Topological Relations in Hierarchical Partitions

• Authors: Stephan Winter
• Venue: COSIT '99 Proceedings of the International Conference on Spatial Information Theory: Cognitive and Computational Foundations of Geographic Information Science
• Year: 1999

A hierarchical spatial reasoning is proposed to determine the topological relation between two regions in independent spatial partitions. Hierarchical partitions considered are raster images as uniform regular partitions -- extended to image pyramids --, and quadtrees as hierarchical regular partitions. The hierarchical approach starts at the root level with total uncertainty about a topological relation. A recursive determination level by level refines the results, excluding relations that are definitely not true. The process stops immediately when the refined information is sufficient to answer a given query. The efficiency of the approach even can be improved by doing the recursion incrementally, examining only the locations that contribute new information. Both together increases efficiency significantly compared to non-hierarchical procedures. The topological relation can be determined by intersection sets or by region connection calculus. We apply the method with intersection sets here. Relations are determined for binary classified partition elements, distinguishing the interior and the exterior of a region. By the hierarchic approach mixed partition elements are included.