Denoising tensors via Lie group flows

Y. Gur, N. Sochen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The need to regularize tensor fields arise recently in various applications. We treat in this paper tensors that belong to matrix Lie groups. We formulate the problem of these SO(N) flows in terms of the principal chiral model (PCM) action. This action is defined over a Lie group manifold. By minimizing the PCM action with respect to the group element, we obtain the equations of motion for the group element (or the corresponding connection). Then, by writing the gradient descent equations we obtain the PDE for the Lie group flows. We use these flows to regularize in particular the group of N-dimensional orthogonal matrices with determinant one i.e. SO(N). This type of regularization preserves their properties (i.e., the orthogonality and the determinant). A special numerical scheme that preserves the Lie group structure is used. However, these flows regularize the tensor field isotropically and therefore discontinuities are not preserved. We modify the functional and thereby the gradient descent PDEs in order to obtain an anisotropic tensor field regularization. We demonstrate our formalism with various examples.

Original languageEnglish
Title of host publicationVariational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings
Pages13-24
Number of pages12
DOIs
StatePublished - 2005
Event3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005 - Beijing, China
Duration: 16 Oct 200516 Oct 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3752 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005
Country/TerritoryChina
CityBeijing
Period16/10/0516/10/05

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