In spatial data models for various applications, such as geographical
information systems (GISs) the importance of topological relations is
widely recognized. Topology makes very general statements about the st
ructure and the relations of spatial objects. A refinement of topology
by means of other geometric aspects can help to bend the various mode
ls that have been developed for topological relations towards a more e
ffective description of geographic space. The introduction of broad bo
undaries is a direction to define approximate topological relations be
tween spatial objects. In this paper, approximate topological relation
s are destined to capture boundary uncertainty, variations over time,
proximity measures, and vector-raster representations. Approximate top
ological relations are structured in conceptual neighborhood graphs th
at have a twofold interpretation: two neighboring relations are at top
ological distance I in terms of the nine-intersection model and can be
obtained one from the other, by an elementary continuous deformation.
(C) 1997 Elsevier Science Inc.