Single-holed regions: Their relations and inferences

Abstract

The discontinuities in boundaries and exteriors that regions with holes expose offer opportunities for inferences that are impossible for regions without holes. A systematic study of the binary relations between single-holed regions shows not only an increase in the number of feasible relations (from eight between two regions without holes to 152 for two single-holed regions), but also identifies the increased reasoning power enabled by the holes. A set of quantitative measures is introduced to compare various composition tables over regions with and without holes. These measures reveal that inferences over relations for holed regions are overall crisper and yield more unique results than relations over regions without holes. Likewise, compositions that involve more holed regions than regions without holes provide crisper inferences, which supports the need for relation models that capture holes explicitly. © 2008 Springer-Verlag Berlin Heidelberg.