Probabilistic composition of cone-based cardinal direction relations

Composition tables play a significant role in qualitative spatial reasoning (QSR). At present, a couple of composition tables focusing on various spatial relations have been developed in a qualitative approach. However, the spatial reasoning processes are usually not purely qualitative in everyday life, where probability is one important issue that should be considered. In this paper, the probabilistic compositions of cone-based cardinal direction relations (CDR) are discussed and estimated by making some assumptions. Consequently, the form of composition result turns to be {(R1,P1), (R2,P2), ..., (Rn,Pn)}, where Pi is the probability associated with relation Ri. Employing the area integral method, the probabilities in each composition case can be computed with the assumption that the target object is uniformly distributed in the corresponding cone regions.