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Article Dans Une Revue Nonlinearity Année : 2020

MUMFORD -SHAH FUNCTIONALS ON GRAPHS AND THEIR ASYMPTOTICS

Résumé

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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Dates et versions

hal-02342959 , version 1 (01-11-2019)

Identifiants

Citer

Marco Caroccia, Antonin Chambolle, Dejan Slepčev. MUMFORD -SHAH FUNCTIONALS ON GRAPHS AND THEIR ASYMPTOTICS. Nonlinearity, 2020, 33 (8), pp.3846--3888. ⟨10.1088/1361-6544/ab81ee⟩. ⟨hal-02342959⟩
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