Istituto di Scienza e Tecnologie dell'Informazione     
Biasotti S., Falcidieno B., Giorgi D., Spagnuolo M. Mathematical tools for shape analysis and description. 140 p. Brian A. Barsky (Series Editor) (ed.). (Synthesis Lectures on Computer Graphics and Animation, vol. 16). San Rafael, Calif., USA: Morgan & Claypool Publishers, 2014.
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.
URL: http://www.morganclaypool.com/doi/abs/10.2200/S00588ED1V01Y201407CGR016
DOI: 10.2200/S00588ED1V01Y201407CGR016
Subject Computational topology
Differential geometry
Algebraic topology
Spectral methods
Shape invariants
Distance measures
Shape transformations
3D shape analysis
3D shape description
3D shape retrieval
Morse theory
Topological persistence
I.3 Computer Graphics
68 Computer Science

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