2007/10/09 by Marcos Craizer, Craizer, Marcos, Moacyr Alvim +3
Computer Science · Mathematics · #14R99 #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities #math.DG #msc:14R99
paper · pdf · doi:10.48550/arxiv.0710.1854
14 pages 18 figures
openalex publication_date 2007/10/09 · arxiv created 2008/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.