Shapes are complex objects to apprehend, as mathematical entities, in terms also suitable for computerized analysis and interpretation. This volume provides the background that is required for this purpose, including different approaches that can be used.

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.

direct application of the theory presented in the book is a branch of the computerized analysis of medical images, called computational anatomy provides the background that is required for apprehending shapes in terms that also are suitable for computerized analysis and interpretation explores, in particular, the interesting connections between shapes and the objects that naturally act on them, diffeomorphisms Includes supplementary material: sn.pub/extras

Autorentext

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.

Klappentext

Shapes are complex objects, which are difficult to apprehend as mathematical entities, in ways that can also be amenable to 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.

Inhalt
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.