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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.
List 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.
Summary
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.
Additional text
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)
Report
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)
