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Numerical Geometry of Non-Rigid Shapes

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

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As well as providing an overview of the current state of science in the analysis and synthesis of non-rigid shapes, the authors include everyday examples to explain concepts. Practice problems follow at the end of each chapter, along with detailed solutions.

Full Description

  • ISBN13: 978-0-3877-3300-5
  • 368 Pages
  • User Level: Students
  • Publication Date: September 18, 2008
  • Available eBook Formats: PDF
  • eBook Price: $49.95
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Full Description
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

Table of Contents

  1. Introduction.
  2. A Taste of Geometry.
  3. Discrete Geometry.
  4. Shortest Paths and Fast Marching Methods.
  5. Numerical Optimization.
  6. In the Rigid Kingdom.
  7. Multidimensional Scaling.
  8. Spectral Embedding.
  9. Non
  10. Euclidean Embedding.
  11. Isometry
  12. Invariant Similarity.
  13. Partial Similarity.
  14. Non
  15. Rigid Correspondence and Calculus of Shapes.
  16. Three
  17. Dimensional Face Recognition.
  18. Epilogue.
  19. Solutions of Selected Problems.
  20. Software.
  21. Notation.
  22. Acronyms.
  23. Glossary.
  24. References.
  25. Subject Index.
  26. Author Index.
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