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

版	2nd ed. 2019.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2019
本文言語	英語
大きさ	XXIII, 558 p. 47 illus., 14 illus. in color : online resource
著者標目	*Younes, Laurent author SpringerLink (Online service)
件　名	LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Biometry LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Geometry, Differential LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Biomathematics FREE:Mathematical Applications in Computer Science FREE:Biostatistics FREE:Global Analysis and Analysis on Manifolds FREE:Differential Geometry FREE:Calculus of Variations and Optimization FREE:Mathematical and Computational Biology
一般注記	Preface to the 2nd Edition -- Preface to the 1st Edition -- Parametrized Plane Curves -- Medial Axis -- Local Properties of Surfaces -- Computations on Triangulated Surfaces- 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 -- Analyzing Shape Datasets -- Appendices: Elements from Functional Analysis -- Elements from Differential Geometry -- Ordinary Differential Equations -- Introduction to Optimization and Optimal Control Theory. - Principal Component Analysis -- Dynamic Programming -- References -- Index This book covers mathematical foundations and methods for the computerized analysis of shapes, providing the requisite background in geometry and functional analysis and introducing various algorithms and approaches to shape modeling, with a special focus on the interesting connections between shapes and their transformations by diffeomorphisms. A direct application is to computational anatomy, for which techniques such as large‒deformation diffeomorphic metric mapping and metamorphosis, among others, are presented. The appendices detail a series of classical topics (Hilbert spaces, differential equations, Riemannian manifolds, optimal control). The intended audience is applied mathematicians and mathematically inclined engineers interested in the topic of shape analysis and its possible applications in computer vision or medical imaging. The first part can be used for an advanced undergraduate course on differential geometry with a focus on applications while the later chaptersare suitable for a graduate course on shape analysis through the action of diffeomorphisms. Several significant additions appear in the 2nd edition, most notably a new chapter on shape datasets, and a discussion of optimal control theory in an infinite-dimensional framework, which is then used to enrich the presentation of diffeomorphic matching. HTTP:URL=https://doi.org/10.1007/978-3-662-58496-5

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