Integrative Reasoning with Topological, Directional and Size Information Based on MBR

It is inadequate considering only one aspect of spatial information in practical problems, where several aspects are usually involved together. Reasoning with multi-aspect spatial information has become one of the focuses of qualitative spatial reasoning. Current research about the integrative reasoning concentrates on the reasoning with two aspects information and lacks the work over three or more aspects. To solve this problem, the extended rectangle relation is proposed to realize the integrative representing and reasoning of topology, direction and size information. Considering the high cost of representing and reasoning with single aspect spatial information and the need of efficiency, the minimal bounding rectangle (MBR) is used to approximate regions; so the spatial relations between regions can be presented by the relevant relations between the projections of MBRs on each axis. The translating algorithm which converts the RCC8, cardinal direction and size relations into extended rectangle relations is given. The basic reverse and composing operations are discussed, and it is pointed out that the composition of extended rectangle relations is based on consistency not existence. According to the definitions of convex and strongly preconvex extended rectangle relations, the consistency of the network consisting of these two sets of relations is proved to be decided in polynomial time.