{
  "id": "0710.1854",
  "version": "v2",
  "published": "2007-10-09T18:50:23.000Z",
  "updated": "2008-01-28T17:58:57.000Z",
  "title": "Area distances of Convex Plane Curves and Improper Affine Spheres",
  "authors": [
    "Marcos Craizer",
    "Moacyr Alvim",
    "Ralph Teixeira"
  ],
  "comment": "14 pages 18 figures",
  "categories": [
    "math.DG"
  ],
  "abstract": "The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both theories. The concepts of the theory of affine spheres lead to a new definition of an area distance on the outer part of a convex plane arc. Also, based on the theory of discrete affine spheres, we propose fast algorithms to compute the area distances. On the other hand, area distances provide a good geometrical understanding of improper affine spheres.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-01-28T17:58:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R99"
    ],
    "keywords": [
      "improper affine spheres",
      "area distance",
      "convex plane curve",
      "convex plane arc",
      "discrete affine spheres"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0710.1854C"
    }
  }
}