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基本説明
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.
Full Description
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.
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.
