Topological relations in hierarchical partitions

Abstract

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 suffcient to answer a given query. The effciency of the approach even can be improved by doing the recursion incrementa..