Qualitative spatial reasoning about relative point position

Abstract

Qualitative spatial reasoning (QSR) abstracts metrical details of the physical world. The two main directions in QSR are topological reasoning about regions and reasoning about orientations of point configurations. Orientations can refer to a global reference system, e.g. cardinal directions or instead only to relative orientation, e.g. egocentric views. Reasoning about relative orientations poses additional difficulties compared to reasoning about orientations in an absolute reference frame. Qualitative knowledge about relative orientation can be naturally expressed in the form of ternary point calculi. Designing such calculi requires compromising between desired mathematical properties and the power to describe and model concrete “real-world” problems. Research has shown that using basic notions such as granularity leads to imprecise reasoning and as a consequence to underdetermined knowledge which is difficult to handle efficiently. Concrete problems need a combination of qualitative knowledge of orientation and qualitative knowledge of distance. We present a calculus based on ternary relations where we introduce a qualitative distance measurement based on two of the three points. Its main advantage is that it utilizes finer distinctions than previously published calculi. Furthermore, it permits differentiations which are useful in realistic application scenarios such as robot navigation that cannot be directly dealt with in coarser calculi.