{
  "id": "1903.02349",
  "version": "v1",
  "published": "2019-03-06T13:06:01.000Z",
  "updated": "2019-03-06T13:06:01.000Z",
  "title": "Approximation of the Mumford-Shah Functional by Phase Fields of Bounded Variation",
  "authors": [
    "Sandro Belz",
    "Kristian Bredies"
  ],
  "comment": "27 pages, 4 Figures, 1 Table, 31 References",
  "categories": [
    "math.AP",
    "math.NA"
  ],
  "abstract": "In this paper we introduce a new phase field approximation of the Mumford-Shah functional similar to the well-known one from Ambrosio and Tortorelli. However, in our setting the phase field is allowed to be a function of bounded variation, instead of an H1-function. In the context of image segmentation, we also show how this new approximation can be used for numerical computations, which contains a total variation minimization of the phase field variable, as it appears in many problems of image processing. A comparison to the classical Ambrosio-Tortorelli approximation, where the phase field is an H1-function, shows that the new model leads to sharper phase fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-06T13:06:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J45",
      "26A45",
      "68U10"
    ],
    "keywords": [
      "bounded variation",
      "phase field approximation",
      "total variation minimization",
      "sharper phase fields",
      "mumford-shah functional similar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}