Publication 16-CNA-002
A Chromaticity-Brightness Model for Color Images Denoising in a Meyer's "u + v" Framework
Rita Ferreira
King Abdullah University of Science and Technology (KAUST)
CEMSE Division
Thuwal 23955-6900
Saudi Arabia
rita.ferreira@kaust.edu.sa
Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu
M. Luisa Mascarenhas
Departamento de Matemática & C.M.A. - F.C.T./U.N.L.
Quinta da Torre, 2829-516 Caparica, Portugal
mascar@fct.unl.pt
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 $\epsilon$ > 0. The
asymptotic behavior as $\epsilon \to 0^+$ 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
$\Gamma$-convergence and relaxation techniques.
Get the paper in its entirety as 16-CNA-002.pdf
« Back to CNA Publications
