3D Shape Analysis

An in-depth description of the state-of-the-art of 3D shape analysis techniques and their applications This book discusses the different topics that come under the title of &quote;3D shape analysis&quote;. It covers the theoretical foundations and the major solutions that have been presented in the literature. It also establishes links between solutions proposed by different communities that studied 3D shape, such as mathematics and statistics, medical imaging, computer vision, and computer graphics. The first part of 3D Shape Analysis: Fundamentals, Theory, and Applications provides a review of the background concepts such as methods for the acquisition and representation of 3D geometries, and the fundamentals of geometry and topology. It specifically covers stereo matching, structured light, and intrinsic vs. extrinsic properties of shape. Parts 2 and 3 present a range of mathematical and algorithmic tools (which are used for e.g., global descriptors, keypoint detectors, local feature descriptors, and algorithms) that are commonly used for the detection, registration, recognition, classification, and retrieval of 3D objects. Both also place strong emphasis on recent techniques motivated by the spread of commodity devices for 3D acquisition. Part 4 demonstrates the use of these techniques in a selection of 3D shape analysis applications. It covers 3D face recognition, object recognition in 3D scenes, and 3D shape retrieval. It also discusses examples of semantic applications and cross domain 3D retrieval, i.e. how to retrieve 3D models using various types of modalities, e.g. sketches and/or images. The book concludes with a summary of the main ideas and discussions of the future trends. 3D Shape Analysis: Fundamentals, Theory, and Applications is an excellent reference for graduate students, researchers, and professionals in different fields of mathematics, computer science, and engineering. It is also ideal for courses in computer vision and computer graphics, as well as for those seeking 3D industrial/commercial solutions.

Auteur

HAMID LAGA, PHD, is an Associate Professor and Head of the Information Technology discipline in the School of Engineering and IT, Murdoch University, Australia. He is also Adjunct Associate Professor at the Phenomics and Bioinformatics Research Centre, University of South Australia, Australia. YULAN GUO, PHD, is an Assistant Professor in the College of Electronic Science, National University of Defense Technology (NUDT), China. He is also a Research Fellow at the Institute of Computing Technology, Chinese Academy of Sciences, China. HEDI TABIA, PHD, is an Associate Professor at École Nationale Supérieure de l'Électronique et de ses Applications (ENSEA), France. ROBERT B. FISHER, PHD, is a Professor at The University of Edinburgh, United Kingdom, where he was previously Dean of Research in the College of Science and Engineering. MOHAMMED BENNAMOUN, PHD, is a Winthrop Professor in the School of Computer Science and Software Engineering at The University of Western Australia, Australia.

Texte du rabat
AN IN-DEPTH DESCRIPTION OF THE STATE-OF-THE-ART OF 3D SHAPE ANALYSIS TECHNIQUES AND THEIR APPLICATIONS This book discusses the different topics that come under the title of "3D shape analysis". It covers the theoretical foundations and the major solutions that have been presented in the literature. It also establishes links between solutions proposed by different communities that studied 3D shape, such as mathematics and statistics, medical imaging, computer vision, and computer graphics. The first part of 3D Shape Analysis: Fundamentals, Theory, and Applications provides a review of the background concepts such as methods for the acquisition and representation of 3D geometries, and the fundamentals of geometry and topology. It specifically covers stereo matching, structured light, and intrinsic vs. extrinsic properties of shape. Parts 2 and 3 present a range of mathematical and algorithmic tools (which are used for e.g., global descriptors, keypoint detectors, local feature descriptors, and algorithms) that are commonly used for the detection, registration, recognition, classification, and retrieval of 3D objects. Both also place strong emphasis on recent techniques motivated by the spread of commodity devices for 3D acquisition. Part 4 demonstrates the use of these techniques in a selection of 3D shape analysis applications. It covers 3D face recognition, object recognition in 3D scenes, and 3D shape retrieval. It also discusses examples of semantic applications and cross domain 3D retrieval, i.e. how to retrieve 3D models using various types of modalities, e.g. sketches and/or images. The book concludes with a summary of the main ideas and discussions of the future trends. 3D Shape Analysis: Fundamentals, Theory, and Applications is an excellent reference for graduate students, researchers, and professionals in different fields of mathematics, computer science, and engineering. It is also ideal for courses in computer vision and computer graphics, as well as for those seeking 3D industrial/commercial solutions.

Contenu
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

2.1.1 Parametric Curves 13

2.1.2 Continuous Surfaces 15

2.1.2.1 Differential Properties of Surfaces 17

2.1.2.1.1 First Fundamental Form 17

2.1.2.1.2 Second Fundamental Form and Shape Operator 18

2.1.2.2 Curvatures 19

2.1.2.3 Laplace and LaplaceBeltrami Operators 21

2.1.3 Manifolds, Metrics, and Geodesics 22

2.1.4 Discrete Surfaces 24

2.1.4.1 Representations of Discrete Surfaces 24

2.1.4.2 Mesh Data Structures 28

2.1.4.3 Discretization of the Differential Properties of Surfaces 29

2.2 Shape, Shape Transformations, and Deformations 30

2.2.1 Shape-Preserving Transformations 31

2.2.1.1 Normalization for Translation 32

2.2.1.2 Normalization for Scale 32

2.2.1.3 Normalization for Rotation 32

2.2.1.3.1 Rotation Normalization Using Principal Component Analysis (PCA) 33

2.2.1.3.2 Rotation Normalization Using Planar Reflection Symmetry Analysis 34

2.2.2 Shape Deformations 35

2.2.3 Bending 35

2.2.4 Stretching 37

2.3 Summary and Further Reading 38

3 3D Acquisition and Preprocessing 41

3.1 Introduction 41

3.2 3D Acquisition 41

3.2.1 Contact 3D Acquisition 43

3.2.1.1 Coordinate Measuring Machine (CMM) 43

3.2.1.2 Arm-Based 3D Scanner 44

3.2.2 Noncontact 3D Acquisition 44

3.2.2.1 Time-of-Flight 44

3.2.2.1.1 Pulse-Based TOF 44

3.2.2.1.2 Phase Shift-Based TOF 45

3.2.2.2 Triangulation 45

3.2.2.3 Stereo 47

3.2.2.4 Structured Light 50

3.2.2.4.1 Temporal Coded Patterns 51

3.2.2.4.2 Spatial Coded Patterns 52

3.2.2.4.3 Direct Coded Patterns 55

3.2.2.5 Shape from X 55

3.3 Preprocessing 3D Models 56

3.3.1 Surface Smoothing and Fairing 57

3.3.1.1 Laplacian Smoothing 57

3.3.1.2 Taubin Smoothing 58

3.3.1.3 Curvature Flow Smoothing 58

3.3.2 Spherical Parameterization of 3D Surfaces 58

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

4.2.1 Point Sampling 69

4.2.2 Geometric Features 70

4.2.2.1 Geometric Attributes 70

4.2.2.2 Differential Attributes 71

4.2.3 Signature Construction and Comparison 72

4.3 View-Based 3D Shape Descriptors 73

4.3.1 The Light Field Descriptors (LFD) 74

4.3.2 Feature Extraction 75

4.3.3 Properties 76

4.4 Spherical Function-Based Descriptors 77

4.4.1 Spherical Shape Functions 78

4.4.2 Comparing Spherical Functions 80

4.4.2.1 Spherical Harmonic Descriptors 80

4.4…