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＜電子ブック＞
Shapes and Diffeomorphisms / by Laurent Younes
(Applied Mathematical Sciences. ISSN:2196968X ; 171)

版	1st ed. 2010.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2010
本文言語	英語
大きさ	XVI, 438 p. 36 illus : online resource
著者標目	*Younes, Laurent author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Mathematical analysis LCSH:Mathematical models LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Information visualization FREE:Differential Geometry FREE:Analysis FREE:Mathematical Modeling and Industrial Mathematics FREE:Global Analysis and Analysis on Manifolds FREE:Data and Information Visualization
一般注記	Parametrized Plane Curves -- Medial Axis -- Moment-Based Representation -- Local Properties of Surfaces -- Isocontours and Isosurfaces -- Evolving Curves and Surfaces -- Deformable templates -- Ordinary Differential Equations and Groups of Diffeomorphisms -- Building Admissible Spaces -- Deformable Objects and Matching Functionals -- Diffeomorphic Matching -- Distances and Group Actions -- Metamorphosis 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 HTTP:URL=https://doi.org/10.1007/978-3-642-12055-8

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