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This book is a guide for researchers and practitioners to the new frontiers of 3D shape analysis and the complex mathematical tools most methods rely on. The target reader includes students, researchers and professionals with an undergraduate mathematics background, who wish to understand the mathematics behind shape analysis. The authors begin with a quick review of basic concepts in geometry, topology, differential geometry, and proceed to advanced notions of algebraic topology, always keeping an eye on the application of the theory, through examples of shape analysis methods such as 3D segmentation, correspondence, and retrieval. A number of research solutions in the field come from advances in pure and applied mathematics, as well as from the re-reading of classical theories and their adaptation to the discrete setting. In a world where disciplines (fortunately) have blurred boundaries, the authors believe that this guide will help to bridge the distance between theory and practice.Table of Contents: Acknowledgments / Figure Credits / About this Book / 3D Shape Analysis in a Nutshell / Geometry, Topology, and Shape Representation / Differential Geometry and Shape Analysis / Spectral Methods for Shape Analysis / Maps and Distances between Spaces / Algebraic Topology and Topology Invariants / Differential Topology and Shape Analysis / Reeb Graphs / Morse and Morse-Smale Complexes / Topological Persistence / Beyond Geometry and Topology / Resources / Bibliography / Authors' Biographies

This book constitutes the refereed proceedings of the Second International Conference on Semantics and Digital Media Technologies, SAMT 2007, held in Genoa, Italy, in December 2007. The conference brings together forums, projects, institutions and individuals investigating the integration of knowledge, semantics and low-level multimedia processing, including new emerging media and application areas. The papers are organized in topical sections.

Since its very existence as a separate field within computerscience, computer graphics had to make extensive use ofnon-trivial mathematics, for example, projective geometry,solid modelling, and approximation theory. This interplay ofmathematics and computer science is exciting, but also makesit difficult for students and researchers to assimilate ormaintain a view of the necessary mathematics. Thepossibilities offered by an interdisciplinary approach arestill not fully utilized. This book gives a selection ofcontributions to a workshop held near Genoa, Italy, inOctober 1991, where a group of mathematicians and computerscientists gathered to explore ways of extending thecooperation between mathematics and computer graphics.