Area Distances of Convex Plane Curves and Improper Affine Spheres

被引：10
|
作者：
Craizer, Marcos [1 ]
Alvim, Moacyr [2 ]
Teixeira, Ralph [3 ]
机构：
[1] Pontificia Univ Catolica Rio de Janeiro, Dept Math, BR-22453900 Rio De Janeiro, Brazil
[2] Fundacao Getulio Vargas, Ctr Matemat, BR-22250900 Rio De Janeiro, Brazil
[3] Univ Fed Fluminense, Dept Math, BR-24210080 Rio De Janeiro, Brazil
来源：
SIAM JOURNAL ON IMAGING SCIENCES | 2008年 / 1卷 / 03期
关键词：
area distances; improper affine spheres; discrete affine spheres;
D O I：
10.1137/080714610
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
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. Based on this link, we propose an extremely fast algorithm to compute the inner area distance. Moreover, 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 curve. On the other hand, area distances provide a good geometrical understanding of improper affine spheres.
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页码：209 / 227
页数：19
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