Inferences from combined knowledge about topology and directions

Abstract

Separate mechanisms exist for the compositions of binary topological relations and binary direction relations. They are appropriate for homogeneous spatial reasoning, i.e., the inference of new topological relations from a set of topological relations, or the derivation of new direction relations from a set of direction relations; however, these composition mechanisms are insufficient for heterogeneous spatial reasoning, such as the inference of spatial relations from the combination of topological relations and cardinal directions. This paper discusses the shortcomings of current inference methods for heterogeneous spatial reasoning and presents a new method for heterogeneous directiontopology reasoning. The results demonstrate that using a canonical model, in particular Allen's interval relations, leads to a powerful heterogeneous reasoning mechanism. The spatial objects are approximated by their minimum bounding rectangles and the topological and direction relations are mapped onto interval relations. Compositions are performed using the composition table for interval relations. The results of the compositions are then reverse mapped onto directions. This process enables complex three-step inferences over topological and direction relations such as A West of B, B overlap C, and C West of D imply A West of D.

This research was partially supported by the National Science Foundation under grants IRI-9309230 (Principal Investigator: Max J. Egenhofer) and SBR-8810917 for the National Center for Geographic Information and Analysis, and a University of Maine Graduate Research Assistantship (UGRA). This support is gratefully acknowledged.