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Discrete stochastic approximations of the Mumford–Shah functional

par Ruf, Matthias
Référence Annales de l'Institut Henri Poincaré. Analyse non linéaire
Publication Publié, 2019

Article révisé par les pairs

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Résumé :

We propose a new Γ-convergent discrete approximation of the Mumford–Shah functional. The discrete functionals act on functions defined on stationary stochastic lattices and take into account general finite differences through a non-convex potential. In this setting the geometry of the lattice strongly influences the anisotropy of the limit functional. Thus we can use statistically isotropic lattices and stochastic homogenization techniques to approximate the vectorial Mumford–Shah functional in any dimension.