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Shapes and diffeomorphisms

Younes, Laurent.

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Shapes and diffeomorphisms

Record Type:	Electronic resources : Monograph/item
Title/Author:	Shapes and diffeomorphisms/ by Laurent Younes.
Author:	Younes, Laurent.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2019.,
Description:	xxiii, 558 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Shapes. -
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. - Berlin, Heidelberg :Springer Berlin Heidelberg :2019. - xxiii, 558 p. :ill. (some col.), digital ;24 cm. - Applied mathematical sciences,v.1710066-5452 ;. - Applied mathematical sciences ;v.171..

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:

629864
Shapes.

LC Class. No.: QA445 / .Y686 2019

Dewey Class. No.: 516.15

Shapes and diffeomorphisms
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245 1 0 $a Shapes and diffeomorphisms $h [electronic resource] / $c by Laurent Younes.
250 $a 2nd ed.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2019.
300 $a xxiii, 558 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Applied mathematical sciences, $x 0066-5452 ; $v v.171
505 0 $a 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.
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.
650 0 $a Shapes. $3 629864
650 0 $a Diffeomorphisms. $3 699703
650 1 4 $a Mathematical Applications in Computer Science. $3 1567978
650 2 4 $a Statistics for Life Sciences, Medicine, Health Sciences. $3 891086
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
650 2 4 $a Differential Geometry. $3 891003
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 898674
650 2 4 $a Physiological, Cellular and Medical Topics. $3 891099
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Applied mathematical sciences ; $v v.171. $3 3411014
856 4 0 $u https://doi.org/10.1007/978-3-662-58496-5
950 $a Mathematics and Statistics (Springer-11649)