Extensions to geometric approximations of spatial boundaries and assessment of fuzzy spatial relationships

Many spatial data modeling strategies rely upon approximate representations of spatial objects both for computational efficiency issues as well as the simplification of logical modeling strategies. The most widely used approximation is the minimum bounding rectangle (MBR). While the use of MBRs in spatial data modeling is extensive due to their efficiency for storage and relationship calculation, their use as a solitary means of identifying, for example, topological relationships between objects is problematic due to the inconsistency of mappings between relationships of MBRs and corresponding relationships of the objects they represent. In this paper we examine several extensions to the MBR model that reduce the discrepancies between binary spatial relationships of the MBR and those of the contained objects. For each scheme, we consider the implications to the determination of fuzzy spatial relationships and the impact on computational issues