Geometric and Topological Mesh Feature Extraction for 3D Shape Analysis

✍ Scribed by Hetroy-Wheeler, Franck; Mari, Jean-Luc; Subsol, Gérard

• Publisher: John Wiley & Sons, Incorporated
• Year: 2020
• Tongue: English
• Leaves: 199
• Category: Library

✦ Table of Contents

Cover......Page 1
Half-Title Page......Page 3
Title Page......Page 5
Copyright Page......Page 6
Contents......Page 7
Preface......Page 11
I.1. Context: 3D shape analysis......Page 13
I.2. Background on meshes......Page 14
I.3. Definition of a feature......Page 16
I.3.2. Surface feature from a perceptual point of view......Page 17
I.3.3. Surface feature from a machine vision point of view......Page 19
I.3.4. Surface features from a mathematical point of view......Page 21
1.1. Introduction......Page 23
1.2.1. Fundamental forms and normal curvature......Page 24
1.2.2. Principal curvatures and shape index......Page 27
1.2.3. Principal directions and lines of curvature......Page 28
1.2.4. Weingarten equations and shape operator......Page 31
1.2.5. Practical computation of differential parameters......Page 34
1.2.6. Euler’s theorem......Page 35
1.2.7. Meusnier’s theorem......Page 37
1.2.8. Local approximation of the surface......Page 38
1.2.9. Focal surfaces......Page 39
1.3.2. Some notations......Page 41
1.3.3. Computing normal vectors......Page 42
1.3.5. Discrete differential geometry operators......Page 44
1.3.7. Tensor of curvature: Taubin’s formula......Page 50
1.3.8. Tensor of curvature based on the normal cycle theory......Page 52
1.3.9. Integral estimators......Page 56
1.3.11. Discussion of the methods......Page 60
1.4.1. Introduction......Page 68
1.4.2. Lines of curvature......Page 69
1.4.3. Crest/ridge lines......Page 77
1.4.4. Feature lines based on homotopic thinning......Page 101
1.5.1. Mesh segmentation......Page 106
1.5.2. Shape description based on graphs......Page 109
1.6. Conclusion......Page 120
2.1. Mathematical background......Page 121
2.1.1. A topological view on surfaces......Page 122
2.1.2. Algebraic topology......Page 125
2.2.1. Connected components and genus......Page 128
2.2.2. Homology groups......Page 129
2.3. Combining geometric and topological features......Page 133
2.3.1. Persistent homology......Page 134
2.3.2. Reeb graph and Morse–Smale complex......Page 137
2.3.3. Homology generators......Page 140
2.3.4. Measuring holes......Page 143
2.4. Conclusion......Page 150
3.2. Medicine: lines of curvature for polyp detection in virtual colonoscopy......Page 153
3.3. Paleo-anthropology: crest/ridge lines for shape analysis of human fossils......Page 155
3.4. Geology: extraction of fracture lines on virtual outcrops......Page 159
3.5. Planetary science: detection of feature lines for the extraction of impact craters on asteroids and rocky planets......Page 162
3.6. Botany: persistent homology to recover the branching structure of plants......Page 165
Conclusion......Page 167
References......Page 171
Index......Page 191
Other titles from iSTE in Numerical Methods in Engineering......Page 193
EULLA......Page 197

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