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