Qualitative representation of positions in 2-D

Abstract

We focus on 2-D projections of 3-D scenes. In order to represent the relative position of two objects in 2-D space qualitatively we define a small set of spatial relations from the two relevant dimensions topology and orientation. The relative position is given by a topological/orientation relation pair. A complete set of topological relations can be derived from the combinatorial variations of the point set intersection of boundaries and interiors of the involved objects by imposing the constraints of physical space on them. The orientation dimension results from the transfer of distinguished reference axes from an observer to the reference object. Relative orientations must be given w.r.t. a reference frame, which can be intrinsic (orientation given by some inherent property of the reference object), extrinsic (orientation imposed by external factors), or deictic (orientation imposed by point of view). When reasoning about orientations, the reference frame is implicitly assumed to be the intrinsic orientation of the parent object (i.e., the one containing the objects involved), unless explicitly stated otherwise.