Discrete combinatorial geometry

doi:10.1016/S0031-3203(97)00001-0

1997-10-01

PRE

Yukiko Kenmochi⋆

Atsushi Imiya

Akira Ichikawa

DOI：10.1016/S0031-3203(97)00001-0

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摘要

En 中文

In computer vision, one of the ultimate aims is the determination of geometric properties of 3-dimensional objects in our real world from measured data. As an expression intermediate between measured raw data and geometric properties, we need a method of representing objects in computers. For the object representations, geometry which uses only finite-precision numbers is necessary because in computers we can only manipulate finite-precision numbers. In this paper, we develop a new geometry, which we call discrete combinatorial geometry due to the discreteness of the space of finite-precision numbers, applying fundamental definitions of classical combinatorial geometry. Using discrete combinatorial geometry, we introduce a new method for representing curves, surfaces and objects in computers. We also show that our new representation is based on the fact that the boundary of a surface consists of curves and the boundary of an object consists of surfaces. (C) 1997 Pattern Recognition Society. Published by Elsevier Science Ltd.

Keyword:

combinatorial geometry

simplex

complex

curve

surface

object

boundary