Reducing 9-Intersection to 4-Intersection for Identifying Relations in Region Connection Calculus

Several region connection calculi have been proposed for use in Qualitative Spatial Reasoning (QSR). Perhaps the most well-known model is RCC-8, which uses a 9-Intersection framework to identify the spatial relation between two regions. The calculation of the 9-Intersection matrix is particularly computationintensive in 3D. Herein we show that 9-Intersection calculations can be replaced with 2-Intersection, 3Intersection, and (at most) 4-Intersection calculations for each RCC-8 relation, yielding the same results. This reduces the computational effort considerably while retaining the same accuracy. Mathematical proofs are given to show the equivalence of the 9Intersection and the ≤4-Intersection.