Mumford-Shah functionals on graphs and their asymptotics

被引：10

作者：

Caroccia, Marco ^{[1
]}

Chambolle, Antonin ^{[2
]}

Slepcev, Dejan ^{[3
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] Ecole Polytech, CMAP, F-91128 Palaiseau, France

[3] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

来源：

NONLINEARITY | 2020年 / 33卷 / 08期

基金：

美国安德鲁·梅隆基金会;

关键词：

nonlocal variational problems; variational problems with randomness; discrete to continuum limit; asymptotic consistency; Gamma convergence; regression; FINITE-DIFFERENCE APPROXIMATION; CONSISTENCY; RECOVERY;

D O I：

10.1088/1361-6544/ab81ee

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：3846 / 3888

页数：43

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