Comparing Relations with a Multi-holed Region

Relation models have treated multi-holed regions relations either the same as hole-free regions relations, loosing this way the peculiarities of the holed topology, or with methods dependent on the number of holes. This paper discusses a model of relations between a hole-free and a multi-holed region that departs from past approaches by using the frequencies of the relations in which the holes participate to summarize the relation. The model is independent of the number of holes and builds on the 23 topological relations between a hole-free and a singleholed region. With the help of a balanced algorithm the relation model is used in a method that compares relations for their topological similarity, by computing the cost of transforming one relation into the other. The placement of the holes in relation to the hole-free region is found to be of same importance as the placement of the host of the holes, for similarity comparisons.