Calculus of Variations and Geometric Measure Theory
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M. Ruf

Discrete stochastic approximations of the Mumford-Shah functional

created by ruf on 17 Oct 2017

[BibTeX]

preprint

Inserted: 17 oct 2017

Year: 2017

ArXiv: 1710.05571 PDF

Abstract:

We propose a $\Gamma$-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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