Table Of ContentSpringer Series in Information Sciences 34
Springer-Verlag Berlin Heidelberg GmbH
ONLINE LIBRARY
Physics and Astronomy
http:// www.spri nger.de/phys/
Springer Series in Information Sciences
Editors: Thomas S. Huang Teuvo Kohonen Manfred R. Schroeder
30 Self-Organizing Maps
By T. Kohonen 3rd Edition
31 Music and Schema Theory
Cognitive Foundations of Systematic Musicology
By M. Leman
32 The Maximum Entropy Method
By N. Wu
33 A Few Steps Towards 3D Active Vision
By T. Vieville
34 Calibration and Orientation of Cameras in Computer Vision
Editors: A. Gruen and T. S. Huang
35 Computer Speech
Recognition, Compression, Synthesis
By M. R. Schroeder
Volumes 1-29 are listed at the end of the book.
Armin Gruen Thomas S.Huang (Eds.)
Calibration
and Orientation
of Cameras
in Computer Vision
With 77 Figures and 25 Tables
Springer
Professor Armin Gruen
ETH-Hiinggerberg
Institut fiir Geodăsie und Photogrammetrie
8093 Ztirich, SWITZERLAND
Professor Thomas S. Huang
University of Illinois
2039 Beckman Institute, 405 N. Mathews
Urbana, IL 61801, USA
Series Editors:
Professor Thomas S. Huang
University of Illinois, 2039 Beckman Institute, 405 N. Mathews,
Urbana, IL 61801, USA
Professor Teuvo Kohonen
Helsinki University of Technology, Neural Networks Research Centre
P.O. Box 5400,
02150 HUT, Espoo, FINLAND
Professor Dr. Manfred R. Schroeder
Drittes Physikalisches Institut, Universităt Giittingen, Btirgerstrasse 42-44
37073 Giittingen, GERMANY
ISSN 0720-678X
ISBN 978-3-642-08463-8
Library of Congress Cataloging-in-Publication Data
Calibration and orientatÎon of cameras in computer vision /
Armin Gruen. Thomas S. Huang (eds.).
p. cm. - (Springer series in information sciences, ISSN 0720-678X; 34)
Includes bibliographical references.
ISBN 978-3-642-08463-8 ISBN 978-3-662-04567-1 (eBook)
DOI 10.1007/978-3-662-04567-1
1. Computer vision. 2. Photogrammetry. 3. Cameras-Calibration.
I. Gruen, A. (Armin) II. Huang, Thomas S .. 1936- III. Series.
TA1634.C35 2001 62 1.39'9-dc2 I 2001020735
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Preface
This book was conceived during the Workshop "Calibration and Orientation
of Cameras in Computer Vision" at the XVIIth Congress of the ISPRS (In
ternational Society of Photogrammetry and Remote Sensing), in July 1992 in
Washington, D.C. The goal of this workshop was to bring photogrammetry
and computer vision experts together in order to exchange ideas, concepts
and approaches in camera calibration and orientation. These topics have been
addressed in photogrammetry research for a long time, starting in the sec
ond half of the 19th century. Over the years standard procedures have been
developed and implemented, in particular for metric cameras, such that in
the photogrammetric community such issues were considered as solved prob
lems. With the increased use of non-metric cameras (in photogrammetry they
are revealingly called "amateur" cameras), especially CCD cameras, and the
exciting possibilities of acquiring long image sequences quite effortlessly and
processing image data automatically, online and even in real-time, the need to
take a new and fresh look at various calibration and orientation issues became
obvious. Here most activities emerged through the computer vision commu
nity, which was somewhat unaware as to what had already been achieved in
photogrammetry. On the other hand, photogrammetrists seemed to ignore
the new and interesting studies, in particular on the problems of orienta
tion, that were being performed by computer vision experts. And it seems
that even nowadays the main interest that photogrammetrists take in the
work of computer vision scientists is in the areas of image analysis and scene
understanding.
For various reasons it took almost a decade to finally put this book to
gether and publish it. Nevertheless, the content of this book is still relevant.
Since 1992 there has been of course some progress in the understanding and
solving of orientation problems and also in calibration, but we hope to have
captured at least some of these developments through a recent chapter up
dating cycle.
We have brought together internationally renowned authors, both from
photogrammetry and computer vision, all of them experts in their respective
fields. We present in total seven chapters, with four contributions from pho
togrammetrists and three by computer vision experts. This is not a textbook.
Therefore, it is neither consistent in diction nor in content. It is not complete
VI Preface
in the coverage of all interesting issues and it has certain overlaps. This is
intended and simply reflects the current situation in the research fields of
photogrammetry and computer vision.
We hope that this book represents interesting study material for students,
researchers, developers and practitioners alike. If readers from photogramme
try and computer vision find the material equally rewarding then one of our
original goals is achieved: To bring both communities together on the basis
of some very exciting scientific and technical subjects.
It is with great pleasure and respect that I thank the authors for their
stimulating contributions and enduring patience and the publisher for not
giving up on this book over the many years of preparation.
Zurich, March 2001 Armin Gruen
Contents
1 Introduction 1
Armin Gruen
2 Minimum Solutions for Orientation 7
Bernhard P. Wrobel
Summary...................................................... 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Standard Orientation Tasks of Photogrammetry
and Computer Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Minimum Solutions for Orientation
Using Correspondent Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.1 2D-2D Relative Orientation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.2 2D-3D Image Orientation (Space Resection) . . . . . . . . . . . . . . . . 29
2.3.3 3D-3D Absolute Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Uniqueness Conditions of Basic Orientation Tasks.. . . . . . . . . . . . . . . 35
2.4.1 Representation of Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.2 The Terms Critical Configurations of First and Second Kind:
a Geometrical Interpretation by Two Examples . . . . . . . . . . . . . 38
2.4.3 Uniqueness Conditions of 2D-2D Relative Orientation. . . . . . . . 41
2.4.4 Uniqueness Conditions
of 2D-3D Image Orientation (Space Resection) . . . . . . . . . . . . . . 48
2.5 Conclusion.................................................. 54
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3 Generic Estimation Procedures for Orientation
with Minimum and Redundant Information . . . . . . . . . . . . . . . . . . 63
Wolfgang Forstner
Summary ...................................................... 63
3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2 Problem Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.1 Error Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2.2 Issues in Error Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.3 Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3.1 Quality Assurance....................................... 68
3.3.2 Instabilities of Estimates or "How Small is too Small?" . . . . . . . 70
VIII Preface
3.3.3 Model Errors or "How Sensitive is the Result?" . . . . . . . . . . . . . 74
3.3.4 Robust Estimation or "How to React on Blunders" . . . . . . . . . . 82
3.4 Generic Estimation Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.4.1 Rules for Choosing Robust Estimation Techniques. . . . . . . . . . . 86
3.4.2 Integrating Robust Estimation and Diagnosis . . . . . . . . . . . . . . . 89
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Appendix
A Algebraic Expression for the Normal Equations of Spatial Resection
with Four Parts in Symmetric Position. . . . . . . . . . . . . . . . . . . . . . . . . . 92
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4 Photogrammetric Camera Component Calibration:
A Review of Analytical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Clive S. Fraser
Summary ...................................................... 95
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2 Analytical Restitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2.1 Interior and Exterior Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2.2 Collinearity Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.2.3 The DLT ............................................... 101
4.3 Parameterization of Departures from Collinearity ................ 102
4.3.1 Sources of Perturbation .................................. 102
4.3.2 Radial Distortion ........................................ 103
4.3.3 Decentering Distortion ................................... 105
4.3.4 Focal Plane Unfiatness ................................... 106
4.3.5 Focal Plane Distortion ................................... 108
4.3.6 A Practical Model for In-Plane and Out-of-Plane Effects ..... 108
4.3. 7 Interior Orientation Elements ............................. 109
4.4 Determination of Camera Calibration Parameters ................ 112
4.4.1 A General Photogrammetric Model ........................ 112
4.4.2 Test-Range Calibration .................................. 113
4.4.3 Self-Calibration ......................................... 114
4.4.4 Distortion Calibration via the Plumbline Technique .......... 116
4.5 Concluding Remarks ......................................... 118
References ..................................................... 119
5 Least-Squares Camera Calibration
Including Lens Distortion and Automatic Editing
of Calibration Points ......................................... 123
Donald B. Gennery
Summary ...................................................... 123
5.1 Introduction ................................................. 123
5.2 Definition of Camera Model .................................. 124
5.2.1 Camera Model Without Distortion ........................ 124
5.2.2 Inclusion of Distortion ................................... 125
Preface IX
5.3 Partial Derivatives ........................................... 127
5.4 Adjustment of Camera Model ................................. 128
5.4.1 Data for Adjustment ..................................... 128
5.4.2 Initialization ............................................ 129
5.4.3 Iterative Solution ....................................... 130
5.5 Use of Camera Model ........................................ 133
5.5.1 Projecting from Object Space to Image Space ............... 133
5.5.2 Projecting from Image Space to Object Space ............... 134
Acknowledgements .............................................. 136
References ..................................................... 136
6 Modeling and Calibration
of Variable-Parameter Camera Systems ....................... 137
Reg G. Willson and Steven A. Shafer
Summary ...................................................... 137
6.1 Abstract Camera Models ...................................... 137
6.1.1 Building Multi-Degree-of-Freedom Camera Models ........... 138
6.1.2 Applying MDOF Camera Models to Vision Tasks .., ......... 149
6.1.3 A General Theory of Camera Modeling and Calibration ...... 155
Acknowledgements .............................................. 160
Reference ...................................................... 161
7 System Calibration Through Self-Calibration .............. 163
Armin Gruen and Horst A. Beyer
Summary ...................................................... 163
7.1 Introduction ................................................. 163
7.2 The Concept of Self-Calibration ............................... 164
7.2.1 The Bundle Method ..................................... 164
7.2.2 Least Squares Estimation ................................. 166
7.2.3 Systematic Error Compensation by Self-Calibration .......... 168
7.2.4 Treatment of Additional Parameters ....................... 170
7.3 Determinability of Self-Calibration Parameters
Under Various Network Conditions ............................. 172
7.4 A Final System Test ......................................... 180
7.5 Conclusions ................................................. 183
Appendix
A Algebraic Determinability of Additional Parameters ............... 184
B Trace Check of Covariance Matrix .............................. 186
C Results of Computational Versions for the Determinability
of Additional Parameters ..................................... 189
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
X Preface
8 Self-Calibration of a Stereo Rig
from Unknown Camera Motions and Point Correspondences 195
Quang-Tuan Luong and Olivier D. Faugeras
Summary ...................................................... 195
8.1 Introduction ................................................. 195
8.1.1 The Stereo Calibration Problem ........................... 195
8.1.2 What do we Mean by Self-Calibration ...................... 197
8.1.3 An Outline of our Autonomous Approach .................. 199
8.2 Computing the Fundamental Matrix ............................ 201
8.2.1 The Fundamental Matrix and the Epipolar Transformation ... 201
8.2.2 A Robust Method for the Determination
of the Fundamental Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
8.3 Computing the Intrinsic Parameters
of the Cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
8.3.1 The Principle of the Method .............................. 204
8.3.2 Kruppa Equations
Arising from an Epipolar Transformation ................... 205
8.3.3 Kruppa Coefficients and Intrinsic Parameters ............... 206
8.3.4 Solving the Kruppa Equations ............................ 207
8.4 Computing the Motion of the Camera .......................... 208
8.4.1 Two Approaches Based on the Computation
of the Fundamental Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
8.4.2 An Experimental Comparison ............................. 210
8.5 Computing the Extrinsic Parameters of a Stereo Rig ............. 213
8.5.1 A Direct Approach: Binocular and Trinocular Stereo Rig ..... 215
8.5.2 An Indirect, Monocular Approach ......................... 216
8.6 Experimental Results ......................................... 219
8.6.1 An Example of Calibration of a Binocular Stereo Rig ........ 219
8.6.2 Reconstructions from a Triplet of Uncalibrated Images
Taken by a Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
8. 7 Conclusion .................................................. 226
Acknowledgements .............................................. 226
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Index ......................................................... 231
