Identification of Relations in Region Connection Calculus: 9-Intersection Reduced to 3⁺-Intersection Predicates

Abstract

The intersection between objects relates to a class of problems where either precise intersection is required or imprecise intersection is acceptable. The calculation of intersection between two 2D/3D objects is a computation-intensive process. For qualitative spatio-temporal reasoning, it is sufficient to know the existence of intersection instead of the precise intersection. In order to identify RCC8 relations, the 9-Intersection model considers the pairwise intersection of interiors, boundaries, and exteriors of objects. It was determined that the 9-Intersection is sufficient for identifying spatial relations. Later, it was shown that a 4-Intersection model is sufficient to achieve the same results making the definition (and implementation) of the RCC8 relations worth studying in greater detail. Herein we prove that the 9-Intersection model can be further reduced to almost three intersection predicates, producing a 3⁺-Intersection model. This results in improved algorithmic and computational efficiency as a consequence of fewer predicates and faster intersection operations.

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