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Foreword | |
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About the Authors | |
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Preface | |
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Introduction | |
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Similarity of non-rigid shapes | |
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Correspondence problems | |
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A landscape of problems | |
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Notes | |
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A Taste of Geometry | |
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Basic terms in metric geometry and topology | |
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Isometries | |
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Length spaces | |
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Manifolds | |
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Embedded surfaces | |
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Curvature and the second fundamental form | |
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Intrinsic view on geometry of surfaces | |
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Bending and rigidity | |
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Intrinsic invariants | |
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Suggested reading | |
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Problems | |
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Notes | |
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Discrete Geometry | |
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Point clouds and sampling | |
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Farthest point sampling | |
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Voronoi tessellation | |
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Centroidal Voronoi sampling and the Lloyd-Max algorithm | |
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Connectivity | |
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Delaunay tessellation | |
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Triangular meshes | |
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Local feature size and curvature-dependent sampling | |
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Approximation quality | |
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Suggested reading | |
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Software | |
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Problems | |
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Notes | |
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Shortest Paths and Fast Marching Methods | |
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The shortest path problem | |
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Dijkstra's shortest path algorithm | |
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Fast marching methods | |
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Fast marching on parametric surfaces | |
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Marching even faster | |
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Parallel distance computation | |
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Minimal geodesics | |
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Suggested reading | |
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Software | |
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Problems | |
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Notes | |
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Numerical Optimization | |
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Local versus global optimization | |
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Optimality conditions | |
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Unconstrained optimization algorithms | |
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The quest for a descent direction | |
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Preconditioning | |
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Let Newton be! | |
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Truncated Newton | |
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Quasi-Newton algorithms | |
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Non-convex optimization | |
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Constrained optimization | |
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Penalty and barrier methods | |
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Augmented Lagrangian method | |
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Suggested reading | |
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Software | |
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Problems | |
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Notes | |
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In the Rigid Kingdom | |
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Moments of joy, moments of sorrow | |
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Iterative closest point algorithms | |
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Enter numerical optimization | |
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Rigid correspondence | |
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Suggested reading | |
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Software | |
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Problems | |
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Notes | |
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Multidimensional Scaling | |
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Isometric embedding problem | |
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Multidimensional scaling | |
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SMACOF algorithm | |
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Second-order methods | |
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Variations on the stress theme | |
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Multiresolution methods | |
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Multigrid MDS | |
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Vector extrapolation | |
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A trouble with topology | |
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Suggested reading | |
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Software | |
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Problems | |
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Notes | |
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Spectral Embedding | |
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Classic MDS | |
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Local methods | |
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The Laplace-Beltrami operator | |
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To hear the shape of the drum | |
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Discrete Laplace-Beltrami operator | |
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Suggested reading | |
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Software | |
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Problems | |
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Notes | |
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Non-Euclidean Embedding | |
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Spherical embedding | |
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Generalized multidimensional scaling | |
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Representation issues | |
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Geodesic distance computation | |
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Minimization of the generalized stress | |
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Multiresolution encore | |
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Suggested reading | |
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Software | |
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Problems | |
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Notes | |
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Isometry-Invariant Similarity | |
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Equivalence, similarity, and distance | |
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Embedding distance | |
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Gromov-Hausdorff distance | |
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Intrinsic symmetry | |
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Suggested reading | |
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Problems | |
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Partial Similarity | |
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Recognition by parts | |
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Paretian approach to partial similarity | |
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Scalar partial similarity | |
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Fuzzy approximation | |
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Extrinsic partial similarity | |
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Intrinsic partial similarity | |
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Not only size matters | |
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Suggested reading | |
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Problems | |
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Notes | |
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Non-rigid Correspondence and Calculus of Shapes | |
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Intrinsic parameterization | |
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An image processing approach | |
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Minimum distortion correspondence | |
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Texture mapping and transfer | |
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Morphing | |
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Guaranteed self-intersection free morph | |
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Calculus of shapes | |
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Suggested reading | |
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Software | |
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Problems | |
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Notes | |
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Three-dimensional Face Recognition | |
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Some terminology | |
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A retrospective | |
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Isometric model of facial expressions | |
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Expression-invariant face recognition | |
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Comparison of photometric properties | |
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Suggested reading | |
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Notes | |
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Epilogue | |
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Solutions of Selected Problems | |
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Software | |
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Notation | |
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Acronyms | |
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Glossary | |
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References | |
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Subject Index | |
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Author Index | |