Mumford-Shah functionals on graphs and their asymptotics
Analysis of PDEs
2020-08-26 v2 Machine Learning
Abstract
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.
Cite
@article{arxiv.1906.09521,
title = {Mumford-Shah functionals on graphs and their asymptotics},
author = {Marco Caroccia and Antonin Chambolle and Dejan Slepčev},
journal= {arXiv preprint arXiv:1906.09521},
year = {2020}
}