Dimension-refined topological predicates

Topological predicates, as derived from the 9-intersection model, have been widely recognized in GIS, spatial database systems, and many other geo-related disciplines. They are based on the evaluation of nine Boolean predicates checking the intersections of the boundary, interior, and exterior of a spatial object with the respective parts of another spatial object for inequality to the empty set. In this paper, we replace each Boolean predicate, which is a topological invariant, by another topological invariant. This new invariant is given as a function yielding the dimension of the respective intersection in the 9-intersection matrix, resulting in a dimension matrix. The goal of this paper is to determine the definition and semantics of all predicates that can be derived from this matrix for all combinations of spatial data types. It turns out that these dimension-based predicates are special refinements of the aforementioned topological predicates; hence, we call them dimension-refined topological predicates. We show that these predicates allow us to pose a class of more fine-grained topological queries.