Image-Based Modeling (eBook)

Long Quan is a Professor of the Department of Computer Science and Engineering at the Hong Kong University of Science and Technology. He received a Ph.D. degree in Computer Science from France, and has been a CNRS researcher at INRIA. Professor Quan is a Fellow of the IEEE Computer Society.

Foreword 6
Preface 7
Acknowledgements 9
Notation 10
Contents 11
Introduction 15
Part I Geometry: fundamentals of multi-view geometry 19
Geometry prerequisite 20
2.1 Introduction 21
2.2 Projective geometry 21
2.2.1 The basic concepts 21
2.2.2 Projective spaces and transformations 23
2.2.3 Affine and Euclidean specialization 29
2.3 Algebraic geometry 34
2.3.1 The simple methods 34
2.3.2 Ideals, varieties, and Gr¨obner bases 36
2.3.3 Solving polynomial equations with Gr¨obner bases 37
Multi-view geometry 41
3.1 Introduction 42
3.2 The single-view geometry 42
3.2.1 What is a camera? 42
3.2.2 Where is the camera? 47
3.2.3 The DLT calibration 49
3.2.4 The three-point pose algorithm 51
3.3 The uncalibrated two-view geometry 54
3.3.1 The fundamental matrix 55
3.3.2 The seven-point algorithm 57
3.3.3 The eight-point linear algorithm 58
3.4 The calibrated two-view geometry 59
3.4.1 The essential matrix 59
3.4.2 The five-point algorithm 61
3.5 The three-view geometry 65
3.5.1 The trifocal tensor 66
3.5.2 The six-point algorithm 70
3.5.3 The calibrated three views 75
3.6 The N-view geometry 78
3.6.1 The multi-linearities 78
3.6.2 Auto-calibration 80
3.7 Discussions 84
3.8 Bibliographic notes 84
Part II Computation: from pixels to 3D points 86
Feature point 87
4.1 Introduction 88
4.2 Points of interest 88
4.2.1 Tracking features 88
4.2.2 Matching corners 90
4.2.3 Discussions 91
4.3 Scale invariance 92
4.3.1 Invariance and stability 92
4.3.2 Scale, blob and Laplacian 92
4.3.3 Recognizing SIFT 93
4.4 Bibliographic notes 94
Structure from Motion 95
5.1 Introduction 96
5.1.1 Least squares and bundle adjustment 96
5.1.2 Robust statistics and RANSAC 98
5.2 The standard sparse approach 100
5.2.1 A sequence of images 102
5.2.2 A collection of images 103
5.3 The match propagation 104
5.3.1 The best-first match propagation 104
5.3.2 The properties of match propagation 107
5.3.3 Discussions 111
5.4 The quasi-dense approach 113
5.4.1 The quasi-dense resampling 113
5.4.2 The quasi-dense SFM 114
5.4.3 Results and discussions 121
5.5 Bibliographic notes 127
Part III Modeling: from 3D points to objects 129
Surface modeling 130
6.1 Introduction 131
6.2 Minimal surface functionals 132
6.3 A unified functional 133
6.4 Level-set method 133
6.5 A bounded regularization method 134
6.6 Implementation 136
6.7 Results and discussions 138
6.8 Bibliographic notes 145
Hair modeling 146
7.1 Introduction 147
7.2 Hair volume determination 148
7.3 Hair fiber recovery 149
7.3.1 Visibility determination 149
7.3.2 Orientation consistency 150
7.3.3 Orientation triangulation 150
7.4 Implementation 151
7.5 Results and discussions 153
7.6 Bibliographic notes 157
Tree modeling 158
8.1 Introduction 159
8.2 Branche recovery 162
8.2.1 Reconstruction of visible branches 162
8.2.2 Synthesis of occluded branches 164
8.2.3 Interactive editing 166
8.3 Leaf extraction and reconstruction 168
8.3.1 Leaf texture segmentation 168
8.3.2 Graph-based leaf extraction 171
8.3.3 Model-based leaf reconstruction 174
8.4 Results and discussions 176
8.5 Bibliographic notes 183
Fac¸ade modeling 185
9.1 Introduction 186
9.2 Fac¸ade initialization 188
9.2.1 Initial flat rectangle 189
9.2.2 Texture composition 189
9.2.3 Interactive refinement 191
9.3 Fac¸ade decomposition 192
9.3.1 Hidden structure discovery 192
9.3.2 Recursive subdivision 193
9.3.3 Repetitive pattern representation 194
9.3.4 Interactive subdivision refinement 195
9.4 Fac¸ade augmentation 196
9.4.1 Depth optimization 196
9.4.2 Cost definition 198
9.4.3 Interactive depth assignment 198
9.5 Fac¸ade completion 200
9.6 Results and discussions 200
9.7 Bibliographic notes 205
Building modeling 207
10.1 Introduction 208
10.2 Pre-processing 209
10.3 Building segmentation 211
10.3.1 Supervised class recognition 211
10.3.2 Multi-view semantic segmentation 213
10.4 Building partition 215
10.4.1 Global vertical alignment 216
10.4.2 Block separator 216
10.4.3 Local horizontal alignment 217
10.5 Fac¸ade modeling 218
10.5.1 Inverse orthographic composition 219
10.5.2 Structure analysis and regularization 221
10.5.3 Repetitive pattern rediscovery 224
10.5.4 Boundary regularization 225
10.6 Post-processing 226
10.7 Results and discussions 227
10.8 Bibliographic notes 232
List of Algorithms 234
List of Figures 235
References 243
Index 255