Evolution of Region Connection Calculus to VRCC-3D+

Abstract

Qualitative spatial reasoning (QSR) is useful for deriving logical inferences when quantitative spatial information is not available. QSR theories have applications in areas such as geographic information systems, spatial databases, robotics, and cognitive sciences. The existing QSR theories have been applied primarily to 2D. The ability to perform QSR over a collection of 3D objects is desirable in many problem domains. Here we present the evolution (VRCC-3D+) of RCC-based QSR from 2D to both 3D (including occlusion support) and 4D (a temporal component). It is time consuming to construct large composition tables manually. We give a divide-and-conquer algorithm to construct a comprehensive composition table from smaller constituent tables (which can be easily handcrafted). In addition to the logical consistency entailment checking that is required for such a system, clearly there is a need for a spatio-temporal component to account for spatial movements and path consistency (i.e. to consider only smooth transitions in spatial movements over time). Visually, these smooth movement phenomena are represented as a conceptual neighborhood graph. We believe that the methods presented herein to detect consistency, refine uncertainty, and enhance reasoning about 3D objects will provide useful guidelines for other studies in automated spatial reasoning.