent analysis. Results Mission S imulation and P lanning Compared to parallel optical axes which is the case for nadir photography conve rging optical axes of the camera exposure stations provide stronger geometry for the intersection of the rays of light traced from an object to the lens, with the strongest geometry occurring at an angle of intersection of 90. With a tilt angle of 45, th e intersections of light rays of the targets in the scene will be much nearer to 90 in converging pairs of photos. This expected increase in accuracy is supported by the bundle adjustment results presented in Figure 3 6 The change in GSD in the directio n of flight as tilt increases is shown in Figure 3 7 At a tile of 45, a drastic increase in GSD presents itself along the format in the direction of flight. It becomes apparent that the desire for a more accurate bundle adjustment (and, assumedly, a more accurate reconstruction of the scene) must be balanced with the need for a relatively small GSD.

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64 This balance should be not difficult to achieve, as the increased accuracies of the bundle adjustments begin to level off around 30 degrees of tilt; at the a rbitrarily chosen flying height of 80 m, 30 of tilt does not present an unreasonable difference between the GSDs at either end of the format. Quantitative Checkpoint Analysis The results for the checkpoint analysis are detailed in Tables 3 3:5. The nadir and oblique reprojected checkpoint errors first underwent a Shapiro Wilk test to test for the assumption of normal distribution of the errors within sample. The nadir and oblique samples returned values of 0.17 and 0.68, respectively; for both samples, the null hypothesis of normality is not rejected. Under the assumption of normality, further statistical testing could proceed. Because the variances for the two samples were quite different ( ), an F test was performed, which verified the variances were significantly different ( ). Thus, the final test is the two sample test. The null hypothesis of equivalence is rejected in favor of the alternative hypothesis that the mean of the nadir errors is greater than the mean of the oblique errors ( Qualitative CHM Analysis At the stand level, the oblique imagery appears to produce a more accu rate reconstruction of the scene when compared to the nadir imagery (Figures 3 8 and 3 10). This is further corroborated by comparing the two differenced CHMs comparing nadir and oblique each to lidar, as shown in Figures 3 9 and 3 11. Summary statistics f or all five of the CHMs can be found in Table 3 tree canopies. However, closer inspection reveals that the oblique imagery may be encountering reconstruction errors of its own. T his is further discussed in the Conclusion.

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65 Application: Individual Tree Detection (ITD) ( To determine the effectiveness of using oblique imagery in a common forestry application, the following concurrent work by Luiz Ramalho de Oliveira is presented here. ) Methods Using the rLIDAR package in the R programming language (Silva et al., 2017), each CHM was smoothed by a mean filter under various smoothing window sizes (SWS). The rLIDAR package identifies individual trees in a smoothed CHM using local maxima de tection, in which the CHM is searched for local maxima using a fixed window size (FWS). The accuracy of the ITD was evaluated in terms of true positive (TP, correct detection), false negative (FN, omission error) and false positive (FP, commission error). From these values, the recall ( r tree detection rate), precision ( p correctness of the detected trees) and F score ( F overall accuracy), as explained by Li et al. (2012), are calculated using the following equations (Mohan et al., 2017): (3 4) (3 5) (3 6) Various SWS and FWS were used to best accommodate the various stem spacings found in the stand which is noted in the results. Both the SWS and FWS windows sizes were optimized for each subplot wi thin the study area in an effort to maximize the score. The subplots are planted at two different spacings, Narrow (N), 1.83 x 3.65 m, and Wide (W), 3.65 x 3.65 m. These plots

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66 are also either thinned (T = 1) or not thinned (T = 0). There is additionally an independent plot called Biomass (B) (3.65 x 1.83 m, no thinning). Results The complete results of ITD in the three datasets if found in Tables 3 7:9. When compared to ITD in the lidar CHM ( ITD in the nadir CHM ( ) performs notably bette r than ITD in the oblique CHM ( The performance of ITD in both of the datasets is similar except for one striking difference: only 52 false positives are detected in the nadir CHM as compared to 119 in the oblique CHM. The ITD in the nadir CHM thu s garners a higher score, or correctness of detected trees which makes the difference between the two datasets. Further discussion of these results can be found in the Conclusion.

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67 Figure 3 forested scenes generated from low altitude nadir photography. The false positives manifest both above and below ground. Figure courtesy of Dr. Ben Wilkinson, University of Florida. Figure 3 2. Geometry of exposure stati ons. The geometry of exposure stations impacts the accuracy of the reconstructed scene, especially in the dimension parallel to the optical axes. The possible error of the reconstructed point is reflected in the intersection of the two cones of uncertainty colored gray ( Hartley and Zisserman, 2012).

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68 Figure 3 3. Jonesville Park study site with mission plans. Flight lines are shown for the nadir (yellow) and oblique (magenta) missions. GCPs (triangle) and checkpoints (diamond) are shown as well. Background i mage cou rtesy of Google. Figure 3 4 University of Florida Agricultural Experimental Station with mission plans. Referred to also as the Millhopper site, the f light lines are shown for the lidar (cyan), nadir (yellow), and oblique (magenta) missions. GCPs show n as triangles. Background i mage courtesy of Google.

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69 Figure 3 5 Oblique mission simulation. This diagram depicts a simulated mission generated by the MATLAB simulation software. The exposure stations are shown along the top, the array of 3D points are shown in th e middle, and the footprints of the exposure stations are shown in dotted lines along the bottom.

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70 Figure 3 6 Simulated bundle adjustment results. Figure 3 7 Ground sample distance along format as a function of tilt. 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 tilt [ ] endlap 80%, sidelap 60%, h = 80 m sX [rms, m] sY [rms, m] sZ [rms, m] 95% sph [m] 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 tilt [ ] endlap 80%, sidelap 60%, h = 60 m 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 tilt [ ] endlap 80%, sidelap 60%, h = 80 m 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 tilt [ ] endlap 80%, sidelap 60%, h = 100 m

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71 Figure 3 8. Canopy height models, Millhopper study site. Clockwise from top left: lidar, nadir imagery, and oblique imagery.

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72 Figure 3 9. Differenced canopy height models, Millhopper study site. The summary statistics for these can be found in Table 3 6. Figure 3 10. Hi stograms of canopy height models. Clockwise from top left: lidar, nadir imagery, and oblique imagery.

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73 Figure 3 1 1 Histograms of differenced canopy height models. Figure 3 1 2 Distortion in dense matching reconstruction of the scene. In the nadir dense matching point cloud (left), the canopies appear less distorted than in the oblique cloud (right). Direction of flight with respect to each image is left right.

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74 Table 3 1. PhotoScan processing details. Jonesville Millhopper Nadir Oblique Na dir Oblique Aligned cameras 128 149 369 502 RMS projection error [pix] 0.348 0.335 0.364 0.401 Max reprojection error [pix] 1.338 0.697 1.387 2.524 Matching time (h:mm:ss) 00:01:52 00:01:33 00:03:19 00:04:24 Alignment time 00:00:57 00:00:47 00:02:27 0 0:02:54 Depth maps generation time 01:17:00 00:37:51 00:17:17 00:48:19 Dense cloud generation time 00:16:49 00:11:28 00:19:43 01:10:00 Table 3 2. Processing specifications. Computer model Dell Precision T3610 CPU Intel Xeon E5 1620 @ 3.70 GHz (4 core s) GPU NVIDIA K4000 RAM 16 GB DDR3 PhotoScan version 1.4.2 build 6205 Table 3 3. Checkpoint error results. Oblique Nadir Point X [cm] Y [cm] Z [cm] Total X [cm] Y [cm] Z [cm] Total P1 0.2 0.7 1.5 1.7 0.0 1.5 2.0 2.5 P2 0.1 1.4 0.7 1.5 0.3 1.4 2.6 3.0 P3 0.0 0.9 2.9 3.0 0.2 2.1 3.0 3.6 P4 0.5 1.5 2.4 2.9 0.2 1.9 2.7 3.3 P5 0.9 0.7 3.6 3.8 0.3 0.6 0.7 1.0 P6 1.6 0.0 3.3 3.7 1.6 0.4 1.1 1.9 P7 0.4 1.3 3.9 4.1 1.1 1.5 0.5 1.9 P8 1.3 0.8 3.1 3.5 0.3 0.7 1.7 1.9 P9 1.2 2.1 3.7 4.4 1.9 1.9 5.1 5.8 P10 0.1 0.8 2.1 2.3 0.2 0.9 4.7 4.8 P11 1.8 1.7 3.1 4.0 2.4 1.2 3.8 4.7 P12 0.5 0.8 1.6 1.9 0.8 0.5 5.9 5.9 P13 1.0 1.5 1.5 2.4 1.2 1.0 7.8 7.9 P14 0.6 1.4 2.6 3.1 0.5 0.8 4.8 4.9 P1 5 0.0 0.3 3.5 3.5 1.5 0.2 8.2 8.3 P16 0.2 3.0 2.8 4.1 1.8 1.6 6.8 7.2 P17 0.5 1.3 2.1 2.5 1.0 1.1 3.4 3.7 P18 0.8 0.4 2.7 2.8 0.7 1.0 2.9 3.2 P19 0.0 0.8 0.5 0.9 0.3 1.5 1.5 2.1 P20 1.3 0.2 2.8 3.0 0.8 0.7 0.7 1.3 RMS E 0.19 0.29 0.60 0.69 0.24 0.28 0.93 1.00 0.86 1.31 1.30 0.96 1.02 1.28 2.57 2.18

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75 Table 3 4. Checkpoint analysis, F test results. Nadir Oblique Mean 3.95 m 2.95 m Variance 4.76 m 0.92 m Observations 20 20 Degrees of freedom 19 19 5.157 one tail 0.0004 one tail 2.168 Table 3 5. t test results. Nadir Oblique Mean 3.95 m 2.95 m Variance 4.76 m 0.92 m Observations 20 20 Hypothesized mean difference 0 Degrees of freedom 26 1.88 one tai l 0.04 one tail 1.71 Table 3 6. Summary statistics for the canopy height models. Lidar Nadir Oblique Nadir lidar Oblq. lidar Mean [m] 8.00 6.76 7.96 1.24 0.04 [m] 3.85 4.61 4.27 3.02 2.74 Note: All units in this table are me ters.

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76 Table 3 7. Individual tree detection results from lidar CHM. Spacing Thinning Genotype Invntry SWS FWS Detect FP FN TP r p F B NA G1 57 5x5 7x7 48 1 10 47 0.82 0.98 0.9 B NA G2 58 5x5 7x7 58 0 0 58 1 1 1 B NA G3 59 5x5 7x7 56 1 4 55 0.93 0.98 0.9 6 B NA G4 59 5x5 7x7 57 0 2 57 0.97 1 0.98 N 0 G1 60 5x5 7x7 60 0 0 60 1 1 1 N 0 G2 65 5x5 7x7 63 0 2 63 0.97 1 0.98 N 0 G3 71 5x5 7x7 70 2 3 68 0.96 0.97 0.96 N 0 G4 69 5x5 7x7 67 1 3 66 0.96 0.99 0.97 N 0 G5 71 5x5 7x7 68 1 4 67 0.94 0.99 0.96 N 1 G1 140 5x5 7x7 137 6 9 131 0.94 0.96 0.95 N 1 G2 143 5x5 7x7 143 2 2 141 0.99 0.99 0.99 N 1 G3 141 5x5 7x7 135 1 7 134 0.95 0.99 0.97 N 1 G4 140 5x5 7x7 134 2 8 132 0.94 0.99 0.96 N 1 G5 140 5x5 7x7 131 1 10 130 0.93 0.99 0.96 W 0 G1 63 9x9 9x9 60 0 3 60 0.95 1 0.98 W 0 G2 71 9x9 9x9 71 0 0 71 1 1 1 W 0 G3 72 9x9 9x9 73 1 0 72 1 0.99 0.99 W 0 G4 69 9x9 9x9 68 0 1 68 0.99 1 0.99 W 0 G5 65 9x9 9x9 62 0 3 62 0.95 1 0.98 W 1 G1 109 9x9 9x9 108 0 1 108 0.99 1 1 W 1 G2 120 9x9 9x9 120 0 0 120 1 1 1 W 1 G3 121 9x9 9x9 121 0 0 121 1 1 1 W 1 G4 117 9x9 9x9 116 1 2 115 0.98 0.99 0.99 W 1 G5 119 9x9 9x9 117 0 2 117 0.98 1 0.99 Total 2199 2143 20 76 2123 0.96 0.99 0.98

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77 Table 3 8. Individual tree detection results from nadir CHM. Spacing Thinning Genotype Invntry SWS FWS Detect FP FN TP r p F B NA G1 57 3x3 7x7 47 1 11 46 0.81 0.98 0.88 B NA G2 58 3x3 7x7 57 1 2 56 0.97 0.98 0.97 B NA G3 59 3x3 7x7 55 3 7 52 0.88 0.95 0.91 B NA G4 59 3x3 7x7 60 4 3 56 0.95 0.93 0.94 N 0 G1 60 3x3 7x7 58 0 2 5 8 0.97 1 0.98 N 0 G2 65 3x3 7x7 60 0 5 60 0.92 1 0.96 N 0 G3 71 3x3 7x7 72 6 5 66 0.93 0.92 0.92 N 0 G4 69 3x3 7x7 68 3 4 65 0.94 0.96 0.95 N 0 G5 71 3x3 7x7 72 3 2 69 0.97 0.96 0.97 N 1 G1 140 3x3 7x7 112 3 31 109 0.78 0.97 0.87 N 1 G2 143 3x3 7x7 1 35 2 10 133 0.93 0.99 0.96 N 1 G3 141 3x3 7x7 121 5 25 116 0.82 0.96 0.89 N 1 G4 140 3x3 7x7 135 2 7 133 0.95 0.99 0.97 N 1 G5 140 3x3 7x7 115 1 26 114 0.81 0.99 0.89 W 0 G1 63 7x7 7x7 60 0 3 60 0.95 1 0.98 W 0 G2 71 7x7 7x7 73 2 0 71 1 0.97 0.99 W 0 G3 72 7x7 7x7 82 10 0 72 1 0.88 0.94 W 0 G4 69 7x7 7x7 70 2 1 68 0.99 0.97 0.98 W 0 G5 65 7x7 7x7 61 1 5 60 0.92 0.98 0.95 W 1 G1 109 7x7 7x7 104 0 5 104 0.95 1 0.98 W 1 G2 120 7x7 7x7 119 0 1 119 0.99 1 1 W 1 G3 121 7x7 7x7 122 1 0 121 1 0.99 1 W 1 G4 117 7x7 7x7 117 2 2 115 0.98 0.98 0.98 W 1 G5 119 7x7 7x7 111 0 8 111 0.93 1 0.97 Total 2199 2086 52 165 2034 0.93 0.97 0.95

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78 Table 3 9. Individual tree detection results from oblique CHM. Spacing Thinning Genotype Invntry SWS FWS Detect FP F N TP r p F B NA G1 57 5x5 7x7 48 3 12 45 0.79 0.94 0.86 B NA G2 58 5x5 7x7 58 4 4 54 0.93 0.93 0.93 B NA G3 59 5x5 7x7 63 7 3 56 0.95 0.89 0.92 B NA G4 59 5x5 7x7 56 3 6 53 0.9 0.95 0.92 N 0 G1 60 5x5 7x7 61 6 5 55 0.92 0.9 0.91 N 0 G2 65 5x5 7x7 67 9 7 58 0.89 0.87 0.88 N 0 G3 71 5x5 7x7 74 10 7 64 0.9 0.86 0.88 N 0 G4 69 5x5 7x7 64 3 8 61 0.88 0.95 0.92 N 0 G5 71 5x5 7x7 71 8 8 63 0.89 0.89 0.89 N 1 G1 140 5x5 7x7 134 18 24 116 0.83 0.87 0.85 N 1 G2 143 5x5 7x7 140 5 8 135 0.94 0.96 0.95 N 1 G 3 141 5x5 7x7 134 16 23 118 0.84 0.88 0.86 N 1 G4 140 5x5 7x7 138 9 11 129 0.92 0.93 0.93 N 1 G5 140 5x5 7x7 130 9 19 121 0.86 0.93 0.9 W 0 G1 63 9x9 9x9 60 0 3 60 0.95 1 0.98 W 0 G2 71 9x9 9x9 71 0 0 71 1 0.97 0.99 W 0 G3 72 9x9 9x9 73 1 0 72 1 0.94 0.97 W 0 G4 69 9x9 9x9 68 1 2 67 0.99 0.94 0.96 W 0 G5 65 9x9 9x9 61 1 5 60 0.92 1 0.96 W 1 G1 109 9x9 9x9 102 0 7 102 0.94 1 0.97 W 1 G2 120 9x9 9x9 119 0 1 119 0.99 1 1 W 1 G3 121 9x9 9x9 126 6 1 120 1 0.9 0.95 W 1 G4 117 9x9 9x9 114 0 3 114 0.99 0 .98 0.99 W 1 G5 119 9x9 9x9 115 0 4 115 0.94 0.99 0.97 Total 2199 2147 119 171 2028 0.92 0.94 0.93

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79 CHAPTER 4 A STEM BASED APPROACH TO SEMI AUTOMATED ESTIMATION OF PINE MORPHOLOGY F ROM LOW ALTITUDE 3D MAPPING Introduction Forest management often u ses remote sensing as a tool to provide accurate information on the morphology and spectral attributes of forests. An emerging platform for the remote sensing of forests is the unmanned aerial system (UAS), which consists of a remotely piloted or preprogra mmed robotic aircraft equipped with a remote sensing payload. UAS are quickly becoming the tool of choice for local scale remote sensing projects due to their low entry cost and on demand access to data collection, two traits that distinguish it from the m ore prevalent manned aircraft and satellite platforms. Particularly fascinating is the resurgence of photogrammetry that has accompanied the rise of UAS remote sensing. In parallel with the advent of accessible aerial platforms, the emergence of structure from motion (SfM) photogrammetry (Westoby et al., 2012) has made it possible for users to produce dense, three dimensional (3D) reconstructions of the scene, similar to the data acquired via airborne laser scanning, using relatively inexpensive software to process photos taken with a commercial, off the shelf camera. The typically low flying heights of UAS missions allow for ground sample distances (GSDs) of the photos on the order of 1 3 cm, revealing the physical structure, or morphology, of the forest at a resolution that is unattainable from conventional remote sensing platforms. The problem now facing the photogrammetrist and forest manager is analyzing this rich source of 3D data. Aerial Photogrammetry in Forestry Forest inventory and mensuration, cons idering the area and density of the typical forest, sampling by a forester in the field to measure and estimate forest parameters such as tree count,

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80 diameter at breast height (DBH), tree height, stem form, and other physical traits (van Laar and Aka, 2007). Beginning in the 1920s, foresters tapped aerial photography as a mensuration tool, of producing stand maps (Spurr, 1948). Alongside these early methods, which relied greatly on interpretation by an expert of 2D photo mosaics, methods for interpreting stereopairs of images were also developed (Lyons, 1966), but never came to prominence as an effective forest sampling method. Despite the advances in photogrammetry since the middle of the 20th century, aerial photogrammetry conducted from a manned aircraft comes with inherent limitations. For reasons of cost effectiveness and safety, aerial photogrammetric missions are flown from considerable height above ground (typically >500 m), and the scale of the subsequent photographs limit the precision s tand map created from conventional aerial photography, tree heights are determined manually through either photointerpretation or manual, 3D location of treetops via stereoscopic plotting. Without reliable information about the sub canopy terrain, e.g. a d igital terrain model, these tree heights are subject to interpretation i.e., a good guess. Developments in forest inventory and mensuration in the early part of this century included a fusion of airborne laser scanning (lidar) and low altitude digital imag ery (Bohlin et al., 2012; Korpela et al., 2007; St Onge and Achaichia, 2001; Surez et al., 2005). Both lidar and low altitude aerial imagery allow for the 3D reconstruction of forests at the stand level (and, depending on the mission parameters, the indiv idual tree level), which makes possible the recovery of allometric data through more indirect means than conventional, ground based forest mensuration methods. Though these data can be acquired with the sensors on the ground (e.g. Kankare et al., 2013; Kir ly and Brolly, 2007; Moskal and Zheng, 2011; Watt and Donoghue,

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81 2005), the more efficient approach is to equip an aircraft with a sensor payload to cover a greater area from the aerial vantage. The spatial resolution of these data is dependent on, among o ther conditions, the distance between the sensor and the forest; however, the spatial resolution of the aerial data is often much greater than that available from satellite imagery. The latest trend in forest inventory and mensuration is the use of automa ted systems, both for the collection and the processing of data (Dandois and Ellis, 2013; Karpina et al., 2016; Lisein et al., 2013; Tang and Shao, 2015; Watts et al., 2012; Yilmaz et al., 2016; Zarco Tejada et al., 2014). Interest in the use of unmanned a ircraft systems (UAS) has been growing in large part because they are more readily deployed and less cost prohibitive than manned aircraft. UAS can be equipped with a small sensor payload and can be flown over a sizeable area. Of particular interest is the ability of low altitude UAS missions to collect data at a much higher spatial resolution than satellite based and high altitude, aerial based sensors, which allows for the 3D reconstruction of forested areas in extraordinary detail. Automated Forest Mens uration from Point Clouds A mong the more intriguing developments in forest inventory and mensuration is the automatic determination of forest parameters from lidar or photogrammetric point clouds (Aschoff and Spiecker, 2004; Korpela et al., 2007; Maas et a l., 2008; Simonse et al., 2003). The amount of data that can be acquired and analyzed is staggering when compared to what is possible via conventional means : UAS orthoimagery resolution is often on the order of 1 3 cm ground resolution, compared to ground resolution on the order of 1 m from high resolution orthoimagery from conventional aircraft. J ust as remarkable is the accuracy, repeatability, and efficiency with which these d ata can be collected The process by which individual tree parameters such as s tem count, DBH, and tree height (to name a few) can potentially be

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82 identified is made possible not simply by advances in computing, but also by the increase in the amount of data regarding the 3D structure of the tree. Dense matching point clouds. In earl ier photogrammetric approaches, a handful of crucial 3D points (e.g. the highest point of a crown) were manually located by a trained operator using a stereoscopic plotter, an instrument for manually recording the 3D positions of objects in overlapping (or stereo) images. Area based image matching methods, such as those used in auto aerotriangulation (AT), could automatically generate match points between consecutive stereo images, but only under certain geometric and radiometric conditions (e.g. non conver gent photography, presence of contrast/texture). The dense, accurate 3D reconstruction of the forested area via SfM is more efficient than auto AT, in that it can produce feature matches in multiple, uno rdered images in various geometric configurations (Lingua et al., 2009). In a dense matching point cloud that same tree is likely to have hundreds, possibly thousands, of 3D points associated with it; these results cannot be matched by conventional auto A T or a manual operator. UAS lidar point clouds. Early airborne laser scanning (ALS) data exhibited low return density, which led to underestimation of tree heights (e.g. Nilsson, 1996). As lidar sensor technology advanced, the pulse rate and therefore ret urn density attainable from lidar sensors increased to the point that sensing individual treetops became possible. The amount of subcanopy information attainable via ALS also increased as lidar sensor technology advanced to multiple return and full wavefor m systems. ALS data progressed from offering a low density picture of the top of forest canopy and the ground below to many ) worth of information per tree. Low altitude UAS lidar data collection offers not only an

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83 e ven higher return density but also a higher probability of acquiring information about tree stems, a part of the tree that is often unattainable from high altitude ALS data. Canopy Based Versus Stem Based Individual Tree Detection From the richness of the low altitude lidar or dense matching point cloud arises the challenge of interpreting the data. These low altitude point clouds often contain information of the individual stems of trees, which is potentially valuable information for the forest manager or silviculturalist. Interpreting these stem data can be done manually, as certain computer programs allow a user to manually select points and make basic measurements within a point cloud. As presented above, some algorithms have been developed to interpret individual stems in a semi automated manner in terrestrial lidar data. However, most methods of individual tree detection (ITD) from high density point clouds are canopy based. In many canopy based methods, s egmentation of individual tree s in a stand is a ccomplished by applying image processing methods to a rasterized canopy height model (CHM) such as watershed segmentation (e.g. Wang et al., 2004) or local maxima detection (e.g. Mohan et al., 2017) One novel method exploits the subcanopy information pres ent in high density lidar data by applying a generalized normalized cut segmentation to voxelized (a sort of three dimensional raster) point clouds (Reitberger et al., 2009) T his study takes a novel approach, present ing a lgorithms designed to estimate a n umber of morphological traits of a forest stand namely stem count, stem location, stem height, and DBH by exploiting the presence of stem information in the point cloud. Methods Data Collection and Processing Baseline study site OSBS. A baseline study wa s conducted at the Ordway Swisher Biological Station (OSBS) situated about 20 miles east of Gainesville, FL (Figure 4 1) A small, open portion of a slash pine ( Pinus elliottii ) plot with ten trees (average nearest neighbor spacing

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84 of about 9 m) was select ed for this pilot study. These trees range in size from 18 cm to nearly 40 cm DBH. A tripod mounted Trimble GX terrestrial laser scanner (TLS) was used to scan the test plot from three scan stations. Th horizontal field of view is 360 and its vertic al field of view is 60, the latter of which was compensated for by scanning the study site from a greater distance to ensure full coverage of the trees. The angular resolution of each scan was set as to assure a minimum point spacing of 3 cm at the most d istant tree in the scan; due to the varying range of trees from the scan stations and to overlap from the multiple scan stations, the average point spacing is > 3 cm. The data was processed and registered using Trimble PointScape The color (RGB) images fo r dense matching point cloud generation were acquired with a Nikon D60 DSLR with a focal length of 27 mm. Several photos were taken from a r oad adjacent to the study area in landscape orientation from approximately 1.7 m above the ground looking towards th e targeted area. Figure 4 2 illustrates the locations and orientations of the exposure stations. Culling blurry and redundant imagery, a total of 179 photos were used to generate the photogrammetric point cloud using Agisoft PhotoScan. The photos were alig ned using a self filtering settings. Both the TLS and dense matching point clouds were georeferenced to the local scanner coordinate system of the first TLS scan station. This study is considered as a baseline because of the highly controlled manner in which the data was collected, which ensured the resulting point clouds would be dense and exhibiting fewer errors. These data are used as a tes t site, so to speak, for developing and optimizing the detection and estimation algorithms presented below. Study site ACMF. The next study was conducted at Austin Cary Memorial Forest (ACMF) near Gainesville, Florida, in the summer of 2016 (Figure 4 3) T he study site within

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85 ACMF is a roughly 2.2 acre stand of slash pine ( P elliottii ) with a 2.7 m average nearest neighbor distance (i.e. stem spacing). Vertical RGB imagery was collected with the Canon EOS Rebel SL1 ( 40 mm) onboard a DJI S1000 vertical tak e off and landing (VTOL) UAS flying at 80 m above ground level (AGL) When the RGB imagery was initially collected, it was not expected that the resulting dense matching point cloud would feature stem information. This unexpected result was the catalyst for the study. The RGB images were processed in Agisoft PhotoScan and dense matching was filtering settings. The point cloud was georeferenced with ground control points ( GCPs ) in the scen e; the GCP locations were surveyed with an RTK GNSS system The resulting dense, 3D point cloud was further processed using ground, effectively normalizing (or flattening) the terra in. From the point cloud of the entire study site, a 5050 m subplot was selected for use in the algorithms described below. The subplot contains 69 tree stems (66 of which are alive) while containing approximately 70% fewer points than the point cloud of the entire study area and was deemed a suitable sample size Study site Flatwoods The final study was conducted at Longleaf Flatwoods Preserve southeast of Gainesville, FL (Fig ure 4 4) The preserve features many stands of slash pine ( P ell i ottii ) in various stages of growth. For this study, two circular plots 13 m in radius were selected. The two plots are thinned plot s of 28 and 29 stems respectively, with an average nearest neighbor distance of about 3 m The stems average about 18 cm DBH and 17 m in height. The row planted stand has 12 ft (3.6 m) row spacing where every fourth row has been thinned.

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86 Lidar data was collected over the site using the GatorEye Unmanned Flying La boratory, a sensor suite aboard a DJI Matrice 600 VTOL UAS. The lidar sensor is a Velodyne VLP 16 PUCK Lite, a dual return system with a 300,000 points/s pulse rate (Figure 4 5) The lidar data was collected from a height of 40 m AGL. The point cloud was d irectly georeferenced by a process similar to that outlined in Chapter 1. The resulting point cloud has an average point density of 450 points/m 2 This point cloud was also normalized for subsequent analysis using the method described above. Timber c ruise d ata To serve as ground truth for the subsequent algorithm estimations a timber cruise was conducted of both main study site s The DBH of each stem was determined with a tree tape and stem heights determined with a hypsometer. (Tree heights were not reco rded at the OSBS site, as those data were used only for the development of the stem detection and DBH estimation algorithm s .) For the ACMF site, stem locations were determined via horizontal angle offsets with a total station. Stem locations at the Flatwoo ds site were initially found using a compass and a sonar based hypsometer from the plot centers, but these measurements suffered from systematic biases in both range and bearing and were replaced by stem locations taken directly from the lidar point cloud. Stem Detection Algorithm A natural thought is to cluster the points according to their coordinates. The algorithm developed by Maas et al. (2008) is adopted. The main idea of this method is to cluster points using a moving window in the p lane ( Figure 4 6 ). First, all the points within a slice are projected onto the plane. The square window, which is divided into quadrants, begins in an arbitrary position within the slice. If the number of points within the window is greater than a predetermined threshold, the algorithm deems those points as belonging to a cluster. The

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87 window moves by one half its length in the plane towards the quadrants which contained data points, and the algorithm repeats, terminating once it reaches an area wher e the moving window contains fewer than the threshold number of points. Clusters that are adjacent to one another are determined to be the same cluster. A circle is then fitted to each of the final clusters; if the fitted circle is above a minimum threshol d radius (to avoid detection of smaller objects), and the root mean square error (RMSE) of the fitted circle is below a predetermined maximum, the cluster is determined to be from a tree stem. Although the circle fitting test could identify some of the ste ms, clusters which fail the test also have the possibility of containing stems. For instance, when a stem is tightly surrounded by high understory growth it is probable to cluster the stem with the understory growth which causes the cluster to fail the f itting test. Thus, the stem detection method presented here augments the moving window strategy presented by Mass et al. by performing a Hough transform on those clusters which were initially not identified as stems ( Figure 4 7 ). The Hough transform is a r obust method for detecting a model in this case, a circle in point data. For both the Maas et al. algorithm and the Hough transform, the centers of the detected circles are recorded. Those detected circles whose centers are within 0.5 m of each other are d eemed to be from the same tree stem, and the points from each of the grouped, detected circles are combined to form the detected stem. A flowchart of the entire stem detection algorithm is shown in Figure 4 8. Diameter at Breast Height Estimation Algorithm The detected stems are passed to a RANSAC (Fischler and Bolles, 1981) cylinder fitting based on the cylinder fitting method presented by Schnabel et al. (2007). In the Schanbel et al. method, two points and their associated surface normals are chosen at random. The two lines

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88 defined by each point and its corresponding surface normal are projected onto the plane defined by the cross product of the two normals. The intersection of the two lines is taken to be a point along the axis of the cylinder, and the direction of the cross product is the direction of the axis ( Figure 4 9 ). The distance from the first of the randomly chosen points to the axis is taken as the ra dius of the cylinder. This process is repeated t times, where (4 1) In the above equation, is the predefined percentage of points expected a priori to be outliers The value is the number of points that sele cted to fit to the model. (In this case, the model is a cylinder, and the number of points randomly selected is 2.) The value of is the certainty that, once all the trials have run, that at least one trial did not contain any outliers. For this st udy, For each iteration, the RMSE of the residuals of all points to the RANSAC estimated cylinder is calculated. After all iterations, the initial cylinder with the lowest RMSE is selected, and the percentage of points with the lowest re siduals are fitted to a final cylinder via ordinary least squares (OLS). As a final step, o nly those points within the predefined height threshold above and below breast height are passed to this algorithm. This threshold typically does not extend too far below breast height as to avoid understory growth; however, the threshold above breast height can be adjusted more freely to ensure sufficient points are passed into the cylinder fitting algorithm. The RANSAC cylinder fitting algorithm for this study has b een augmented from the Schnabel et al. method in three ways: 1. When two random points (and their associated normals) are selected for the initial cylinder fitting, the points are not kept unless the angle between the normals is between 30 and 150;

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89 2. t he init ial cylinder fit is not kept unless the cylinder is oriented near vertically (i.e., the unit vector representing the direction of the axis must have a z component ; and 3. a s described above, an OLS fitted cylinder is applied to the inlier points as id entified in the RANSAC process. Double the radius of the final OLS fitted cylinder is taken as the estimate for DBH. Height Estimation Algorithm The locations of the detected stems are used as an initial search area for the local maxima of the entire dense point cloud. Using LASTools, all points whose coordinates (i.e., with the highest height above ground is taken as the highest point of the tree stem. This method is not a general solution for estim horizontal position, or a significant lean of the stem, could cause the horizontal position of the detected local maximum to not fall within an 0.5 m radius of the horizontal position of the s tem. Assuming the stem locations are accurate, the proposed method for estimating the heights of stems will be sufficient, as no stems in the study area exhibit significant lean. For two stems whose tops are within 0.5 m of each other, this algorithm would record only the height of the taller stem. For two stems to be this close together is an unlikely scenario based on a priori information about the pine stands used for this study. Equivalence Testing To determine if the DBH and height estimation algorithm s are effective at estimating the average DBH and stem height at the stand level the means of the cruise and estimation data will be subject to equivalence testing, specifically, the two one sided t test (TOST). This test begins with the null hypothesis t limit Put briefly, TOST finds the confidence interval for the difference between

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90 the two means; if that confidence interval lies entirely inside the interval then the two difference between two means is found by : (4 2) whe re (4 3 ) For this study, the limit of will be used to determine if the means of the DBH and height estimation results are within 10% of the cruise data. Results Terrestrial Data, Preliminary Study As the stem detection algorithm was adapted from a method developed specifically for TLS data, results were expectedly positive. The algorithm det ected all ten of the stems in both the lidar and dense matching clouds under various configurations of slice height, slice minimum, and the tunable parameters of the algorithm (i.e., search window size, radius threshold, goodness of fit). These preliminary tests provided useful guidance for efficient use of the algorithm: 1. Excluding near ground and crown data slices from the stem detection algorithm led to runtime improvements of over 95%. The majority of data in those slices are non stem data which unnecess arily slows the clustering subroutine. Adding a low and high height threshold provides a significant advantage. 2. The speed of the cluster detection routine is inversely proportional to the size of the search window. Increasing the size of the search window from the Mass et al. recommendation of 20 cm to 50 cm led to a further 10% improvement in runtime. As mentioned previously, t he stem detection algorithm will return only those points deemed to be part o f the ste m, which is not necessarily a depiction of th e entire stem (Figure 4 10) Portions of the stem below or above the height thresholds set in the pre processing stage, as well as

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91 portions within the thresholds that were not deemed circular during the clustering, will not be returned as part of the stem. For the preliminary testing of the DBH estimation algorithm, the aim was to find the ideal outlier ratio. Numerous trials were performed on both the lidar and dense matching detected stems at outlier ratios ranging from 70% to 1%, with those trials with a n outlier ratio 40% and lower showing favorable results (Figure 4 11). Although these trials proved useful for developing the algorithms, they did not particularly challenge the robustness of the algorithms against noisy data. From the terrestrial pose, af ter reasonable outlier filtering was performed, both the TLS and terrestrial dense matching point clouds exhibited little noise. Dense Matching, ACMF Site Stem detection performed reasonably well within the UAS dense matching cloud at the ACMF site (Figure 4 12) With a slice height of 20 cm and a slice minimum of 5, the algorithm detected 61 of the 69 stems in the study plot. Of the 61 detected stems, 58 were alive and included in the timber cruise. The DBH estimation for these 58 stems proved to be unreli able at the individual tree level A range of outlier ratios from 70% 1% were attempted, with 10% producing the least inaccurate results. L inear regression with a fixed intercept comparing the cruise and estimated DBH, surprisingly, returned a negative val ue of (Figure 4 13) Cylinder fitting failed on five of the 58 stems. Comparison of the means was somewhat more promising (cruise 20.8 cm, 5.1 versus detected 22.9 cm, 12.9), but in the TOST, the null hypothesis o f inequivalence was not rej ected at ( value 0.51).

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92 Estimating the heights of the trees in the study plot showed a somewhat greater level of success presenting an of 0.44 in the fixed intercept model (Figure 4 14) The means also fail to reject the null hypothesis of the TOST at 95% ( ). To what extent this can be attributed to a possible underestimation of the heights as measured by hypsometer cannot be said (cruise mean 18.8 m versus detection mean 19.8 m), but the regression fit does strongly suggest the inad equacy of the dense matching cloud to provide reliable stem heights on an individual tree level. Lidar, Flatwoods Site Stem detection proved more difficult with the lidar point cloud (Figure 4 15) Despite the ability of lidar to penetrate canopy, the stem s in the scene tended to consist of fewer points than those in the dense matching cloud from the ACMF site. The optimal configuration for stem detection for the Flatwoods plots proved to be 200 cm slices, with a slice minimum of 1. Regardless, only 40 of t he 56 stems were positively detected. The DBH estimation algorithm performed similarly in the lidar data as it did in the dense matching data, showing no reliability at the individual level ( 0.03, fixed intercept) (Figure 4 16) and overestimating a t the plot level (20.1 cm, 3.6 to 24.0 cm, 10.5). DBH estimation fails to reject the null hypothesis of inequivalence in the TOST at 95% ( 0.77). For both the dense matching and lidar data, the variance of the DBH estimations is much higher than the variance of the cruise data. Height estimation also performed similarly in the lidar and dense matching data exhibiting unreliable precision for estimation of the heights of individual stems ( ) (Figure 4 17) while overestimating heights a t the stand level (18.9 m mean detection versus 17.7 m mean cruise). The means in the TOST do not reject the null hypothesis of inequivalence at

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93 95% ( 0.13). For both the dense matching and lidar height estimations, the variance of the estimations is lo wer than that of the cruise data. Summaries of stem detection, DBH estimation, and height estimation for both the ACMF an Flatwoods sites can be found in Tables 4 1:3.

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94 Figure 4 1. Baseline study site at Ordway Swisher Biological Station near Gaines ville, FL. TOP: Satellite view; the stems used are outlined in yellow. Image courtesy of Google. BOTTOM: Oblique views of the TLS (left) and dense matching (right) point clouds.

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95 Figure 4 2. Locations and orientations of exposure stations for terrestrial dense matching point cloud. Figure 4 3 Oblique view of ACMF dense matching point cloud. One of the obstacles that the stem detection and cylinder fitting algorithms must overcome is missing information along the tree stem, which is due mainly from o cclusion from the canopy. Though the point cloud retains color information from the RGB photos, these data are not used in the algorithms.

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96 Figure 4 4. Longleaf Flatwoods Reserve study site. LEFT: Satellite view with study plots outlined in yellow. Imag e courtesy of Google. RIGHT: Plan view of lidar point cloud colorized by height. Figure 4 5. GatorEye Unmanned Flying Laboratory (UFL) The GatorEye UFL is a sensor suite shown here on board the DJI Matrice 600. Image courtesy of Dr. Eben Broadbent ( ww w.spaclab.org/gatoreye.html ).

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97 Figure 4 6 Moving window search strategy. The points in the point cloud are here labeled as o m the 3D reconstruction of the scene through SfM ph otogrammetry (Maas et al., 2008). Figure 4 7 Circle recognition by Hough transform. Depicted is a plan view of a cluster not deemed a tree stem by the Maas et al. method. The points are shown here in a planimetric (top down) view, with the points dete rmined by the Hough transform to be from the tree stem shown in orange (right).

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98 Figure 4 8 Flowchart of the stem detection method. Once this algorithm has been repeated at all horizontal slices, the recorded centers undergo a final clustering to deter mine which detected circles belong to the same tree stems.

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99 Figure 4 9 RANSAC cylinder fitting. A selection of points from the detected stem around breast height (1.4 m) is selected (shown in red, left); these points are passed to the cylinder fitting algorithm, where the initial RANSAC cylinders (top right) and final least squares cylinder (bottom right) are found. Figure 4 10. Steam detection results, TLS data, OSBS study site.

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100 Figure 4 1 1 Outlier ratio trials for RANSAC DBH cylinder fitting f or DBH estimation. Figure 4 1 2 Stem detection results, dense matching cloud, ACMF study plot. 0 10 20 30 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.05 0.01 RMSE [cm] Outlier ratio RANSAC outlier ratio trials, OSBS SfM TLS 1 21 1 3 1 4 1 2 1 71 2 6 2 3 1 36 4 5 2 7 2 1 1 11 1 69 3 50 1 13 1 24 4 1 3 51 1 12 2 8 1 40 3 47 1 43 4 8 1 68 1 7 1 42 3 53 1 38 1 72 1 37 2 2 3 54 1 10 1 19 2 5 1 5 4 3 2 4 4 6 1 1 1 41 1 67 1 16 3 49 4 9 1 18 4 4 4 7 4 2 1 9 1 8 1 6 1 17 1 14 1 15 1 33 3 52 1 22 3 48 1 70 1 35 1 25 1 23 1 20 T140 T180 T187 T229 T30 T35 T58 T82 T10 T101 T11 T114 T115 T12 T124 T13 T130 T134 T136 T15 T155 T17 T176 T178 T18 T195 T2 T20 T21 T22 T223 T234 T252 T254 T255 T27 T274 T282 T285 T29 T31 T316 T32 T323 T33 T36 T40 T41 T42 T44 T45 T47 T48 T53 T61 T66 T67 T68 T7 T79 T8 T80 T84 T9 T96 T98 3292540 3292550 3292560 3292570 3292580 3292590 3292600 3292610 383850 383860 383870 383880 383890 383900 383910 383920 Northing [m] Easting [m] Stem detection results, ACMF Cruise Detected

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101 Figure 4 1 3 DBH estimation results, dense matching cloud, ACMF study plot. Fixed intercept linear regression line in black; linear regression without fix ed intercept in red. Figure 4 1 4 Height estimation results, dense matching cloud, ACMF study plot. Fixed intercept linear regression line in black; linear regression without fixed intercept in red. y = 0.4866x + 33.11 R = 0.0384 y = 0.9974x R = 0.34 0 10 20 30 40 50 60 0 10 20 30 40 estimated DBH [cm] cruise DBH [cm] DBH, ACMF y = 0.6761x + 7.1599 R = 0.6282 y = 1.0465x R = 0.4337 10 12 14 16 18 20 22 24 26 10 12 14 16 18 20 22 24 26 estimated h [m] cruise h [m] Height, ACMF

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102 Figure 4 1 5 Stem detection results, lidar cloud Flatwoods site. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 T1 T10 T16 T17 T19 T20 T24 T26 T27 T28 T3 T34 T37 T38 T4 T40 T44 T45 T5 T6 T7 T8 3270170 3270175 3270180 3270185 3270190 3270195 3270200 380975 380980 380985 380990 380995 381000 381005 Northing [m] Easting [m] PLOT 2 DETECTION RESULTS Cruise Data Detected 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 T1 T10 T11 T12 T13 T14 T16 T17 T18 T19 T2 T20 T21 T23 T24 T25 T27 T29 T30 T32 T37 T44 T5 T59 T61 T62 T69 T7 3270140 3270145 3270150 3270155 3270160 3270165 3270170 380970 380975 380980 380985 380990 380995 381000 381005 Northing [m] Easting [m] PLOT 3 DETECTION RESULTS Cruise Data Detected

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103 Figure 4 1 6 DBH estimation results, lidar cloud, Flatwoods study plots. Fixed intercept linear regression line in black; linear regression without fixed intercept in red. Figure 4 1 7 Height estimation results, lidar cloud, Flat woods study plots. Fixed intercept linear regression line in black; linear regression without fixed intercept in red. y = 1.1583x R = 0.0384 y = 0.7612x + 8.3379 R = 0.0532 10 15 20 25 30 35 40 45 50 55 60 10 15 20 25 30 detected DBH [cm] cruise DBH [cm] DBH, Flatwoods y = 1.0543x R = 0.217 y = 0.471x + 10.561 R = 0.3843 8 10 12 14 16 18 20 22 24 8 10 12 14 16 18 20 22 24 detected h [m] cruise h [m] Height, Flatwoods

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104 Table 4 1. Stem detection summary. Match type Dense matching, ACMF Lidar, Flatwoods True positive 58 (61) 40 False positive 8 (5) 10 False negative 8 18 Note: Three of the stems detected at the ACMF site were not included in the cruise because they were dead. They are included here because the stem detection algorithm successfully detected their presence in the point cloud. Table 4 2. DBH estimation summary. Dense matching, ACMF Lidar, Flatwoods DBH_c DBH_e DBH_c DBH_e Mean 20.78 22.87 20.10 23.95 5.10 12.93 3.56 10.54 Table 4 3. Height estimation summary. Dense matching, ACMF Lidar, Flatwoods h_c h_e h_c h_e Mean 18.74 19.83 17.74 18.92 3.37 2.87 2.6 0 1.97

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105 CHAPTER 5 CONCLUSION Recommendations for UAS 3D Remote Sensing In Chapter 2, These gaps ar e most likely to occur as overlap decreases (or overlap is not present), forward velocity increases, and/or the ground is nearly flat. Overlap obviously help s fill in any potential gaps. As forward velocity decreases not only does point density increase, b ut random, back and forth yaw/crab of the airframe helps to fill in gaps. Varying topographic relief tends to break up the repeating gap patterns as well, though as is also the case in conventional ALS, drastic drop offs such as cliffs or ravines, if not a ccounted for, can lead to poor coverage of the lower terrain. The gaps were shown to have more potential to provide degrading quality of coverage as the rotation rate of the scanner head decreased. Velodyne allows the user to adjust the rotation rate betwe en 5 20 Hz. A lower rotation rate may lead to decreased power consumption (thus longer flight times), though this was not confirmed as a part of this study. Concerns of gaps in coverage, especially with respect to flying height, forward velocity, and the s ize of objects of interest in the scene, should be considered in alongside the potential benefits of decreasing the rotation rate of the scanner head. In C hapter 2 it is also suggested that the maximum range of returns be set at some limit below the VLP 16 produce vastly more accurate results. However, this finding has been confined to primarily research missions with narrow flight line spacing and slow forward velocities, where maximiz ing area of coverage was not of concern. This should be weighed carefully when planning a UAS lidar mission.

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106 In chapter 3, Agisoft PhotoScan was used for processing both nadir and oblique imagery. However, it is not immediately clear what method PhotoScan uses for initial approximations of camera orientation without a priori information from direct georeferencing; the manual suggests that nadir (i.e. vertical) images are preferred, or at least expected by default. This notion is supported by the initial dif ficulties encountered in processing the oblique images. Using the angular attitude data for the oblique images as initial approximations during the image alignment (i.e. bundle adjustment) step of the workflow in Agisoft PhotoScan resulted in more photos b eing aligned. Image alignment without these initial approximations resulted in roughly two dozen photos being rejected out of about 500 However, t he rotation data from the Xsens Mti G 710 as reported wa s not compatible with the rotation data accepted by P hotoScan. Conversion of the Xsens rotation data from yaw pitch roll in the Easting Northing Up (ENU) frame to yaw pitch roll in the Northing Easting Down (NED) frame was not trivial; the procedure is detailed in Appendix E. It is important to note for both lidar and photogrammetric UAS data collection the mission planning should take into account the average and maximum heights of the targets of interest in the scene. Overlap, side lap, point density, etc. can be drastically different at the ground and tar get ranges from sensor. For example, for a UAS remote sensing mission flown 50 m AGL, with trees in the scene averaging 15 m, considerations for point coverage, overlap, etc. should be made for both 50 m and 35 m AGL. Especially in a forested scene, critic al information could be lost if image overlap or lidar point density is insufficient at the canopy level. Forest Mensuration from UAS borne Point Clouds In contrast to the results of the quantitative checkpoints study and the qualitative CHM comparisons in Chapter 3, the application study highlighted a weakness of oblique imagery over the forested scene, demonstrating the superiority of the nadir CHM for individual tree detection

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107 (ITD). Inspection of the CHMs and dense matching point clouds for both the nad ir and oblique data show what is possibly two types of errors happening simultaneously which serves to benefit the nadir CHM as it undergoes local maxima detection (the ITD method used in Chapter 3). 1. The nadir data shows a tendency to underestimate canopy presence at a greater radius from the local maximum (i.e. tree t op), as shown in Figures 3 9 and 3 11 2. The oblique data demonstrates what is likely the false positive effect shown in Figure 3 1 in the direction of the optical axes of the cameras, which is no longer vertical, but rather inclined in the direction of flight (Figure 3 12 Table s 3 8 and 3 9 ) Together, these effects lead to more distinct individual crowns in the nadir CHM. This is useful for ITD but may lead to underestimation of other metrics such as crown area or aboveground biomass. This false positive effect in the oblique data may be mitigated by either decreasing the angle of tilt or adding additional flight lines perpendicular to each other, though the latter option increases both flight and processing time. The intended use of the data should be considered before choosing to tilt the camera, if at all, and whether additional flight lines would provide a net benefit. The stem detection results suggest that the augmented Maas et al. stem de tection algorithm could be suitable for areas similar to those plots under study i.e. homogeneous scene s where the only objects in the search area are tree stems with limited understory growth. (Concurrent work has shown that this stem detection method i s not as effective in a heterogeneous u rban scene.) It cannot be readily determined if the overestimation bias shown by the height estimation algorithm is due to inaccurate point cloud data or underestimation during the field cruise a conceivable error wh en using a hypsometer to measure tree heights. The algorithm for finding the DBH of individual stems shows promise of producing accurate results under certain conditions and with anticipated future improvements in sensor technology The shape of the reco nstructed tree stems in the dense matching point clouds is

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108 highly irregular due to the geometry of the photos and the occlusions of the canopy; even using RANSAC, a model fitting method suited for noisy data, the results so far have been highly imprecise a nd inaccurate. These irregularities are typically due to canopy occlusion, as the results from the baseline terrestrial study produced exceptional results. In the lidar point clouds, the lidar sensor in the airborne did not provide enough stem information for reliable cylinder fitting. The information available may also be less accurate due to the range dependent error and large beam divergence of the VLP 16 scanner With improvements in miniature GNSS/INS technology, this range dependent error will decreas e, leading to more relatively accurate features in the lidar point cloud. Current State of the Art A stem based approach to either ITD or stand level sampling is currently not advantageous when compared to canopy based estimation techniques under the condi tions present in this study. As the accuracy of UAS borne lidar sensors increases, sufficient, accurate information can be gathered about the individual stems of trees in a forested scene Bear in mind that c anopy based methods of crown delineation are sti ll prone to certain pitfalls, namely: 1. f ailure to detect trees below canopy 2. f ailure to delineate when presented with overlapping crowns and 3. s ensitivity of tree count estimation with respect to the method of smoothing the CHM and distinctness of the tree c rowns One of the greatest strengths of the UAS platform in remote sensing is how often it can be deployed. The high temporal resolution of UAS remote sensing data offers new insight into dynamic processes. Stem based ITD is more effective as a forest matu res and its trees become larger and more widely spaced. This is not necessarily a dynamic time in the life cycle of a tree, excepting external processes such as fire, disease, or logging. The most value in monitoring the

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109 life cycle of a stand comes when th e trees are younger, with smaller stems and typically closer spacing. Stem based ITD is ineffective at this stage, and canopy based ITD can only provide so much information about detected trees. I am led to conclude that structural remote sensing from the UAS platform currently best tool, capable of quickly and repeatedly sampling plots and delivering useful information at the plot level. Individual tree inventor y from UAS remote sensing accurate to some arbitrarily acceptable value (say 5% or 10%) is not yet attainable for the typical Florida pine stand using stem based methods Canopy based methods may provide this level of accuracy, but cannot offer individual stem information. As sensor technology improves, the goal of ITD with stem information may soon be attainable.

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110 APPENDIX A VLP 16 CHARACTERIZATION EQUATIONS Note: The following equations and derivations include the work of Travis Whitley. Point Density Pr obability Density Function The first assumption that is presented is the angle of the laser firing from the lidar unit can be modeled as a uniform random variable i.e. This is valid since the lasers are being fired at a constant rate fro m the scanner head which is rotating at a constant angular velocity. The angle axis, as depicted in Figure B 1. It is also assumed that the sensor is travelling parallel to the ground along its axis of rotation i.e., at a constant height above ground at a constant velocity The frequency of the laser firings is designated as the variable The cumulative distribution function (CDF) of is: Note that this function limits to the range because no pulses emitted outside of this range will intersect with the ground below (see Figure A 1). The next step is to find the probability density function (PDF) of another random variable defined as the lateral distance of each laser return (in the direction) from the centerline of the laser return pattern (i.e., the line directly nadir to the flight line of the scanner). is a function of and c an be defined as where is the height of the sensor above the ground. The CDF of can then be defined as

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111 Substituting yields Because h is always positive: In verse tangent is an increasing one to one function, which allows for further rearranging: Substituting further yields The derivative yields the function To convert this PDF to a point density function as a function of or lateral distance from the centerline of the laser return pattern, the PDF is multiplied by the laser pulse frequency and divided by the forward velocity (Note that is divided by 2 because half of the laser firings will not intersect the ground.)

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112 Optimal Separation of Parallel Flight Lines With the equation for point density as a function of distance normal to the direction of flight, an equation can be derived that dictates the optimal separation distance betwe en two consecutive, parallel flight lines (defined as ) in order to achieve a desired minimum point density in the overlapping laser return pattern. This minimum point density will occur exactly halfway between the two centerlines of the overlapp ing laser return patterns. (This can be proven, as is an even function, but this proof will not be presented here.) To restate the equation for : Substituting the halfway point for and setting it equal to yields Solving for w yields This equation can be used in conjunction with the percent overlap of the field of view of the sensor. To find th e overlap, first the furthest lateral laser return is found using simple trigonometry : where is the maximum laser return range of the sensor. Once this is obtained, the percent overlap is defined as

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113 Substituting for yields Possible Positions of Coverage Gaps As discussed in Chapter 2, gaps in coverage of laser returns along the ground can occur in strips parallel to the direction of flight. These gaps may occur when consecutive hyperbolic paths of points (from consecutive passes of the scanner head through the range of downward facing azimuths ) intersect with each other, creating clusters of overlapping laser returns. These intersections will only occur where the separation between consecutive channels equals some integer multiple of the distance traveled by the scanner during one rot ation of the scanner head, or where is the forward velocity of the scanner and is the rotation rate of the scanner head. The separation will occur at some ranges from the scanner which can be expressed as where is the angular separation between channels (which, for the VLP 16, is 2). These ranges occur at some angles from nadir to the scanner With the scanner at flying height the lateral distance fr om the flight line of the strips of coverage gaps can be expressed as Because of the relationship between and the equation above can be rewritten as

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114 Substituting for y ields the gap equation Generalizing the Equations for Yaw The preceding derivations assume that the scanner is oriented such that the z axis of the scanner is parallel to the direction of travel to the scanner. In the case of yaw, the z axis of the scanner is rotated at some angle with respect to the direction of travel. The following equations can be further generalized to account for the yaw of scanner with respect to the direction of travel. Point d ensity p robability f unction The PDF of random variable is defined as the lateral distance of each laser return (in the direction) from the centerline of the laser return pattern is a function of (Figure A 1) and the yaw angle and ca n be defined as Thus the CDF of can then be defined as Substituting and rearranging further yields The derivative yields the function

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115 This is then converted to a PDF as a function of or lateral distance from the centerline of the laser return pattern : Optimal s eparation of f light l ines Substituting the halfway point for and setting it equal to where is the desired minimum point density in the overlapping laser return pattern yields Solving for w yields Gap equation Because the solution of the gap position equation is stated in terms of the variable the equation can be generalized to account for yaw simply by multiplying the results by the cosine of the yaw angle:

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116 Figure A 1. Nominal configuration of VLP 16 in relation to ground.

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117 APPENDIX B VLP 16 SIMULATION SOFTWARE Line Plane Intersection The VLP 16 simulation software models the laser return as an intersection of a line (laser pulse) and a plane (fla t ground). The target plane is defined by a point on the plane and a vector normal to the plane The software defines each laser pulse as a line, represented by a point the location of the scanner at the time of firing and a direction (The term is omitted below for simplicity.) This direction is initially represented by two angles, the azimuth and vertical angle reference frame. The software firs t converts this direction to a vector in the scanner frame : This vector is then rotated into the mapping frame The orientation of the scanner is known in terms of tilt and yaw ; these values are f ormed into rotation matrix which is the product axis and z axis : The scanner space vector is then rotated into object space, and is held as the direction of the line: (Note th The intersection of the line and plane is found by the common algebraic method, which is not pr esented here.

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118 Assumptions By default, t h e software models the VLP a target plane at a height of zero, with a normal parallel to the mapping frame +Z axis The laser returns are modeled by lines with a known direction passing through the scanner point and intersecting the target plane. The scanner is assumed to be oriented such that its local axis is coincident with the direction of tra vel, which has been arbitrarily chosen to be the mapping frame +Y axis is coincident with the Z axis in the mapping frame Adjustments to the angular orientation of the scanner namely, tilt and yaw can be made as optional input argu ments to the software. field of view, adjusting the roll would have practically no effect on the laser return pattern. Optimization The VLP 16 emits approximately 300,000 pulses per second; from the aerial pose, however, less than half of those pulses will reach the ground below, and even fewer will be within the maximum range at which the scanner can reliably mark a pulse as a return. To speed up the simulation of the laser return pattern, more than half of the pulses that wou ld be emitted by the VLP 16 need not be modeled. The software can also produce a representative profile of the laser return pattern, in from all sixteen channel s. This representative profile is a repeating pattern; except for the beginning and end of a flight line, an entire single strip of laser returns exhibits this pattern. The scanner need only travel a certain distance forward before such a profile exists in the laser return pattern. Thus, the software only needs to simulate the laser return pattern for a short duration of time (on the order of seconds) before terminating.

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119 Azimuth b ounds The range of azimuths at which laser pulses will produce a return can be found via simple trigonometry : axis ( ) points directly nadir; thus, the range of azimuths for which line plane intersections should be calculated is Note that t he maximum range of the VLP 16 has been found empirically to be 120 m, although the software does allow for manual adjustment to this value for the purposes of planning missions in which returns with ranges greater than a specified distance are eliminated (s ee Chapter 2). Even if the scanner is oriented with nonzero tilt and/or yaw, this range of azimuths is valid. Assuming the VLP 16 had a spherical, 360 field of view in all planes, the radius of this sphere would be The intersection of this sphere with the target plane is a circle, the radius of which is The angle between the point on the target plane directly below the scanner, the scanner itself, and any point along the edge of th is circle is equal to Time Bounds As mentioned earlier, the software can produce a representative profile of the laser return pattern. The scanner model only needs to travel a certain distance to create this profile. Because each second the m plane intersections to be calculated, it is crucial to strictly limit the flight time in the simulation. To limit the time that elapses in the simulation the exact distance the scann er must travel to create this representative profile must be found. The representative profile that receive pulses from all sixteen channels. The beginning of this repeating pattern is the

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120 far thest point at which the most forward facing channel strikes the ground from the which will be called Th e point is a function of the flying height tilt and yaw The scanner, therefore, m ust travel forward until its most rear facing channel reaches The point can be found via line plane intersection. For each line plane intersection calculated, the software requires as input, among other variables, the az imuth of the laser firing. Thus, the maximum azimuth of the channel. This value is not calculated along a line perpendicular to the direction of travel and passing through a point nadir to the scanner, which were the two assumptions used to find previously; a more general formula must be derived. The first assumption is to assume the location of the scanner is directly above the origin of the mapping frame at flying height: The scanner may be oriented with nonzero tilt a nd yaw, which can be represented by It is assumed that s ome laser pulse from the channel will reach the point Thus can be expressed as T his problem is visualized in Figure A 1. ( By the convention used in this paper, rotation matrices are used to rotate reference frames, or coordinate systems. For the problem of solving for the goal is to solve for a value in the that is define d in the scanner frame, ; thus, the inverse of the rotation matrix must be used to rotate the mapping frame into the scanner frame. The inverse of the rotation matrix could alternately defined as ) The equation above can be expan ded as:

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121 Solving for can be simplified by limiting the solution to only the z value of which, because it is on the target plane, is equal to zero: The simplification employed here results in an equation that is not a function of yaw. This is acceptable, because yaw has no effect on the orientation of a vector in the scanner frame. By virtue of this simplification, t he scope of this equation is limited to solving for the azimuth which is the laser pulse that reaches As stated previously, to create a representative p rofile, the scanner must travel some distance until its most rear facing channel reaches The scanner must then travel from that point for the time it takes for the scanner head to complete one full rotation, in order to assure tha t the laser return pattern is repeated at least once. The symmetry of the scan pattern can be exploited in order to find If the most forward reaching laser pulse reaches then it follows that, if the scanner is directly above the origin as previously assumed, the most rear facing laser pulse reaches The distance is the difference between the y components of and : The length of the repeating pattern is a function of forward speed ; but at most sensible speeds, this length is quite short, on the order of decimeters. For the sake of making the pattern more visible to a human user, the software allows for the representative profile to be of a predefined length usually on the order of 3 5 m. Thus, the software simulates the scanner traveling a

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122 distance of and only returns those points within the bounds of the representative profile. Because the simulation begins with the scanner above the origin and traveling in the +Y direct ion in the mapping frame, the points inside the profile are those with Y coordinates

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123 Figure B y and z axes are shown in red, green, and blue, respectivel y.

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124 APPENDIX C DERIVATION OF OBLIQUE UAS PHOTOGRAMMETRY EQUATIONS Air B ase and Air W idth The length of the extent of coverage of an image, or footprint in the direction of the tilt of the camera can be found as follows: In the above equations, flying height is denoted as field of view in the direction of flight at tile of the camera from nadir a s and the values and are intermediate values (Figure C 1). The air base for the exposure stations is expressed as a percentage of the length of the footprint in the direction of flight, which is reflected in the equation as presented in Chapte r 3. The width of the footprint is variable in the direction of travel of the camera. The footprint of a rectangular format camera, when tilted with respect to the target plane, will be in the shape of a trapezoid. For mission planning purposes, th e width of the footprint at a line intersecting and normal to the optical axis is used:

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125 where is the focal length. Similarly, the air width for the exposure stations is expressed as a percentage of the length of the footprint normal to the direction of flight, as expressed in the equation as presented in Chapter 3. Ground Sample Distance The ground sample distance (GSD) of a pixel in column is variable along the direction of tilt. Fo r columns of pixels, the GSD of a pixel in the direction of tilt or is expressed by :

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126 Figure C 1. Air base Figure C 2. Ground sample distance in the direction of tilt.

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127 APPENDIX D SIMULATING IMAGES IN MATLAB One facet of the UAS photogrammetric mission planning software described in Chapte r 4 involves creating simulated images of a simple test scene in a simulated object space. Each image is the projection of this test scene an array of 3D points onto the focal plane of a virtual camera. The position and angular attitude i.e., the external orientation parameters, of EOPs of each camera is defined by the mission parameters of flying height, tilt of camera from which itself is a function of focal length and size of format.) In other words, the position and orientation of each virtual focal plane is known with respect to the positions of the 3D array in the test scene. The position of a point in the test scene on the virtual image is where the line This alignment satisfies the collinearity condition; s olving for these positions, therefore, can be achieved using the collinearity equations. Furthermore, the collineari ty equations will be used to transform coordinates from object space to image space, so using a homogeneous representation of the collinearity equations will simplify the problem (Wolf et al. 2014). The collinearity equations as stated by Wolf et al. (2014 ) are These equations can be represented homogeneously as

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128 where are the homogeneous for point in image space; is the perspective projection transformation matrix which projects the homogeneous point onto the focal plane in image space; is the rotation matrix which represents the rotation of object space into image space; the translation matrix which represents the position of the focal point in object space; and the vector whi ch contains the coordinates for the object space point being projected. Although and above are represented as column vectors, they can in fact be and matrices, respectively, consisting of concatenated column vectors. Thus, multiple points in object space can be projected onto a single focal plane at once Simulating the images in MATLAB thus requires as input the 3D, object space coordinates of the points in the test scene, the EOPs of each camera, and the focal length (in pixels ) of the simulated camera. The projection is solved using the method described above, and the results in matrix represent the image space coordinates on the image place The final image space coordinates (i.e., the image space coordinates on plane ) are found by where the values of are in pixels. The image simulation also requires the size of the camera format (in pixels) so that all ize can be omitted from the image. Also, as stated in Chapter 3, random noise is added to the image projections. The noise values are pseudorandom numbers drawn from a standard Gaussian distribution, multiplied by to simulate noise of 0.5 pixel.

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129 APPENDIX E CONVERSION OF ROTATION DATA BETWEEN ENU AND NED FRAMES As stated in the Conclusion, the rotation data reported by the Xsens Mti G 710 is not directly useable as input in Agisoft PhotoScan. A conversion between the rotation angles reported by th e Xsens in the Easting Northing Up (ENU) frame and the rotations expected by PhotoScan in the Northing Easting Down (NED) frame is presented. Note that all coordinate systems presented here are right hand Cartesian systems. The convention used for camera o rientation is such that the image axis runs from left to right wing of the aircraft; the image axis runs from tail to nose; and the axis points downward perpendicular to the plane. PhotoScan accepts input for rotation angles in one of the following formats. 1. Omega phi kappa angles : sequential counterclockwise (CCW) rotations about the , and axes, respectively, of the image, where an image taken at results in a vertical (nadir) image oriented su ch that its horizontal axis is parallel with the easting axis of the local tangential plane (LTP) and its vertical axis is parallel with LTP northing. Put another way, the rotations are defined with respect to the ENU frame, which is parallel with the basis of the LTP. 2. Yaw pitch roll angles : sequential, CCW rotations about the down, easting, and northing axes of the airframe, where an image taken at indicates an image oriented as described above. Put differently, th e rotations are defined with respect to the Nor thing Easting Down (NED) frame. (The following definitions are found in the PhotoScan 1.4 User Manual (2018). Due to the configuration of the Xsens used during image collection, the rotation angles prov ided for each image are called yaw, pitch, and roll, but are defined differently than above. The Xsens standard defines yaw pitch roll as sequential CCW rotation s about the , and axe s; these rotations are referred to hereafter as Also by the Xsens standard, the axis, or roll axis, of the unit should point from tail to nose of the aircraft. Thus, the orientation of an image parallel with the LTP is reported as (Xsens, 2018).

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130 Conversion from to or is possible if a rotation matrix is defined for each system. To facilitate the conversion, the rotation matrix for each system will be defined in the ENU frame. Rotation Matrix from Yaw Pitch Roll, Xsens De finition The constr uction of a rotation matrix for must account for the convention of the roll axis of the unit being parallel with the axis of the image. This is achieved by constructing the rotation matrix using the reported values for yaw, pitch, and roll, and then rotating this rotation matrix by 90 about the twice rotated axis The r otation matrix is a series of transpose Givens rotations (Givens rotations as commonly defined rotate vectors in space; the tran spose will effectively rotate the space itself, which is the convention in photogrammetry.) For brevity, cosine and sine of some angle are denoted as and respectively. The values of the omega phi kapp a rotation angles can be found from this matrix using the definitions provided by Wolf et al. (2014):

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131 For the special case of gimbal lock, in which the twice rotated axis becomes either parallel or antiparallel to the once rotated axis, which would allow for ambiguous solutions. In the case of gimbal lock, is held and Rotation from Yaw Pitch Roll, Aviation Convention Yaw pitch roll is more commonly defined in the NED frame, as described in definition # 2 above. To construct a rotation matrix in the ENU frame from angl es, the orthogonal relationship of the NED and ENU frames can be exploite d to f o rm the alternate definition of as sequential, CCW rotations about the , and axes of the image. By alternately defining a CCW rotation about the axis as a clockwise (CW) rotation about the axis, the rotation matrix ca n be constructed as follows: From the original values for can be found by

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132 In the case of gimbal lock, where is held, and The following is presented as a proof of a simpler relationship between the Xsens and the conventional Through substitution it can be shown that This simple algebraic conversion was used in Chapter 3 to convert the reported rotation angles of the Xsens Mti G 710 from the Xsens convention to the PhotoScan conventi on.

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133 LIST OF REFERENCES Agisoft, 2018. Agisoft PhotoScan user manual, professional edition, version 1.4. Available: http://www.agisoft.com/pdf/photoscan pro_1_4_en.pdf (last date accessed: 02 July 2018). Avery, G., 1958. Helicopter stereo photography of f orest plots. Photogrammetric Engineering Vol. 24, no. 4, pp. 617 624. Baltsavias, E.P., 1999. Airborne laser scanning: basic relations and formulas. ISPRS Journal of Photogrammetry and Remote Sensing Vol. 54, pp. 199 214. Bohlin, J., J. Wallerman and J. E.S. Fransson, 2012. Forest variable estimation using photogrammetric matching of digital aerial images in combination with a high resolution DEM Scandinavian Journal of Forest Research Vol. 27, pp. 692 699. Clark, P.J. and F.C. Evans, 1954. Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology Vol. 35, pp. 445 453. Dandois, J.P. and E.C. Ellis, 2013. High spatial resolution three dimensional mapping of vegetation spectral dynamics using computer vision. Remote Sensin g of Environment Vol. 136, pp. 259 276. Dhondt, S., N. Wuyts and D. Inz, 2013. Cell to whole plant phenotyping: the best is yet to come. Trends in Plant Science Vol. 18, pp. 428 439. El Sheimy, N., 2008. Georeferencing component of LiDAR systems. In To pographic Laser Ranging and Scanning CRC Press, Boca Raton, FL. Fischler, M.A. and R.C. Bolles, 1981. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM Vol. 24, pp. 381 395. Fonstad, M.A., J.T. Dietrich, B.C. Courville, J.L. Jensen and P.E. Carbonneau, 2013. Topographic structure from motion: a new development in photogrammetric measurement. Earth Surface Processes and Landforms Vol. 38, no. 4, pp. 421 430. Frit z, A., T. Kattenbornand B. Koch, 2013. UAV based photogrammetric point clouds tree stem mapping in open stands in comparison to terrestrial laser scanner point clouds. International Archives of the Photogrammetry, Remote Sensing and Spatial Information S ciences Vol. 40, part 1/W2, pp. 141 146. Gagnon, P.A, J.P. Agnard and C. Nolette, 1993. Evaluation of a soft copy photogrammetry system for tree plot measurements. Canadian Journal of Forest Research Vol. 23, no. 9, pp. 1781 1785. Glennie, C. and D.D. L ichti, 2010. Static calibration and an a lysis of the Velodyne HDL 64E S2 for high accuracy mobile scanning. Remote Sensing, Vol. 2, pp. 1610 1624.

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134 Hartley, R. and A. Zimmerman, 2003. Multiple view geometry in computer vision. Cambridge University Press, New York. Isenburg, M., 2012. LAStools efficient tools for LiDAR processing. Available: http://www.cs.unc.edu/~isenburg/lastools/ (last date accessed: 02 June 2018). James, M.R. and S. Robson, 2014. Mitigating systematic error in topographic models derived fr om UAV and ground based image networks. Earth Surface Processes and Landforms Vol. 39, pp. 1413 1420. Kankare, V., M. Holopainen, M. Vastaranta, E. Puttonen, X. Yu, J. Hyypp, M. Vaaja, H. Hyypp and P. Alho, 2013. Individual tree biomass estimation usin g terrestrial laser scanning. ISPRS Journal of Photogrammetry and Remote Sensing Vol. 75, pp. 64 75. Rychard, P. Tymkw and A. Borkowski, 2016. UAV based automatic tree growth measurement for biomass estimation. Proceedings of th e 23 rd ISPRS Congress 12 19 July, Prague, Czech Republic, Vol. 41, part B8, pp. 685 688. Khosravipour, A., A.K. Skidmore, M. Isenburg, T. Wang, and Y.A. Hussin, 2014. Generatibe pit free canopy height models from airborne lidar. Photogrammet r ic Engineerin g & Remote Sensing Vol. 80, no. 9, pp. 863 872. Kirly, G. and G. Brolly, 2007. Tree height estimation methods for terrestrial laser scanning in a forest reserve. International Archives of Photogrammetry and Remote Sensing Vol. 36, part 3/W52, pp. 211 21 5. Korpela, I., B. Dahlin, H. Schfer, E. Bruun, F. Haapaniemi, J. Honkasalo, S. Ilvesniemi, V. Kuuti, M. Linkosalmi, J. Mustonen, M. Salo, O. Suomi and H. Virtanen, 2007. Single tree forest inventory using LiDAR and aerial images for 3D treetop positionin g, species recognition, height and crown width estimation. International Archives of Photogrammetry and Remote Sensing Vol. 36, part 3/W52, pp. 227 233. Limentani, G.B., M.C. Ringo, F. Ye, M.L. Bergquist and E.O. McSorley, 2005. Beyond the t test: statist ical equivalence testing. Analytical Chemistry Vol. 77, pp. 221A 226A. Li, W., Q. Guo, M.K. Jakubowski, and M. Kelly, 2012. A new method for segmenting individual trees from the lidar point cloud. Photogrammetric Engineering & Remote Sensing Vol. 78, pp. 75 84. Lin, Y., J. Hyypp and A. Jaakkola, 2011. Mini UAV borne lidar for fine scale mapping. IEEE Geoscience and Remote Sensing Letters, Vol. 8, pp. 426 430. Lingua, A., D. Marenchino and F. Nex, 2009. Performance analysis of the SIFT operator for autom atic feature extraction and matching in photogrammetric applications. Sensors Vol. 9, pp. 3745 3766.

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138 BIOGRAPHICAL SKETCH H. Andre w Lassiter received a Ph.D. in f orest r esources and c onservation, with a specialty in geomatics, from the University of Florida in 2018. His research focuses on mission planning for UAS remote sensing, particularly the development of simulation software for both lidar and structure from motion (SfM) photogra mmetric data collection, and quality assessment of data collected from different sensor configurations. He has also conducted research in automated and semi automated estimation of key traits of forest stands from point clouds collected from the terrestria l, mobile, and aerial stances. In partnership with the USGS National UAS Proje ct Office, Andrew joined the UF UAS Research Program in 2016 to assist in the collection and processing of lidar, photogrammetric, and hyperspectral data. Andrew served as a teac hing assistant at UF from 2013 2017 for the courses of Advanced Photogrammetry, Forest Resource Information Systems, Spatial Measurement Systems, and Geomatics. Prior to that, he worked as a survey technician in Panama City, Florida, in both the public and private sectors.