Numerical Geometry of Non-Rigid Shapes

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.

Deformable objects are ubiquitous in the world, on all levels from micro to macro. Study and modeling of such shapes arises in a wide spectrum of applications, ranging from medicine to security. Non-rigid shapes have attracted a growing interest, leading 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 provides an overview of the current state of science in analysis and synthesis of non-rigid shapes. Everyday examples are used to illustrate and explain concepts and techniques. The presentation unfolds systematically, with numerous figures to enrich the exposition. Practice exercises follow at the end of each chapter, with detailed solutions to selected problems in the appendix. A gallery of color images enhances the text.

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

Inhalt
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.