Mathematical tools for shape analysis and description

Biasotti S., Falcidieno B., Giorgi D., Spagnuolo M.

Morse theory  Shape invariants  Topological persistence  Differential geometry  3D shape retrieval  3D shape description  Algebraic topology  Distance measures  Shape transformations  Computational topology  Spectral methods  3D shape analysis 

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.

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