Calculus of Variations and Geometric Measure Theory
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M. Caroccia - A. Chambolle - D. SlepĨev

Mumford - Shah on graphs and their asymptotics

created by caroccia on 19 Jun 2019
modified on 17 May 2020


Accepted Paper

Inserted: 19 jun 2019
Last Updated: 17 may 2020

Journal: Nonlinearity
Year: 2019


We consider adaptations of the Mumford-Shah functional to graphs. These are based on discretizations of nonlocal approximations to the Mumford-Shah functional. Motivated by applications in machine learning we study the random geometric graphs associated to random samples of a measure. We establish the conditions on the graph constructions under which the minimizers of graph Mumford-Shah functionals converge to a minimizer of a continuum Mumford-Shah functional. Furthermore we explicitly identify the limiting functional. Moreover we describe an efficient algorithm for computing the approximate minimizers of the graph Mumford-Shah functional.


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