Transformations among Topological Relation Representation Models for Regions with Holes Using the 25-intersection Method

A variety of topological relation representation models for complex regions with holes have been put forward nowadays.Establishing the connections among different models can give full play to the advantages of these models in the derivation and analysis of topological relations.Based on the point-set topology theory and region decomposition,six topological relation representation models were analyzed.Two 25-intersection (25I) Boolean matrix operators were defined and used for computing the binary topological relations between complex regions while the relations between the decomposed regions were known.Based on the operators,transformations among the description models were realized.Theoretical analysis proved that the relational matrix table and extended 9-intersection model have the same accurate expression of topological relations and can be transformed with each other,and so do the 4-tuple model and 25I model.Furthermore,the method of relational matrix table can be transformed to 25I model and classical 9-intersection model.The experimental analysis shows that our method can be used to link different topological relation representation models and derive topological relations between complex regions with holes