2016/03/24 by Rita Ferreira, Ferreira, Rita, Irene Fonseca +4
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Numerical methods in inverse problems #math.AP
paper · pdf · doi:10.48550/arxiv.1603.07647
arxiv created 2016/03/24 · openalex publication_date 2016/03/24 · arxiv updated 2016/03/25 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
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→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 L1-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.