Calculus of Variations and Geometric Measure Theory

M. Ruf

Discrete stochastic approximations of the Mumford-Shah functional

created by ruf on 17 Oct 2017
modified on 25 Feb 2019


Accepted Paper

Inserted: 17 oct 2017
Last Updated: 25 feb 2019

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2018
Doi: 10.1016/j.anihpc.2018.10.004

ArXiv: 1710.05571 PDF


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.