
Foreword

Preface
Intended use  Features  Synopsis  How to use this book  Acknowledgement  Feedback and support

Introduction
Similarity of nonrigid 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 LloydMax algorithm 
Connectivity 
Delaunay tessellation 
Triangular meshes 
Local feature size and curvaturedependent 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 
QuasiNewton algorithms 
Nonconvex 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 
Secondorder methods 
Variations on the stress theme 
Multiresolution methods 
Multigrid MDS 
Vector extrapolation 
A trouble with topology

Spectral Embedding
Classic MDS 
Local methods 
The LaplaceBeltrami operator 
To hear the shape of the drum 
Discrete LaplaceBeltrami operator

NonEuclidean Embedding
Spherical embedding 
Generalized multidimensional scaling 
Representation issues 
Geodesic distance computation 
Minimization of the generalized stress 
Multiresolution encore

IsometryInvariant Similarity
Equivalence similarity and distance 
Embedding distance 
GromovHausdorff 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

Nonrigid Correspondence and Calculus of Shapes
Intrinsic parameterization 
An image processing approach 
Minimum distortion correspondence 
Texture mapping and transfer 
Morphing 
Guaranteed selfintersection free morph 
Calculus of shapes

Threedimensional Face Recognition
Some terminology 
A retrospective 
Isometric model of facial expressions 
Expressioninvariant face recognition 
Comparison of photometric properties

Epilogue

Solutions to Selected Problems

Software

Notation

Acronyms

Glossary

References

Subject Index

Author Index

