{
  "id": "1503.07685",
  "version": "v1",
  "published": "2015-03-26T11:04:43.000Z",
  "updated": "2015-03-26T11:04:43.000Z",
  "title": "The matching problem between functional shapes via a BV-penalty term: a $Γ$-convergence result",
  "authors": [
    "B. Charlier",
    "G. Nardi",
    "A. Trouvé"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper we study a variant of the matching model between functional shapes introduced in [3]. Such a model allows to compare surfaces equipped with a signal and the matching energy is defined by the $L^2$-norm of the signal on the surface and a varifold-type attachment term. In this work we study the problem with fixed geometry which means that we optimize the initial signal (supported on the initial surface) with respect to a target signal supported on a different surface. In particular, we consider a $BV$ or $H^1$-penalty term for the signal instead of its $L^2$-norm. Several numerical examples are shown in order to prove that the $BV$-penalty improves the quality of the matching. Moreover, we prove a $\\Gamma$-convergence result for the discrete matching energy towards the continuous-one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-26T11:04:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional shapes",
      "convergence result",
      "bv-penalty term",
      "matching problem",
      "varifold-type attachment term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}