  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 $\epsi>0$. The asymptotic
behavior as $\epsi\to0^+$ 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.
