Algorithms for Hierarchical Spatial Reasoning

In several applications, there is the need to reason about spatial relations using multiple local frames of reference that are hierarchically organized. This paper focuses on hierarchical reasoning about direction relations, a special class of spatial relations that describe order in space (e.g., north or northeast). We assume a spatial database of points and regions. Points belong to regions, which may recursively be parts of larger regions. The direction relations between points in the same region are explicitly represented (and not calculated from coordinates). Inference mechanisms are applied to extract direction relations between points located in different regions and to detect inconsistencies. We study two complementary types of inference. The first one derives the direction relation between points from the relations of their ancestor regions. The second type derives the relation through chains of common points using path consistency. We present algorithms for both types of inference and discuss their computational complexity.