3D shape analysis : fundamentals, theory, and applications /: fundamentals, theory, and applications. (2018)

• Record Type: Book
• Further Information: Note: Hamid Laga, Yulan Guo, Hedi Tabia, Robert B. Fisher, Mohammed Bennamoun.
• Authors: Laga, Hamid; Guo, Yulan; Tabia, Hedi; Fisher, R. B; Bennamoun, M (Mohammed)
• Contents: 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 Laplace–Beltrami 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 4.4.2.2 SphericalWavelet Transforms 81 4.4.2.2.1 Wavelet Coefficients as a Shape Descriptor 82 4.4.2.2.2 SphericalWavelet Energy Signatures 82 4.5 Deep Neural Network-Based 3D Descriptors 83 4.5.1 CNN-Based Image Descriptors 84 4.5.2 Multiview CNN for 3D Shapes 85 4.5.2.1 Network Architecture 86 4.5.2.2 View Aggregation using CNN 86 4.5.3 Volumetric CNN 87 4.6 Summary and Further Reading 89 5 Local Shape Descriptors 93 5.1 Introduction 93 5.2 Challenges and Criteria 94 5.2.1 Challenges 94 5.2.2 Criteria for 3D Keypoint Detection 95 5.2.3 Criteria for Local Feature Description 96 5.3 3D Keypoint Detection 96 5.3.1 Fixed-Scale Keypoint Detection 97 5.3.1.1 Curvature-Based Methods 97 5.3.1.1.1 Local Surface Patch (LSP) 98 5.3.1.2 Other Surface Variation-Based Methods 98 5.3.1.2.1 Matei’s Method 99 5.3.1.2.2 Intrinsic Shape Signatures (ISS) 99 5.3.1.2.3 Harris 3D 99 5.3.2 Adaptive-Scale Keypoint Detection 101 5.3.2.1 Extrinsic Scale-Space Based Methods 101 5.3.2.1.1 3D Shape Filtering 101 5.3.2.1.2 Multiscale Surface Variation 104 5.3.2.2 Intrinsic Scale-Space Based Methods 106 5.3.2.2.1 Scale-Space on 2D Parameterized Images 106 5.3.2.2.2 Scale-Space on 3D Shapes 109 5.3.2.2.3 Scale-Space on Transformed Domains 112 5.4 Local Feature Description 113 5.4.1 Signature-Based Methods 114 5.4.1.1 Splash 114 5.4.1.2 Point Signature 115 5.4.2 Histogram Based Methods 115 5.4.2.1 Histogram of Spatial Distributions 115 5.4.2.1.1 Spin Images 116 5.4.2.1.2 3D Shape Context 117 5.4.2.1.3 Intrinsic Shape Signature (ISS) 118 5.4.2.1.4 Rotational Projection Statistics (RoPS) 118 5.4.2.2 Histogram of Geometric Attributes 122 5.4.2.2.1 Point Feature Histograms (PFH) 122 5.4.2.2.2 Fast Point Feature Histograms (FPFH) 123 5.4.2.2.3 Signature of Histograms of Orientations (SHOT) 123 5.4.2.3 Histogram of Oriented Gradients 124 5.4.3 Covariance-Based Methods 124 5.5 Feature Aggregation Using Bag of Feature Techniques 126 5.5.1 Dictionary Construction 127 5.5.1.1 Feature Extraction 127 5.5.1.2 Codebook Construction 127 5.5.2 Coding and Pooling Schemes 128 5.5.2.1 Sparse Coding 128 5.5.2.2 Fisher Vectors 129 5.5.3 Vector of Locally Aggregated Descriptors (VLAD) 129 5.5.4 Vector of Locally Aggregated Tensors (VLAT) 130 5.6 Summary and Further Reading 131 5.6.1 Summary of 3D Keypoint Detection 131 5.6.2 Summary of Local Feature Description 132 5.6.3 Summary of Feature Aggregation 133 Part III 3D Correspondence and Registration 135 6 Rigid Registration 137 6.1 Introduction 137 6.2 Coarse Registration 138 6.2.1 Point Correspondence-Based Registration 138 6.2.1.1 The Typical Pipeline 139 6.2.1.2 Transformation Estimation from a Group of Correspondences 139 6.2.1.3 Transformation Estimation fromThree Correspondences 140 6.2.1.4 Transformation Estimation from Two Correspondences 141 6.2.1.5 Transformation Estimation from One Correspondence 142 6.2.2 Line-Based Registration 143 6.2.2.1 Line Matching Method 143 6.2.2.2 Line Clustering Method 144 6.2.2.2.1 Rotation Estimation 145 6.2.2.2.2 Translation Estimation 146 6.2.3 Surface-Based Registration 146 6.2.3.1 Principal Component Analysis (PCA) 146 6.2.3.2 RANSAC-Based DARCES 147 6.2.3.3 Four-Points Congruent Sets (4PCS) 149 6.2.3.3.1 Affine Invariants of 4-Points Set 149 6.2.3.3.2 Congruent 4-Points Extraction 151 6.2.3.3.3 The 4PCS Algorithm 151 6.3 Fine Registration 152 6.3.1 Iterative Closest Point (ICP) 153 6.3.1.1 Closest Point Search 153 6.3.1.2 Transformation Estimation 153 6.3.1.3 Summary of the ICP Method 154 6.3.2 ICP Variants 155 6.3.2.1 Point Selection 155 6.3.2.2 Point Matching 156 6.3.2.3 Point PairWeighting 156 6.3.2.4 Point Pair Rejection 156 6.3.2.5 Error Metrics 157 6.3.3 Coherent Point Drift 157 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 7.3.1 The Space of Diffeomorphisms 165 7.3.2 Parameterizing Spaces 166 7.
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 006.693; Three-dimensional imaging; Pattern recognition systems; Shapes -- Computer simulation; Machine learning
• Languages: English
• ISBNs: 9781119405191
• Related ISBNs: 9781119405184
• Notes: Note: Description based on CIP data; resource not viewed.
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