single view coplanar photogrammetry and uncertainty analysis for traffic accident reconstruction

104 Pages·2014·2.17 MB·English

SINGLE VIEW COPLANAR PHOTOGRAMMETRY
AND UNCERTAINTY ANALYSIS FOR TRAFFIC
ACCIDENT RECONSTRUCTION
A Thesis
Submitted to the Faculty of Graduate Studies and Research
In Partial Fulfillment of the Requirements for the
Degree of Master of Applied Science in
Industrial Systems Engineering at the
University of Regina

by
Mehrdad Bakhtiari
Regina, Saskatchewan
June 2014

 2014:M.Bakhtiari
UNIVERSITY OF REGINA

FACULTY OF GRADUATE STUDIES AND RESEARCH

SUPERVISORY AND EXAMINING COMMITTEE

Mehrdad Bakhtiari, candidate for the degree of Master of Applied Science in Industrial
Systems Engineering, has presented a thesis titled, Single View Coplanar
photogrammetry and Uncertainty Analysis for Traffic Accident Reconstruction, in an
oral examination held on June 9, 2014. The following committee members have found the
thesis acceptable in form and content, and that the candidate demonstrated satisfactory
knowledge of the subject material.

External Examiner: Dr. Howard Hamilton, Department of Computer Science

Supervisor: Dr. Raman Paranjape, Electronic Systems Engineering

Committee Member: Dr. Amir Henni, Industrial Systems Engineering

Committee Member: Dr. Adisorn Aroonwilas, Industrial Systems Engineering

Chair of Defense: Dr. Jim Farney, Department of Political Science
Abstract
Photogrammetry is defined as the science of measuring distances and objects by using
photographs. Rapid advances in computer technology and digital photography in recent
years have resulted in growing applications of digital photogrammetry. Although various
aspects of photogrammetry have been investigated; the question of uncertainties in
measurement, which is important for forensic applications, such as traffic accident
reconstruction, has not been widely explored. This study attempted to develop an
applicable comprehensive mathematical model to perform coplanar photogrammetry and
provide a measure of uncertainty for its measurements. Photogrammetry requires
information about the interior and exterior orientation of the camera. Process maximum
likelihood estimation (MLE) of the interior parameters of the camera or camera
calibration and methods to provide uncertainty for those parameters are discussed. To
find the maximum likelihood estimation of the exterior orientation of the camera, a new
pose estimation algorithm has been developed that requires only information about the
length of three or more lines in the scene while taking into account nonlinearities due to
lens distortion. Formulation to find the maximum likelihood estimation of back
projection of individual points to world frame considering uncertainties in interior and
exterior orientation has been provided. Finally, all uncertain models have been compiled
into an uncertain comprehensive model for photogrammetric measurement on a coplanar
scene. A computer application equipped with a simulation tool has been developed for
the Windows operating system to implement the model. A simulation has been performed
to investigate the effect of various parameters on photogrammetry measurement and it
was found that the error in the length of reference lines has the most significant effect.
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Aerial photos of a mock accident scene were used for the experimental study. Experiment
results showed that the proposed method can provide distance measurement with an
average error of 1%, while the uncertainty for its measurements follows the three-sigma
rule.
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Acknowledgment
Firsthand and foremost, I am indebted to my supervisor Dr. Raman Paranjape for all the
guidance, supports and encouragements he provided me during my years in University of
Regina, without whom my study would never have been finished. I also owe a particular
thank to my program chair Dr. Amr Henni whom I benefited from his wise advice and
enjoyed his backings at different stages of my study. My gratitude again goes to Sgt.
Ryan Case for providing me with invaluable insight into collision reconstruction science
and the opportunity to perform data collection. Thanks go as well to my colleague in the
University of Regina UAV group Mr. Seang Cau for his assistance in my experiments. I
also need to thank Saskatchewan Government Insurance company for providing financial
support for this project.

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Table of Contents
Abstract ............................................................................................................................... ii
Acknowledgment ............................................................................................................... iv
Table of Contents ................................................................................................................ v
List of Tables ...................................................................................................................... x
List of Figures .................................................................................................................... xi
Nomenclature ................................................................................................................... xiii
1. Introduction ..................................................................................................................... 1
1.1. Definitions ................................................................................................................ 1
1.2. Historical Overview ................................................................................................. 1
1.3. Photogrammetry for Traffic Accident Reconstruction............................................. 3
1.4. Problem Statement ................................................................................................... 6
1.5. Thesis Structure ........................................................................................................ 7
2. Theoretical Foundation and Mathematical Models ........................................................ 9
2.1. Introduction .............................................................................................................. 9
2.2. Camera Projection Model......................................................................................... 9
2.2.1. Central Projection Camera Model and Perspective Transform ......................... 9
2.2.2. Digital Cameras and Pixel Coordinate Representation ................................... 12
2.2.3. Lens Distortion ................................................................................................ 13
2.2.4. Complete Projection Model ............................................................................. 16
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2.3. Camera Calibration ................................................................................................ 17
2.3.1. Introduction ..................................................................................................... 17
2.3.2. Zhang’s Calibration Method ............................................................................ 19
2.3.2.1. Overview .................................................................................................. 19
2.3.2.2. Closed Form Solution .............................................................................. 22
2.3.2.3. Refining intrinsic and extrinsic parameters ............................................. 24
2.3.2.4. Finding Radial Distortion Coefficients .................................................... 25
2.3.2.5. Complete Maximum Likelihood Estimation ........................................... 25
2.3.3. Calibration Parameters .................................................................................... 26
2.4. Planar Scene Reconstruction .................................................................................. 26
2.4.1. Closed Form Initial Guess ............................................................................... 26
2.4.2. Maximum Likelihood Estimation for Back-Projection ................................... 28
2.5. Pose Estimation ...................................................................................................... 28
2.5.1. Overview ......................................................................................................... 28
2.5.2. PnP Pose Estimation Algorithms ..................................................................... 30
2.5.3. Studied PnL Pose Estimation Algorithms ....................................................... 31
2.5.4. Limitations of Conventional Pose Estimation Algorithms .............................. 32
2.5.5. Pose Estimation Algorithm .............................................................................. 34
2.5.6. Proof of Preserving Line Segment Lengths with Proposed Algorithm ........... 34
2.5.7. Maximum Likelihood Estimation for Pose ..................................................... 38
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2.6. Least Square Methods and Maximum Likelihood Estimation ............................... 40
2.6.1. Overview ......................................................................................................... 40
2.6.2. Definitions ....................................................................................................... 40
2.6.3. Gauss-Newton Algorithm ................................................................................ 41
2.6.4. Levenberg-Marquardt Algorithm .................................................................... 43
2.6.5. Uncertainty in Model Parameters .................................................................... 44
2.6.6. Uncertainty in Model Predictions .................................................................... 45
2.6.7. Calculation of Jacobian Matrix ........................................................................ 45
2.6.8. Uncertainties in Camera Intrinsic and Lens Distortion Parameters ................ 46
2.6.9. Uncertainty in Pose Estimation ....................................................................... 47
2.6.10. Uncertainty in Scene Reconstruction ............................................................ 47
2.6.11. Uncertainty in Measured Lengths.................................................................. 47
3. Implementation ............................................................................................................. 49
3.1. Introduction ............................................................................................................ 49
3.2. Developed Computer Software .............................................................................. 51
3.2.1. Overview ......................................................................................................... 51
3.2.2. Calibration Tab ................................................................................................ 51
3.2.3. Pose Estimation Tab ........................................................................................ 52
3.2.4. Photogrammetry Tab ....................................................................................... 52
3.3. Numerical and Image Processing Libraries ........................................................... 53
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3.3.1. Overview ......................................................................................................... 53
3.3.2. Emgu CV ......................................................................................................... 53
3.3.3. ALGLIB........................................................................................................... 54
3.4. Simulation Tool ...................................................................................................... 56
3.5. Summary ................................................................................................................ 58
4. Results and Discussion ................................................................................................. 59
4.1. Overview ................................................................................................................ 59
4.2. Simulation .............................................................................................................. 60
4.2.1. Scene Configuration ........................................................................................ 60
4.2.2. Simulation Results ........................................................................................... 61
4.2.3. Simulation Scenarios ....................................................................................... 61
4.2.4. Effect of Error in Reference Line Measured Length ....................................... 62
4.2.5. Effect of Error in Pixel Selection of Reference Lines ..................................... 64
4.2.6. Effect of Camera Height and Look Direction ................................................. 66
4.2.7. Camera Focal Length and Principal Point ....................................................... 68
4.3. Experiment ............................................................................................................. 70
4.3.1. Overview ......................................................................................................... 70
4.3.2. Experimental Setup.......................................................................................... 70
4.3.3. Measurement with the Total Station ................................................................ 71
4.3.4. Camera Calibration .......................................................................................... 74
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4.3.5. Pose Estimation and Photogrammetry Analysis .............................................. 74
4.3.6. Comparison between Total Station and Photogrammetry ............................... 77
4.3.7. Summary .......................................................................................................... 78
5. Conclusion and Further works ...................................................................................... 80
References ......................................................................................................................... 84

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