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

Thomas Batard; Nir Sochen

doi:10.1007/978-3-642-24785-9_41

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

Thomas Batard^*, Nir Sochen

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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 language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers
Pages	483-494
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-24785-9_41
State	Published - 2012
Event	3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011 - Ein-Gedi, Israel Duration: 29 May 2011 → 2 Jun 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6667 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011
Country/Territory	Israel
City	Ein-Gedi
Period	29/05/11 → 2/06/11

Keywords

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

Access to Document

10.1007/978-3-642-24785-9_41

Cite this

Batard, T., & Sochen, N. (2012). Polyakov action on (ρ,G)-equivariant functions application to color image regularization. In Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers (pp. 483-494). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6667 LNCS). https://doi.org/10.1007/978-3-642-24785-9_41

Batard, Thomas ; Sochen, Nir. / Polyakov action on (ρ,G)-equivariant functions application to color image regularization. Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers. 2012. pp. 483-494 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

keywords = "Differential, bundle-Polyakov, functional-Color image regularization, geometry-Fiber",

author = "Thomas Batard and Nir Sochen",

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Batard, T & Sochen, N 2012, Polyakov action on (ρ,G)-equivariant functions application to color image regularization. in Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6667 LNCS, pp. 483-494, 3rd International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2011, Ein-Gedi, Israel, 29/05/11. https://doi.org/10.1007/978-3-642-24785-9_41

Polyakov action on (ρ,G)-equivariant functions application to color image regularization. / Batard, Thomas; Sochen, Nir.
Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers. 2012. p. 483-494 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6667 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Batard T, Sochen N. Polyakov action on (ρ,G)-equivariant functions application to color image regularization. In Scale Space and Variational Methods in Computer Vision - Third International Conference, SSVM 2011, Revised Selected Papers. 2012. p. 483-494. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-24785-9_41

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

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