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Numerical Geometry of Non-Rigid Shapes [electronic resource] /by Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel.

by Bronstein, Alexander M [author.]; Bronstein, Michael M [author.]; Kimmel, Ron [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Monographs in Computer Science: Publisher: New York, NY : Springer New York, 2009.Description: XXII, 346p. 10 illus. in color. online resource.ISBN: 9780387733012.Subject(s): Computer science | Computer vision | Computer science -- Mathematics | Geometry | Computer Science | Computer Imaging, Vision, Pattern Recognition and Graphics | Geometry | Computational Mathematics and Numerical AnalysisOnline resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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