Anisotropic Mumford-Shah Model and its approximation with Gamma-convergence
Résumé
A new 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 and it introduces as
a new variable a continuous and anisotropic perturbation of the Hausdorff measure. A relaxed
formulation in the special space of functions with bounded variations is given and the existence of
a solution is established. In order to get an energy more adapted for numerics, an approximation
with Γ-convergence and its complete proof are given.
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