Spatial Reasoning with a Hole

Max J. Egenhofer and Maria Vasardani, Spatial Reasoning with a Hole, in: S. Winter, M. Duckham, L. Kulik, and B. Kuipers (eds.), Conference on Spatial Information Theory (COSIT ’07), Melbourne, Australia, Lecture Notes in Computer Science, Vol. 4736, Springer, pp. 303-320, September 2007.

Cavities in spatial phenomena require geometric representations of regions with holes. Existing models for reasoning over topological relations either exclude such specialized regions (9-intersection) or treat them indistinguishably from regions without holes (RCC-8). This paper highlights that inferences over a region with a hole need to be made separately from, and in addition to, the inferences over regions without holes. First the set of 23 topological relations between a region and a region with a hole is derived systematically. Then these relations’ compositions over the region with the hole are calculated so that the inferences can be compared with the compositions of the topological relations over regions without holes. For 266 out of the 529 compositions the results over the region with the hole were more detailed than the corresponding results over regions without holes, with 95 of these refined cases providing even a unique result. In 27 cases, this refinement up to uniqueness compares with a completely undetermined inference for the relations over regions without holes.