Discrete stochastic approximations of the Mumford–Shah functional |
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Authors: | Matthias Ruf |
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Institution: | Département Mathématique, Université libre de Bruxelles (ULB), CP 214, boulevard du Triomphe, 1050 Brussels, Belgium |
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Abstract: | 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. |
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Keywords: | 49M25 68U10 49J55 49J45 Mumford–Shah functional Discrete approximation Γ-convergence Stochastic homogenization |
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