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 (17)

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.

Semidirect product

In mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. There are two closely related concepts of semidirect product: an inner semidirect product is a particular way in which a group can be made up of two subgroups, one of which is a normal subgroup. an outer semidirect product is a way to construct a new group from two given groups by using the Cartesian product as a set and a particular multiplication operation.

Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).

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