2D+ string: a spatial metadata to reason topological and directional relationships

Spatial relationships have gained increasing attention in spatial databases. Reasoning spatial relationships is very expensive since it requires massive geometric computations. In particular, reading and comparing information to reason directional and topological relationships can be repeated as they are processed separately in previous works. In order to avoid the repetition and improve the performance of reasoning spatial relationships, we propose a novel metadata representation scheme, 2D+ (2 dimensional plus) string which contains direction and topology information between objects in a picture, with a generation method of the string, inference rules to reason directional and topological relationships and their application to reasoning. Our analysis of the reasoning performance using 2D+ string show that it depends on the amount of information stored in 2D+ string, which is less than that of previous works. The simplicity and expressive power are the main advantages of 2D+ string.