3D Shape Analysis: Fundamentals, Theory, and Applications (Hardcover)

Contents

Preface vii

Acknowledgements  ix

1 Introduction  1

1.1 Motivation 1

1.2 The 3D shape analysis problem 2

1.3 About this book 5

1.4 Notation 7

Part I  Foundations  11

2 Basic elements of 3D geometry and topology 13

2.1 Elements of differential geometry 13

2.1.1 Parametric curves 13

2.1.2 Continuous surfaces 15

2.1.3 Manifolds, metrics, and geodesics 21

2.1.4 Discrete surfaces 23

2.2 Shape, shape transformations and deformations  29

2.2.1 Shape-preserving transformations  29

2.2.2 Shape deformations 33

2.2.3 Bending 34

2.2.4 Stretching 35

2.3 Summary and further reading  36

3 3D acquisition and pre-processing 39

3.1 Introduction 39

3.2 3D acquisition 39

3.2.1 Contact 3D acquisition 41

3.2.2 Non-contact 3D acquisition 42

3.3 Pre-processing 3D models 52

3.3.1 Surface smoothing and fairing 53

3.3.2 Spherical parameterization of 3D surfaces 55

3.4 Summary and further reading 58

Part II  3D Shape Descriptors  61

4 Global shape descriptors 63

4.1 Introduction 63

4.2 Distribution-based descriptors  65

4.2.1 Point sampling 65

4.2.2 Geometric features 66

4.2.3 Signature construction and comparison 67

4.3 View-based 3D shape descriptors 69

4.3.1 The Light Field Descriptors (LFD) 70

4.3.2 Feature extraction 71

4.3.3 Properties 72

4.4 Spherical function-based descriptors  72

4.4.1 Spherical shape functions 74

4.4.2 Comparing spherical functions 75

4.5 Deep Neural Network-based 3D descriptors 78

4.5.1 CNN-based image descriptors 79

4.5.2 Multiview CNN for 3D shapes 81

4.5.3 Volumetric CNN 82

4.6 Summary and further reading 84

5 Local shape descriptors 87

5.1 Introduction 87

5.2 Challenges and criteria  88

5.2.1 Challenges 88

5.2.2 Criteria for 3D keypoint detection 89

5.2.3 Criteria for local feature description 89

5.3 3D keypoint detection 90

5.3.1 Fixed-scale keypoint detection 91

5.3.2 Adaptive-scale keypoint detection 94

5.4 Local feature description  105

5.4.1 Signature based methods 106

5.4.2 Histogram based methods 108

5.4.3 Covariance based methods 116

5.5 Feature aggregation using Bag of Feature techniques 117

5.5.1 Dictionary construction  118

5.5.2 Coding and pooling schemes 119

5.5.3 Vector of locally aggregated descriptors (VLAD) 120

5.5.4 Vector of Locally Aggregated Tensors (VLAT) 121

5.6 Summary and further reading 122

5.6.1 Summary of 3D keypoint detection 122

5.6.2 Summary of local feature description 123

5.6.3 Summary of feature aggregation 124

Part III 3D Correspondence and Registration  127

6 Rigid registration 129

6.1 Introduction 129

6.2 Coarse registration 130

6.2.1 Point correspondence-based registration 130

6.2.2 Line based registration  134

6.2.3 Surface based registration 137

6.3 Fine registration 143

6.3.1 Iterative Closest Point (ICP) 143

6.3.2 ICP variants 146

6.3.3 Coherent point drift 148

6.4 Summary and further reading  150

7 Nonrigid Registration 153

7.1 Introduction 153

7.2 Problem formulation 154

7.3 Mathematical tools 157

7.3.1 The space of diffeomorphisms 157

7.3.2 Parameterizing spaces 158

7.4 Isometric correspondence and registration  160

7.4.1 Möbius voting 160

7.4.2 Examples 161

7.5 Non-isometric (elastic) correspondence and registration  162

7.5.1 Surface deformation models 163

7.5.2 Square-Root Normal Fields (SRNF) representation 164

7.5.3 Numerical inversion of SRNF maps 166

7.5.4 Correspondence 168

7.5.5 Elastic registration and geodesics 172

7.5.6 Co-registration 174

7.6 Summary and further reading  176

8 Semantic correspondences 179

8.1 Introduction 179

8.2 Mathematical formulation  180

8.3 Graph representation 182

8.3.1 Characterizing the local geometry and the spatial relations  183

8.3.2 Cross mesh pairing of patches 184

8.4 Energy functions for semantic labelling 185

8.4.1 The data term 186

8.4.2 Smoothness terms  186

8.4.3 The inter-mesh term 188

8.5 Semantic labelling 188

8.5.1 Unsupervised clustering 188

8.5.2 Learning the labelling likelihood 190

8.5.3 Learning the remaining parameters 192

8.5.4 Optimization using Graph Cuts 193

8.6 Examples 194

8.7 Summary and further reading  196

Part IV Applications 199

9 Examples of 3D semantic applications 201

9.1 Introduction 201

9.2 Semantics: Shape or Status 201

9.3 Semantics: Class or Identity 204

9.4 Semantics: Behavior 207

9.5 Semantics: Position 210

9.6 Summary and further reading  212

10 3D face recognition 213

10.1 Introduction 213

10.2 3D face recognition tasks, challenges and datasets 213

10.2.1 3D face recognition challenges 215

10.2.2 3D face datasets 217

10.3 3D face recognition methods 218

10.3.1 Holistic approaches 220

10.3.2 Local feature-based matching 223

10.4 Summary 227

11 Object recognition in 3D scenes 229

11.1 Introduction 229

11.2 Surface registration-based object recognition methods  229

11.2.1 Feature matching 230

11.2.2 Hypothesis generation  230

11.2.3 Hypothesis verification 236

11.3 Machine learning-based object recognition methods 242

11.3.1 Hough forest-based 3D object detection 242

11.3.2 Deep learning-based 3D object recognition 246

11.4 Summary and further reading  250

12 3D shape retrieval 253

12.1 Introduction 253

12.2 Benchmarks and evaluation criteria 255

12.2.1 3D datasets and benchmarks 256

12.2.2 Performance evaluation metrics 257

12.3 Similarity measures 260

12.3.1 Dissimilarity measures 261

12.3.2 Hashing and Hamming distance 261

12.3.3 Manifold ranking 263

12.4 3D shape retrieval algorithms 265

12.4.1 Using handcrafted features 265

12.4.2 Deep Learning-based methods 267

12.5 Summary and further reading  268

13 Cross-domain retrieval 271

13.1 Introduction 271

13.2 Challenges and datasets 273

13.2.1 Datasets 274

13.2.2 Training data synthesis 275

13.3 Siamese network for cross-domain retrieval 276

13.4 3D shape-centric deep CNN 278

13.4.1 embedding space construction  279

13.4.2 Learning shapes from synthesized data 282

13.4.3 Image and sketch projection 283

13.5 Summary and further reading  285

14 Conclusions and perspectives 287