Equivalence Classes of Direction Objects and Applications

Abstract

Direction is an important spatial relationship that is used in many fields such as geographic information systems (GIS) and image interpretation. It is also frequently used as a selection condition in spatial queries. In our recent work we have described a novel viewpoint to model direction as a `spatial object' based upon the concepts of vectors, points and angles. This was a departure from the conventional approach of treating direction as a spatial relationship between objects. In this paper, based upon `direction objects', we partition the directional space into a set of equivalence classes. By defining an algebra on equivalence classes we provide a framework to model semantics of direction predicates for qualitative spatial reasoning. We then proceed to extrapolate the definition of direction equivalence classes to define `path' equivalence classes with an application to the landmark-based route description problem. Keywords: Directional relationships, Direction objects, Equivalence Classes, Landmark-based routing.