Polyakov action on (ρ,G)-equivariant functions application to color image regularization

Thomas Batard*, Nir Sochen

*Corresponding author for this work

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

2 Scopus citations

Abstract

We propose a new mathematical model for color images taking into account that color pixels change under transformation of the light source. For this, we deal with (ρ,G)-equivariant functions on principal bundles, where ρ is a representation of a Lie group G on the color space RGB. We present an application to image regularization, by minimization of the Polyakov action associated to the graph of such functions. We test the groups , DC(3) of contractions and dilatations of and SO(3) with their natural matrix representations, as well as with its trivial representation. We show that the regularization has denoising properties if the representation is unitary and segmentation properties otherwise.

Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers
Pages483-494
Number of pages12
DOIs
StatePublished - 2012
Event3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011 - Ein-Gedi, Israel
Duration: 29 May 20112 Jun 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6667 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011
Country/TerritoryIsrael
CityEin-Gedi
Period29/05/112/06/11

Keywords

  • Differential
  • bundle-Polyakov
  • functional-Color image regularization
  • geometry-Fiber

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