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Shapes and Diffeomorphisms

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Shapes and Diffeomorphisms/ by Laurent Younes.
Author:	Younes, Laurent.
Description:	XXIII, 558 p. 47 illus., 14 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Computer science—Mathematics. -
Online resource:	https://doi.org/10.1007/978-3-662-58496-5
ISBN:	9783662584965

Shapes and Diffeomorphisms
Younes, Laurent.

Shapes and Diffeomorphisms[electronic resource] /by Laurent Younes. - 2nd ed. 2019. - XXIII, 558 p. 47 illus., 14 illus. in color.online resource. - Applied Mathematical Sciences,1710066-5452 ;. - Applied Mathematical Sciences,191.

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 chapters are 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. .

ISBN: 9783662584965

Standard No.: 10.1007/978-3-662-58496-5doiSubjects--Topical Terms:

1253519
Computer science—Mathematics.

LC Class. No.: QA76.9.M35

Dewey Class. No.: 004.0151

Shapes and Diffeomorphisms
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520 $a 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 chapters are 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. .
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