Uncertain topological relations between imprecise regions

Spatial databases are repositories of representations of the real world. The 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, consisting of the abstraction of the observed object to a concept and a measurement 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 the uncertainty of observation into qualitative spatial reasoning. The example used in this paper is the determination of topological relations. The topological relation between two regions becomes uncertain if the regions are imprecise in their location. Hence, the decision about a topological relation is made by maximum likelihood classification. The classification allows a quantitative assessment of the decision by its probability, and by the probability of the alternative relations. The method is useful in data set comparison, data matching, and modelling data quality descriptions.