{
  "id": "1906.09521",
  "version": "v1",
  "published": "2019-06-22T23:54:28.000Z",
  "updated": "2019-06-22T23:54:28.000Z",
  "title": "Mumford-Shah functionals on graphs and their asymptotics",
  "authors": [
    "Marco Caroccia",
    "Antonin Chambolle",
    "Dejan Slepčev"
  ],
  "categories": [
    "math.AP",
    "stat.ML"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-22T23:54:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J55",
      "62G20",
      "65N12"
    ],
    "keywords": [
      "asymptotics",
      "graph mumford-shah functionals converge",
      "random geometric graphs",
      "continuum mumford-shah functional",
      "nonlocal approximations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}