Max Egenhofer and Robert Franzosa International Journal of Geographical Information Systems 9 (2): 133-152, 1995.
Abstract
The 4-intersection, a model for binary topological relations, is
based on the intersections of the boundaries and interiors of two
point sets in a topological space, considering the content
invariant (i.e., emptiness/non-emptiness) of the intersections. If
the 4-intersections of two pairs of point sets have different
contents, then their topological relations are different as well;
however, the reverse cannot be stated as there may be different
topological relations that map onto a 4-intersection with the same
content. This paper refines the model of empty/non-empty
4-intersections with further topological invariants to account for
more details about topological relations. The invariants used are
the dimension of the components, their types (touching, crossing,
and different refinements of crossings), their relationships with
respect to the exterior neighborhoods, and the sequence of the
components. These invariants, applied to non-empty
boundary-boundary intersections, comprise a classification
invariant for binary topological relations between homogeneously
2-dimensional, connected point sets (disks) in the plane such that
if two different 4-intersections with the necessary invariants are
equal, then their topological relationships are identical. The
model presented applies to processing GIS queries about whether or
not two pairs of spatial objects have the same topological relation
and gives rise to the formal definition of topological similarity.
Full article
Max Egenhofer and Robert Franzosa
