Max Egenhofer, Eliseo Clementini, and Paolino di Felice International Journal of Geographical Information Systems 8 (2): 129-144, 1994.
Abstract
The 4-intersection, a model for the representation of topological
relations between 2-dimensional objects with connected boundaries
and connected interiors, is extended to cover topological relations
between 2-dimensional objects with arbitrary holes, called regions
with holes. Each region with holes is represented by its
generalized region--the union of the object and its holes--and the
closure of each hole. The topological relation between two regions
with holes, A and B, is described by the set of all
individual topological relations between (1) A's generalized
region and B's generalized region, (2) A's
generalized region and each of B's holes, (3) 's generalized
region with each of A's holes, and (4) each of A's
holes with each of B's holes. As a side product, the same
formalism applies to the description of topological relations
between 1-spheres. An algorithm is developed that minimizes
the number of individual topological relations necessary to
describe a configuration completely. This model of representing
complex topological relations is suitable for a multi-level
treatment of topological relations, at the least detailed level of
which the relation between the generalized regions prevails. It is
shown how this model applies to the assessment of consistency in
multiple representations when, at a coarser level of less detail,
regions are generalized by dropping holes.
Full article
Max Egenhofer, 
Eliseo Clementini, and 
Paolino di Felice
