Foreword | p. VII |
About the Authors | p. IX |
Preface | p. XI |
Introduction | p. 1 |
Similarity of non-rigid shapes | p. 3 |
Correspondence problems | p. 6 |
A landscape of problems | p. 7 |
Notes | p. 9 |
A Taste of Geometry | p. 11 |
Basic terms in metric geometry and topology | p. 11 |
Isometries | p. 13 |
Length spaces | p. 17 |
Manifolds | p. 20 |
Embedded surfaces | p. 21 |
Curvature and the second fundamental form | p. 26 |
Intrinsic view on geometry of surfaces | p. 29 |
Bending and rigidity | p. 31 |
Intrinsic invariants | p. 34 |
Suggested reading | p. 37 |
Problems | p. 37 |
Notes | p. 39 |
Discrete Geometry | p. 41 |
Point clouds and sampling | p. 41 |
Farthest point sampling | p. 43 |
Voronoi tessellation | p. 46 |
Centroidal Voronoi sampling and the Lloyd-Max algorithm | p. 48 |
Connectivity | p. 52 |
Delaunay tessellation | p. 53 |
Triangular meshes | p. 54 |
Local feature size and curvature-dependent sampling | p. 57 |
Approximation quality | p. 61 |
Suggested reading | p. 63 |
Software | p. 63 |
Problems | p. 63 |
Notes | p. 64 |
Shortest Paths and Fast Marching Methods | p. 67 |
The shortest path problem | p. 67 |
Dijkstra's shortest path algorithm | p. 69 |
Fast marching methods | p. 71 |
Fast marching on parametric surfaces | p. 81 |
Marching even faster | p. 83 |
Parallel distance computation | p. 85 |
Minimal geodesics | p. 87 |
Suggested reading | p. 89 |
Software | p. 90 |
Problems | p. 90 |
Notes | p. 91 |
Numerical Optimization | p. 93 |
Local versus global optimization | p. 93 |
Optimality conditions | p. 94 |
Unconstrained optimization algorithms | p. 97 |
The quest for a descent direction | p. 100 |
Preconditioning | p. 104 |
Let Newton be! | p. 105 |
Truncated Newton | p. 106 |
Quasi-Newton algorithms | p. 107 |
Non-convex optimization | p. 108 |
Constrained optimization | p. 110 |
Penalty and barrier methods | p. 112 |
Augmented Lagrangian method | p. 114 |
Suggested reading | p. 116 |
Software | p. 116 |
Problems | p. 116 |
Notes | p. 118 |
In the Rigid Kingdom | p. 119 |
Moments of joy, moments of sorrow | p. 120 |
Iterative closest point algorithms | p. 125 |
Enter numerical optimization | p. 128 |
Rigid correspondence | p. 131 |
Suggested reading | p. 133 |
Software | p. 133 |
Problems | p. 133 |
Notes | p. 134 |
Multidimensional Scaling | p. 137 |
Isometric embedding problem | p. 138 |
Multidimensional scaling | p. 142 |
SMACOF algorithm | p. 143 |
Second-order methods | p. 146 |
Variations on the stress theme | p. 148 |
Multiresolution methods | p. 153 |
Multigrid MDS | p. 156 |
Vector extrapolation | p. 160 |
A trouble with topology | p. 164 |
Suggested reading | p. 165 |
Software | p. 166 |
Problems | p. 167 |
Notes | p. 167 |
Spectral Embedding | p. 169 |
Classic MDS | p. 170 |
Local methods | p. 173 |
The Laplace-Beltrami operator | p. 176 |
To hear the shape of the drum | p. 178 |
Discrete Laplace-Beltrami operator | p. 180 |
Suggested reading | p. 184 |
Software | p. 184 |
Problems | p. 184 |
Notes | p. 185 |
Non-Euclidean Embedding | p. 187 |
Spherical embedding | p. 187 |
Generalized multidimensional scaling | p. 192 |
Representation issues | p. 194 |
Geodesic distance computation | p. 197 |
Minimization of the generalized stress | p. 198 |
Multiresolution encore | p. 202 |
Suggested reading | p. 203 |
Software | p. 203 |
Problems | p. 204 |
Notes | p. 204 |
Isometry-Invariant Similarity | p. 205 |
Equivalence, similarity, and distance | p. 205 |
Embedding distance | p. 207 |
Gromov-Hausdorff distance | p. 208 |
Intrinsic symmetry | p. 211 |
Suggested reading | p. 214 |
Problems | p. 214 |
Partial Similarity | p. 217 |
Recognition by parts | p. 218 |
Paretian approach to partial similarity | p. 221 |
Scalar partial similarity | p. 224 |
Fuzzy approximation | p. 226 |
Extrinsic partial similarity | p. 229 |
Intrinsic partial similarity | p. 230 |
Not only size matters | p. 232 |
Suggested reading | p. 236 |
Problems | p. 236 |
Notes | p. 238 |
Non-rigid Correspondence and Calculus of Shapes | p. 239 |
Intrinsic parameterization | p. 240 |
An image processing approach | p. 241 |
Minimum distortion correspondence | p. 244 |
Texture mapping and transfer | p. 246 |
Morphing | p. 249 |
Guaranteed self-intersection free morph | p. 254 |
Calculus of shapes | p. 255 |
Suggested reading | p. 258 |
Software | p. 258 |
Problems | p. 259 |
Notes | p. 259 |
Three-dimensional Face Recognition | p. 261 |
Some terminology | p. 263 |
A retrospective | p. 264 |
Isometric model of facial expressions | p. 268 |
Expression-invariant face recognition | p. 269 |
Comparison of photometric properties | p. 273 |
Suggested reading | p. 275 |
Notes | p. 275 |
Epilogue | p. 277 |
Solutions of Selected Problems | p. 279 |
Software | p. 293 |
Notation | p. 297 |
Acronyms | p. 299 |
Glossary | p. 301 |
References | p. 307 |
Subject Index | p. 327 |
Author Index | p. 335 |
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