Topological relations in the world of minimum bounding rectangles: a study with R-trees
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Region connection calculus: its models and composition table
Artificial Intelligence
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ACM SIGMOBILE Mobile Computing and Communications Review
Topological relationships between complex spatial objects
ACM Transactions on Database Systems (TODS)
COSIT'07 Proceedings of the 8th international conference on Spatial information theory
A Reference System for Topological Relations between Compound Spatial Objects
ER '09 Proceedings of the ER 2009 Workshops (CoMoL, ETheCoM, FP-UML, MOST-ONISW, QoIS, RIGiM, SeCoGIS) on Advances in Conceptual Modeling - Challenging Perspectives
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Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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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.