Qualitative spatial reasoning in 3d: Spatial metrics for topological connectivity in a region connection calculus

Abstract

In qualitative spatial reasoning, there are three distinct properties for reasoning about spatial objects: connectivity, size, and direction. Reasoning over combinations of these properties can provide additional useful knowledge. To facilitate end-user spatial querying, it also is important to associate natural language with these relations. Some work has been done in this regard for lineregion and region-region topological relations in 2D, and very recent work has initiated the association between natural language, topology, and metrics for 3D objects. However, prior efforts have lacked rigorous analysis, expressive power, and completeness of the associated metrics. Herein we present new metrics to bridge the gap required for integration between topological connectivity and size information for spatial reasoning. The new set of metrics that we present should be useful for a variety of applications dealing with 3D objects.