Image-Based Modeling / Edition 1

by Long Quan

Overview

“This book guides you in the journey of 3D modeling from the theory with elegant mathematics to applications with beautiful 3D model pictures. Written in a simple, straightforward, and concise manner, readers will learn the state of the art of 3D reconstruction and modeling.” —Professor Takeo Kanade, Carnegie Mellon University The computer vision and graphics communities use different terminologies for the same ideas. This book provides a translation, enabling graphics researchers to apply vision concepts, and vice-versa, independence of chapters allows readers to directly jump into a specific chapter of interest, compared to other texts, gives more succinct treatment overall, and focuses primarily on vision geometry. Image-Based Modeling is for graduate students, researchers, and engineers working in the areas of computer vision, computer graphics, image processing, robotics, virtual reality, and photogrammetry.

Product Details

ISBN-13:	9781441966780
Publisher:	Springer US
Publication date:	07/22/2010
Edition description:	2010
Pages:	251
Product dimensions:	6.10(w) x 9.20(h) x 0.80(d)

About the Author

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.

Table of Contents

Foreword vii

Preface ix

Acknowledgements xi

Notation xiii

1 Introduction 1

Part I Geometry: fundamentals of multi-view geometry

2 Geometry prerequisite 7

2.1 Introduction 8

2.2 Projective geometry 8

2.2.1 The basic concepts 8

2.2.2 Projective spaces and transformations 10

2.2.3 Affine and Euclidean specialization 16

2.3 Algebraic geometry 21

2.3.1 The simple methods 21

2.3.2 Ideals, varieties, and Gröbner bases 23

2.3.3 Solving polynomial equations with Gröbner bases 24

3 Multi-view geometry 29

3.1 Introduction 30

3.2 The single-view geometry 30

3.2.1 What is a camera? 30

3.2.2 Where is the camera? 35

3.2.3 The DLT calibration 37

3.2.4 The three-point pose algorithm 39

3.3 The uncalibrated two-view geometry 42

3.3.1 The fundamental matrix 43

3.3.2 The seven-point algorithm 45

3.3.3 The eight-point linear algorithm 46

3.4 The calibrated two-view geometry 47

3.4.1 The essential matrix 47

3.4.2 The five-point algorithm 49

3.5 The three-view geometry 53

3.5.1 The trifocal tensor 54

3.5.2 The six-point algorithm 58

3.5.3 The calibrated three views 63

3.6 The N-view geometry 66

3.6.1 The multi-linearities 66

3.6.2 Auto-calibration 68

3.7 Discussions 72

3.8 Bibliographic notes 72

Part II Computation: from pixels to 3D points

4 Feature point 77

4.1 Introduction 78

4.2 Points of interest 78

4.2.1 Tracking features 78

4.2.2 Matching corners 80

4.2.3 Discussions 81

4.3 Scale invariance 82

4.3.1 Invariance and stability 82

4.3.2 Scale, blob and Laplacian 82

4.3.3 Recognizing SIFT 83

4.4 Bibliographic notes 84

5 Structure from Motion 85

5.1 Introduction 86

5.1.1 Least squares and bundle adjustment 86

5.1.2 Robust statistics and RANSAC 88

5.2 The standard sparse approach 90

5.2.1 A sequence of images 92

5.2.2 A collection of images 93

5.3 The match propagation 94

5.3.1 The best-first match propagation 94

5.3.2 The properties of match propagation 97

5.3.3 Discussions 101

5.4 The quasi-dense approach 103

5.4.1 The quasi-dense resampling 103

5.4.2 The quasi-dense SFM 104

5.4.3 Results and discussions 111

5.5 Bibliographic notes 117

Part III Modeling: from 3D points to objects

6 Surface modeling 121

6.1 Introduction 122

6.2 Minimal surface functionals 123

6.3 A unified functional 124

6.4 Level-set method 124

6.5 A bounded regularization method 125

6.6 Implementation 127

6.7 Results and discussions 129

6.8 Bibliographic notes 136

7 Hair modeling 137

7.1 Introduction 138

7.2 Hair volume determination 139

7.3 Hair fiber recovery 140

7.3.1 Visibility determination 140

7.3.2 Orientation consistency 141

7.3.3 Orientation triangulation 141

7.4 Implementation 142

7.5 Results and discussions 144

7.6 Bibliographic notes 148

8 Tree modeling 149

8.1 Introduction 150

8.2 Branche recovery 153

8.2.1 Reconstruction of visible branches 153

8.2.2 Synthesis of occluded branches 155

8.2.3 Interactive editing 157

8.3 Leaf extraction and reconstruction 159

8.3.1 Leaf texture segmentation 159

8.3.2 Graph-based leaf extraction 162

8.3.3 Model-based leaf reconstruction 165

8.4 Results and discussions 167

8.5 Bibliographic notes 174

9 Façade modeling 177

9.1 Introduction 178

9.2 Façade initialization 180

9.2.1 Initial flat rectangle 181

9.2.2 Texture composition 181

9.2.3 Interactive refinement 183

9.3 Façade decomposition 184

9.3.1 Hidden structure discovery 184

9.3.2 Recursive subdivision 185

9.3.3 Repetitive pattern representation 186

9.3.4 Interactive subdivision refinement 187

9.4 Façade augmentation 188

9.4.1 Depth optimization 188

9.4.2 Cost definition 190

9.4.3 Interactive depth assignment 190

9.5 Façade completion 192

9.6 Results and discussions 192

9.7 Bibliographic notes 197

10 Building modeling 199

10.1 Introduction 200

10.2 Pre-processing 201

10.3 Building segmentation 203

10.3.1 Supervised class recognition 203

10.3.2 Multi-view semantic segmentation 205

10.4 Building partition 207

10.4.1 Global vertical alignment 208

10.4.2 Block separator 208

10.4.3 Local horizontal alignment 209

10.5 Façade modeling 210

10.5.1 Inverse orthographic composition 211

10.5.2 Structure analysis and regularization 213

10.5.3 Repetitive pattern rediscovery 216

10.5.4 Boundary regularization 217

10.6 Post-processing 218

10.7 Results and discussions 219

10.8 Bibliographic notes 224

List of algorithms 227

List of figures 229

References 237

Index 249