Design and implementation of finite resolution crisp and fuzzy spatial objects

Uncertainty management for geometric data is currently an important problem in spatial databases, image databases, and Geographic Information Systems (GIS). Spatial entities 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 spatial fuzziness this paper provides a conceptual and an implementation 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 not on an infinite-precision arithmetic which lead to lacking numerical robustness and to topological inconsistency of implementations on a computer; 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 is a contribution to achieve a uniform treatment of vector and raster data.