Aggregations and constituents: geometric specification of multi-granular objects

The article presents an approach for modeling the regions of large-scale aggregations like forests that is based on an axiomatic geometry formalizing concepts of granularity and local perception: based on a planar geometry of incidence and ordering, congruence of size is characterized using certain geometric entities called places, which are specified to have the same extension in every direction. Size is axiomatized in a comparative and non-numeric manner suitable for qualitative spatial reasoning over granularity. A specification for the granular interior of an aggregation in a global (GGI) and a local variant (LGI) is given. The specification was derived from the observation that objects like forests are perceived locally in an environment. The expressiveness of the characterization is tested on different commonsense notions concerning the representation of aggregations of natural objects.