Overview

Shapes are complex objects to apprehend, as mathematical entities, in terms that also are suitable for 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.

Full Product Details

Author:   Laurent Younes
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2010 ed.
Volume:   171
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   0.836kg
ISBN:  

9783642120541

ISBN 10:   3642120547
Pages:   438
Publication Date:   25 May 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Replaced By:   9783662584958
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   In Print  
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.

Table of Contents

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.

Reviews

From the reviews: The book under review deals with the fascinating subject of shapes. ... This is a book on applied mathematics which provides a description of the wide range of methods that have been invented to represent, detect, or compare shapes ... together with the necessary mathematical background that they require. The book could also be of interest to an engineering- or computer-science-oriented reader, as it gives in several places concrete algorithms and applicable methods, including experimental illustrations. (Luca Granieri, Mathematical Reviews, Issue 2011 h)

From the reviews: The book under review deals with the fascinating subject of shapes. ... This is a book on applied mathematics which provides a description of the wide range of methods that have been invented to represent, detect, or compare shapes ... together with the necessary mathematical background that they require. The book could also be of interest to an engineering- or computer-science-oriented reader, as it gives in several places concrete algorithms and applicable methods, including experimental illustrations. (Luca Granieri, Mathematical Reviews, Issue 2011 h) This book is an attempt at providing a description of a large range of methods used to represent, detect and compare shapes ... together with the mathematical background that they require. ... This book on applied mathematics is of interest to engineers and computer scientists having direct applications in the computerized analysis of medical images. This theory will as well lead to other interesting applications in the future. (Corina Mohorianu, Zentralblatt MATH, Vol. 1205, 2011)

From the reviews: The book under review deals with the fascinating subject of shapes. ! This is a book on applied mathematics which provides a description of the wide range of methods that have been invented to represent, detect, or compare shapes ! together with the necessary mathematical background that they require. The book could also be of interest to an engineering- or computer-science-oriented reader, as it gives in several places concrete algorithms and applicable methods, including experimental illustrations. (Luca Granieri, Mathematical Reviews, Issue 2011 h)

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