Mathematical Tools for Shape Analysis and Description

Mathematical Tools for Shape Analysis and Description

Silvia Biasotti, Bianca Falcidieno, Daniela Giorgi, Michela Spagnuolo
ISBN: 9781627053631 | PDF ISBN: 9781627053648
Copyright © 2014 | 138 Pages | Publication Date: 09/01/2014

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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

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
Authors' Biographies

About the Author(s)

Silvia Biasotti, Consiglio Nazionale delle Ricerche, Italy

Bianca Falcidieno, Consiglio Nazionale delle Ricerche, Italy

Daniela Giorgi, Consiglio Nazionale delle Ricerche, Italy

Michela Spagnuolo, Consiglio Nazionale delle Ricerche, Italy

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