Publication

Mixture Of Kernels And Iterated Semidirect Product Of Diffeomorphisms Groups

Martins Bruveris
2012
Journal Articles

Abstract

In the framework of large deformation diffeomorphic metric mapping (LDDMM), a multiscale theory for the diffeomorphism group is developed based on previous works of the authors. The purpose of this paper is (1) to develop in detail a variational approach for multiscale analysis of diffeomorphisms, (2) to generalize to several scales the the semidirect product representation, and (3) to illustrate the resulting diffeomorphic decomposition on synthetic and real images. We also show that the so-called kernel bundle method and the mixture of kernels are equivalent.

Official source

https://infoscience.epfl.ch/entities/publication/82c61251-5867-4635-92fa-b6df4f0c44f0

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Martins Bruveris
2012
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/82c61251-5867-4635-92fa-b6df4f0c44f0

About this result

Related concepts (28)

Representation theory of finite groups

The representation theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations of groups on vector spaces. Nevertheless, groups acting on other groups or on sets are also considered. For more details, please refer to the section on permutation representations. Other than a few marked exceptions, only finite groups will be considered in this article. We will also restrict ourselves to vector spaces over fields of characteristic zero.

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In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are differentiable. Given two manifolds and , a differentiable map is called a diffeomorphism if it is a bijection and its inverse is differentiable as well. If these functions are times continuously differentiable, is called a -diffeomorphism. Two manifolds and are diffeomorphic (usually denoted ) if there is a diffeomorphism from to .

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