The Representation of Discrete Multi-resolution Spatial Knowledge.
John G. Stell · 2000
The representation of spatial knowledge has been widely studied leading to formal systems such as the Region-Connection Calculus, and various formal accounts of mereotopology. The majority of this work has been in the context of spaces which are continuous and innitely divisible. However, discrete spaces are of practical importance, and arise in several application areas. The present paper contributes to the representation of discrete spatial knowledge on two fronts. Firstly it provides an algebraic calculus for discrete regions, and demonstrates its expressiveness by showing how the concepts of interior, closure, boundary, exterior, and connection can all be formulated in the calculus. The second advance presented is an account of discrete spaces at multiple levels of detail. This is achieved by developing a general theory of coarsening for sets which is then extended to the case of discrete regions.