The Family of Conceptual Neighborhood Graphs for Region-Region Relations

Abstract

This paper revisits conceptual neighborhood graphs for the topological relations between two regions, in order to bridge from the A-B-C neighborhoods defined for interval relations in R1 to region relations in R2 and on the sphere S2. A categorization of deformation types--built from same and different positions, orientations, sizes, and shapes--gives rise to four different neighborhood graphs. They include transitions that are constrained by the regions' geometry, yielding some directed, not undirected neighborhood graphs. Two of the four neighborhood graphs correspond to type B and C. The lattice of conceptual neighborhood graphs captures the relationships among the graphs, showing completeness under union and intersection.