Databases and Information Systems Commons^™

Spatial Refinement As Collection Order Relations, Zhong Zhao

Journal of Spatial Information Science

An abstract examination of refinement (and conversely, coarsening) with respect to the involved spatial relations gives rise to formulated order relations between spatial coverings, which are defined as complete-coverage representations composed of regional granules. Coverings, which generalize partitions by allowing granules to overlap, enhance hierarchical geocomputations in several ways. Refinement between spatial coverings has underlying patterns with respect to inclusion—formalized as binary topological relations—between their granules. The patterns are captured by collection relations of inclusion, which are obtained by constraining relevant topological relations with cardinality properties such as uniqueness and totality. Conjoining relevant collection relations of equality and proper inclusion …