Area distances of Convex Plane Curves and Improper Affine Spheres
Differential Geometry
2008-01-28 v2
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.
Keywords
Cite
@article{arxiv.0710.1854,
title = {Area distances of Convex Plane Curves and Improper Affine Spheres},
author = {Marcos Craizer and Moacyr Alvim and Ralph Teixeira},
journal= {arXiv preprint arXiv:0710.1854},
year = {2008}
}
Comments
14 pages 18 figures