Polyakov Action on (ρ,G)-Equivariant Functions Application to Color Image Regularization

  • Thomas Batard
  • Nir Sochen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6667)


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 \({\rm I\!R}^{+\ast}\), DC(3) of contractions and dilatations of \({\rm I\!R}^3\) and SO(3) with their natural matrix representations, as well as \({\rm I\!R}^{+\ast}\) with its trivial representation. We show that the regularization has denoising properties if the representation is unitary and segmentation properties otherwise.


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


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thomas Batard
    • 1
  • Nir Sochen
    • 1
  1. 1.Department of Applied MathematicsTel Aviv UniversityTel AvivIsrael

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