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  • Textbook
  • © 2009

Numerical Geometry of Non-Rigid Shapes

  • Gives an up-to-date overview of the concepts and techniques in 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

  • Includes supplementary material: sn.pub/extras

Part of the book series: Monographs in Computer Science (MCS)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XXI
  2. Introduction

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 1-9
  3. A Taste of Geometry

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 11-40
  4. Discrete Geometry

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 41-65
  5. Shortest Paths and Fast Marching Methods

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 67-91
  6. Numerical Optimization

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 93-118
  7. In the Rigid Kingdom

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 119-135
  8. Multidimensional Scaling

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 137-167
  9. Spectral Embedding

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 169-186
  10. Non Euclidean Embedding

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 187-204
  11. Isometry Invariant Similarity

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 205-215
  12. Partial Similarity

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 217-238
  13. Non rigid Correspondence and Calculus of Shapes

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 239-259
  14. Three dimensional Face Recognition

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 261-275
  15. Epilogue

    • Alexander Bronstein, Michael Bronstein, Ron Kimmel
    Pages 277-277
  16. Back Matter

    Pages 279-340

About this book

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.

Reviews

From the reviews:

"This book provides an introduction to this geometry. … Overall, the book … does explain relevant mathematical notions, such as Gromov’s metric geometry ideas, in a very understandable and entertaining way, with numerous images and exercises. … I highly recommend it to both computer scientists interested in learning more about the latest advances in computational geometry and to geometers looking for applications. This unique book can serve as an excellent textbook for many related courses, for self-study, or as a reference." (V. Kreinovich, ACM Computing Reviews, May, 2009)

“Numerical geometry of non-rigid shapes by A. Bronstein, M. Bronstein, and R. Kimmel combines the beauty of modern mathematics … with the interesting field of computer vision and pattern recognition. … The book is developed at an intermediate-advanced level. Students will find the material clear and easy to understand, and will benefit from its good presentation.” (Stefan Henn, Mathematical Reviews, Issue 2010 b)

Authors and Affiliations

  • Dept. Computer Science, Technion-Israel Institute of Technology, Technion City, Haifa, Israel

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

Bibliographic Information

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 84.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access