Finite Resolution Crisp and Fuzzy Spatial Objects

Uncertainty management for geometric data is currently an important problem in spatial databases, image databases, and GIS. Spatial objects do not always have homogeneous interiors and sharply defined boundaries but frequently their interiors and boundaries are partially or totally indeterminate and vague. For an important kind of spatial vagueness called fuzziness this paper provides a conceptual model of fuzzy spatial objects that also incorporates fuzzy geometric union, intersection, and difference operations as well as fuzzy topological predicates. In particular, this model is not based on Euclidean space and on an infinite-precision arithmetic which lead to lacking numerical robustness and to topological inconsistency; it rests on a finite, discrete geometric domain called grid partition which takes into account finite-precision number systems available in computers. Last but not least this paper shall also be a contribution to achieve a uniform treatment of vector and raster data.