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

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. © 2012 Springer-Verlag.