An anisotropic Mumford–Shah model

A variational model is introduced for the segmentation problem of thin structures, like tubes or thin plates, in an image. The energy is based on the Mumford–Shah model with a surfacic term perturbed by a Finsler metric. The formulation in the special space of functions with bounded variations is given and, in order to get an energy more adapted for numerics, a result of Γ-convergence is proved.