Description of combined spatial relations between broad boundary regions based on rough set

Abstract

The uncertain regions are modeled by broad boundary regions, while the description and reasoning of combined spatial relations between them are still unresolved problems. So far, the research about describing spatial relations mainly focuses on single-kind of spatial relation between simple and certain objects, rather than the combination of multi-kinds of spatial relations between uncertain regions. In addition, the uncertainty of formalizing combined spatial relations between uncertain regions is still a puzzle problem. Based on this point, the rough set theory is introduced into describing combined spatial relations between broad boundary regions. First, topological relations, exterior direction relations and detailed direction relations are approximated by a lower and an upper rough set, respectively, and then the difference set between the two sets indicates the uncertainty of spatial relations. Finally, the combination of the topological and direction relations between broad boundary regions is used to describe combined spatial relations. © Springer-Verlag Berlin Heidelberg 2006.