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Spatial reasoning with augmented points: Extending cardinal directions with local distances

R. Moratz,J. O. Wallgrün

Published 2012 in J. Spatial Inf. Sci.

ABSTRACT

We present an approach for supplying existing qualitative direction calculi with a distance component to support fully fledged positional reasoning. The general under- lying idea of augmenting points with local reference properties has already been applied in the OPRAm calculus. In this existing calculus, point objects are attached with a local reference direction to obtain oriented points and able to express relative direction using binary relations. We show how this approach can be extended to attach a granular distance concept to direction calculi such as the cardinal direction calculus or adjustable granularity calculi such as OPRAm or the Star calculus. We focus on the cardinal direction calcu- lus and extend it to a multi-granular positional calculus called EPRAm .W e provide a formal specification of EPRAm including a composition table for EPRA2 automatically determined using real algebraic geometry. We also report on an experimental performance analysis of EPRA2 in the context of a topological map-learning task proposed for bench- marking qualitative calculi. Our results confirm that our approach of adding a relative distance component to existing calculi improves the performance in realistic tasks when using algebraic closure for consistency checking.

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