On Robust Interpretation of Topological Relations in Identity and Tolerance Models

In the last few years the amount of available spatial data has increased both in volume and in heterogeneity, so that dealing with this huge amount of information has become an interesting new research challenge. In particular, spatial data are usually represented through a vector model upon which several spatial relations have been defined. Such relations represent the basic tools for querying and manipulating spatial data and their robust evaluation in a distributed heterogeneous environment is an important issue to consider for allowing the effective usage of these data. Among all possible spatial relations, this paper considers the topological ones, since they are generally provided by all existing systems and represent the building blocks for the implementation of other spatial relations. The conditions and the operations needed to make a dataset robust w.r.t. topological interpretations strictly depends on the adopted evaluation model. This paper considers an environment where two different evaluation models for topological relations exist, one in which equality is based on the identity of geometric primitives, and the other one where a tolerance in equality evaluation is introduced. Given such premises, the paper proposes a set of rules for guaranteeing the robustness in both models, and discusses the applicability of available algorithms of the Snap Rounding family, in order to preserve robustness in case of perturbations.