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Computer Science - Image Processing | Numerical Geometry of Non-Rigid Shapes

Numerical Geometry of Non-Rigid Shapes

Bronstein, Alexander M., Bronstein, Michael M., Kimmel, Ron

2009, XXII, 346p. 10 illus. in color.

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  • Gives an up-to-date overview of the concepts and techniques in the analysis and synthesis of non-rigid shapes
  • Bridges the gap between theoretical and applied fields, spanning computer vision, pattern recognition and computer graphics
  • Presents practical state-of-the-art algorithms and methods illustrated in real applications
  • Engages the reader by using numerous figures and everyday examples
  • Reference to public domain and commercial software

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.

Content Level » Research

Keywords » computer graphics - computer vision - discrete geometry - geometric modeling - modeling - numerical geometry - similarity

Related subjects » Computational Science & Engineering - Geometry & Topology - Image Processing

Table of contents 

A Taste of Geometry.- Discrete Geometry.- Shortest Paths and Fast Marching Methods.- Numerical Optimization.- In the Rigid Kingdom.- Multidimensional Scaling.- Spectral Embedding.- Non Euclidean Embedding.- Isometry Invariant Similarity.- Partial Similarity.- Non rigid Correspondence and Calculus of Shapes.- Three dimensional Face Recognition.- Epilogue.

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