Uncertain topological relations between imprecise regions

Spatial databases are repositories of representations of the real world. Th e represented entities have to be observed in the real world and mapped to the database. An observation is interpreted here as a two-level process, co nsisting of the abstraction of the observed object to a concept and a measu rement of the realized concept. Due to the nature of observations, regions representing the location of objects are always imprecise, the explication of a concept succeeds only incompletely, and the measurement is limited in precision. In this paper, the uncertainty in abstraction as well as the imprecision of measurement are modelled statistically. This allows the introduction of th e uncertainty of observation into qualitative spatial reasoning. The exampl e used in this paper is the determination of topological relations. The top ological relation between two regions becomes uncertain if the regions are imprecise in their location. Hence, the decision about a topological relati on is made by maximum likelihood classification. The classification allows a quantitative assessment of the decision by its probability, and by the pr obability of the alternative relations. The method is useful in data set co mparison, data matching, and modelling data quality descriptions.