An Anisotropic Mumford-Shah Model
Résumé
We introduce an anisotropic Mumford-Shah functional in dimension n = 2, 3. The classical Hausdorff measure with dimension n−1 is replaced by an anisotropic surface measures depending on a riemannian metric M. This term contains the geometric a priori on the image we want to get. We give a relaxation of this energy in the set of SBV functions and we prove that with this formulation, the minimizing problem admits solution under suitable conditions. We also prove that a relaxed solution provides in fact a regular solution of the initial problem. Methods are given to construct the metric M.
Origine : Fichiers produits par l'(les) auteur(s)