Shapes and Diffeomorphisms (eBook, PDF) - Younes, Laurent
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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…mehr

Produktbeschreibung
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.

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  • Produktdetails
  • Verlag: Springer-Verlag GmbH
  • Seitenzahl: 438
  • Erscheinungstermin: 17. Mai 2010
  • Englisch
  • ISBN-13: 9783642120558
  • Artikelnr.: 44121014
Autorenporträt
A former student of the Ecole Normale Supérieure in Paris, Laurent Younes received his Ph.D. from the University Paris Sud in 1989. Now a professor in the Department of Applied Mathematics and Statistics at Johns Hopkins University (which he joined in 2003), he was a junior, then senior researcher at CNRS in France from 1991 to 2003. His research is in stochastic modeling for imaging and biology, shape analysis and computational anatomy. He is a core faculty member of the Center for Imaging Science and of the Institute for Computational Medicine at JHU.

Inhaltsangabe
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.
Rezensionen
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)