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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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- Verlag: Springer-Verlag GmbH
- Seitenzahl: 558
- Erscheinungstermin: 17. Mai 2019
- ISBN-13: 9783662584965
- Artikelnr.: 57625264
"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)