A chromaticity-brightness model for color images denoising in a Meyer’s “u + v” framework

Abstract

A variational model for imaging segmentation and denoising color images is proposed. The model combines Meyer's "u+v" decomposition with a chromaticity-brightness framework and is expressed by a minimization of energy integral functionals depending on a small parameter ε > 0. The asymptotic behavior as ε → 0 + is characterized, and convergence of infima, almost minimizers, and energies are established. In particular, an integral representation of the lower semicontinuous envelope, with respect to the L 1 -norm, of functionals with linear growth and defined for maps taking values on a certain compact manifold is provided. This study escapes the realm of previous results since the underlying manifold has boundary, and the integrand and its recession function fail to satisfy hypotheses commonly assumed in the literature. The main tools are Γ-convergence and relaxation techniques.MSC (2010): 49J45, 26B30, 94A08

Piecewise constant reconstruction of damaged color images

“…The other way to represent an image is called Chromaticity/Brightness, where a RGB image u ∈ BV (Ω ; R 3 ) is decomposed into two components: its chromaticity u/|u| and its brightness |u|. The main idea of this model is to reconstruct the two parts independently (see, for instance, [13] and [19]). The total variation model introduced by Fornasier in [16] is a variant of (1.1), and it appeals to the RGB model to represent the image.…”