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Mathematics - Geometry & Topology | Shapes and Diffeomorphisms

Shapes and Diffeomorphisms

Series: Applied Mathematical Sciences, Vol. 171

Younes, Laurent

2010, XVI, 438p. 36 illus..

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  • -direct application of the theory presented in the book is a branch of the computerized analysis of medical images, called computational anatomy
  • -provides the background that is required for apprehending shapes in terms that are also suitable for computerized analysis and interpretation
  • -explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms

Shapes are complex objects, which are difficult to apprehend as mathematical entities, in ways that can also be amenable to computerized analysis and interpretation. This volume provides the background that is required for this purpose, including different approaches that can be used to model shapes, and algorithms that are available to analyze them. It explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms. The book is, as far as possible, self-contained, with an appendix that describes a series of classical topics in mathematics (Hilbert spaces, differential equations, Riemannian manifolds) and sections that represent the state of the art in the analysis of shapes and their deformations.

A direct application of what is presented in the book is a branch of the computerized analysis of medical images, called computational anatomy.

Content Level » Research

Keywords » Curves and Surfaces - Groups of Diffeomorphisms - Riemannian Geometry - Shape Analysis - algorithms - diffeomorphism - differential geometry - manifold - optimization

Related subjects » Analysis - Computational Science & Engineering - Geometry & Topology - Mathematics

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