3D Shape Analysis

Preface xv
Acknowledgments xvii

1 Introduction 1
1.1 Motivation 1
1.2 The 3D Shape Analysis Problem 2
1.3 About This Book 5
1.4 Notation 9

Part I Foundations 11

2 Basic Elements of 3D Geometry and Topology 13
2.1 Elements of Differential Geometry 13
2.2 Shape, Shape Transformations, and Deformations 30
2.3 Summary and Further Reading 38

3 3D Acquisition and Preprocessing 41
3.1 Introduction 41
3.2 3D Acquisition 41
3.3 Preprocessing 3D Models 56
3.4 Summary and Further Reading 62

Part II 3D Shape Descriptors 65

4 Global Shape Descriptors 67
4.1 Introduction 67
4.2 Distribution-Based Descriptors 69
4.3 View-Based 3D Shape Descriptors 73
4.4 Spherical Function-Based Descriptors 77
4.5 Deep Neural Network-Based 3D Descriptors 83
4.6 Summary and Further Reading 89

5 Local Shape Descriptors 93
5.1 Introduction 93
5.2 Challenges and Criteria 94
5.3 3D Keypoint Detection 96
5.4 Local Feature Description 113
5.5 Feature Aggregation Using Bag of Feature Techniques 126
5.6 Summary and Further Reading 131

Part III 3D Correspondence and Registration 135

6 Rigid Registration 137
6.1 Introduction 137
6.2 Coarse Registration 138
6.3 Fine Registration 152
6.4 Summary and Further Reading 160

7 Nonrigid Registration 161
7.1 Introduction 161
7.2 Problem Formulation 162
7.3 Mathematical Tools 165
7.4 Isometric Correspondence and Registration 168
7.5 Nonisometric (Elastic) Correspondence and Registration 171
7.6 Summary and Further Reading 184

8 Semantic Correspondences 187
8.1 Introduction 187
8.2 Mathematical Formulation 188
8.3 Graph Representation 191
8.4 Energy Functions for Semantic Labeling 194
8.5 Semantic Labeling 196
8.6 Examples 202
8.7 Summary and Further Reading 204

Part IV Applications 207

9 Examples of 3D Semantic Applications 209
9.1 Introduction 209
9.2 Semantics: Shape or Status 209
9.3 Semantics: Class or Identity 212
9.4 Semantics: Behavior 216
9.5 Semantics: Position 219
9.6 Summary and Further Reading 221

10 3D Face Recognition 223
10.1 Introduction 223
10.2 3D Face Recognition Tasks, Challenges and Datasets 224
10.3 3D Face Recognition Methods 228
10.4 Summary 239

11 Object Recognition in 3D Scenes 241
11.1 Introduction 241
11.2 Surface Registration-Based Object Recognition Methods 241
11.3 Machine Learning-Based Object Recognition Methods 255
11.4 Summary and Further Reading 265

12 3D Shape Retrieval 267
12.1 Introduction 267
12.2 Benchmarks and Evaluation Criteria 270
12.3 Similarity Measures 275
12.4 3D Shape Retrieval Algorithms 280
12.5 Summary and Further Reading 284

13 Cross-domain Retrieval 285
13.1 Introduction 285
13.2 Challenges and Datasets 287
13.3 Siamese Network for Cross-domain Retrieval 290
13.4 3D Shape-centric Deep CNN 292
13.5 Summary and Further Reading 300

14 Conclusions and Perspectives 301

References 303
Index 337