DISCRETE COMBINATORIAL GEOMETRY

In computer vision, one of the ultimate aims is the determination of g eometric properties of 3-dimensional objects in our real world from me asured data. As an expression intermediate between measured raw data a nd geometric properties, we need a method of representing objects in c omputers. For the object representations, geometry which uses only fin ite-precision numbers is necessary because in computers we can only ma nipulate finite-precision numbers. In this paper, we develop a new geo metry, which we call discrete combinatorial geometry due to the discre teness of the space of finite-precision numbers, applying fundamental definitions of classical combinatorial geometry. Using discrete combin atorial geometry, we introduce a new method for representing curves, s urfaces and objects in computers. We also show that our new representa tion is based on the fact that the boundary of a surface consists of c urves and the boundary of an object consists of surfaces. (C) 1997 Pat tern Recognition Society. Published by Elsevier Science Ltd.