Area distances of Convex Plane Curves and Improper Affine Spheres

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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.
14 pages 18 figures

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Differential Geometry, 14R99

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http://salesiana.dossiersoluciones.com/handle/123456789/146587

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.1854
 http://arxiv.org/abs/0710.1854

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arXiv