Algorithms for Hierarchical Spatial Reasoning

  • Authors:

  • Dimitris Papadias;Max J. Egenhofer

  • Affiliations:

  • Department of Computer Science, Hong Kong University of Science and Technology, Clearwater Bay, Hong Kong, dimitris@cs.ust.hk;National Center for Geographic Information and Analysis and Department of Spatial Information Science and Engineering, Department of Computer Science, University of Maine Orono, ME 04469-5711, USA ...

  • Venue:
  • Geoinformatica
  • Year:
  • 1997

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Abstract

In several applications, there is the need to reason about spatialrelations using multiple local frames of reference that are hierarchicallyorganized. This paper focuses on hierarchical reasoning about directionrelations, a special class of spatial relations that describe order inspace (e.g., north or northeast). We assume a spatial database of points andregions. Points belong to regions, which may recursively be parts of largerregions. The direction relations between points in the same region areexplicitly represented (and not calculated from coordinates). Inferencemechanisms are applied to extract direction relations between points locatedin different regions and to detect inconsistencies. We study twocomplementary types of inference. The first one derives the directionrelation between points from the relations of their ancestor regions. Thesecond type derives the relation through chains of common points using pathconsistency. We present algorithms for both types of inference and discusstheir computational complexity.