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.

Spectral Geometry of Shapes presents unique shape analysis approaches based on shape spectrum in differential geometry. It provides insights on how to develop geometry-based methods for 3D shape analysis. The book is an ideal learning resource for graduate students and researchers in computer science, computer engineering and applied mathematics who have an interest in 3D shape analysis, shape motion analysis, image analysis, medical image analysis, computer vision and computer graphics. Due to the rapid advancement of 3D acquisition technologies there has been a big increase in 3D shape data that requires a variety of shape analysis methods, hence the need for this comprehensive resource.

Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental website contains downloads and additional information.

This considerably enriched new edition provides a self-contained presentation of the mathematical foundations, constructions, and tools necessary for studying problems where the modeling, optimization, or control variable is the shape or the structure of a geometric object.

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more.

Processing, Analyzing and Learning of Images, Shapes, and Forms: Volume 19, Part One provides a comprehensive survey of the contemporary developments related to the analysis and learning of images, shapes and forms. It covers mathematical models as well as fast computational techniques, and includes new chapters on Alternating diffusion: a geometric approach for sensor fusion, Shape Correspondence and Functional Maps, Geometric models for perception-based image processing, Decomposition schemes for nonconvex composite minimization: theory and applications, Low rank matrix recovery: algorithms and theory, Geometry and learning for deformation shape correspondence, and Factoring scene layout from monocular images in presence of occlusion. - Presents a contemporary view on the topic, comprehensively covering the newest developments and content - Provides a comprehensive survey of the contemporary developments related to the analysis and learning of images, shapes and forms