Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel (auth.)9780387733005, 0387733000
Deformable objects are ubiquitous in the world surrounding us, on all levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. In recent years, non-rigid shapes have attracted growing interest, which has led to rapid development of the field, where state-of-the-art results from very different sciences – theoretical and numerical geometry, optimization, linear algebra, graph theory, machine learning and computer graphics, to mention several – are applied to find solutions.
This book gives an overview of the current state of science in analysis and synthesis of non-rigid shapes. Everyday examples are used to explain concepts and to illustrate different techniques. The presentation unfolds systematically and numerous figures enrich the engaging exposition. Practice problems follow at the end of each chapter, with detailed solutions to selected problems in the appendix. A gallery of colored images enhances the text.
This book will be of interest to graduate students, researchers and professionals in different fields of mathematics, computer science and engineering. It may be used for courses in computer vision, numerical geometry and geometric modeling and computer graphics or for self-study.
Table of contents :
Front Matter….Pages I-XXI
Introduction….Pages 1-9
A Taste of Geometry….Pages 11-40
Discrete Geometry….Pages 41-65
Shortest Paths and Fast Marching Methods….Pages 67-91
Numerical Optimization….Pages 93-118
In the Rigid Kingdom….Pages 119-135
Multidimensional Scaling….Pages 137-167
Spectral Embedding….Pages 169-186
Non Euclidean Embedding….Pages 187-204
Isometry Invariant Similarity….Pages 205-215
Partial Similarity….Pages 217-238
Non rigid Correspondence and Calculus of Shapes….Pages 239-259
Three dimensional Face Recognition….Pages 261-275
Epilogue….Pages 277-277
Back Matter….Pages 279-340
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