A comparison of methods for representing topological relationships
Information Sciences—Applications: An International Journal
Composite regions in topological queries
Information Systems
Information Sciences: an International Journal
Topology in Raster and Vector Representation
Geoinformatica
A Formal Definition of Binary Topological Relationships
FOFO '89 Proceedings of the 3rd International Conference on Foundations of Data Organization and Algorithms
Complex Regions in Topological Queries
COSIT '97 Proceedings of the International Conference on Spatial Information Theory: A Theoretical Basis for GIS
A Small Set of Formal Topological Relationships Suitable for End-User Interaction
SSD '93 Proceedings of the Third International Symposium on Advances in Spatial Databases
ER'05 Proceedings of the 24th international conference on Conceptual Modeling
Entity-relationship and object-oriented formalisms for modeling spatial environmental data
Environmental Modelling & Software
Representing mereotopological relations in OWL ontologies with ONTOPARTS
ESWC'12 Proceedings of the 9th international conference on The Semantic Web: research and applications
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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Topological relationships between two spatial features represent important knowledge in Geographical Information Systems (GIS). In the last few years, many models that represent topological relationships have been proposed. But these models cannot represent the topological relationships between heterogeneous geometrycollection features, which are composed of different dimensional geometries. In this paper, the formal definition of regular heterogeneous geometrycollection and regularization rules are given. Based on the spatial model, two methods for representing topological relationships between these complex features are proposed. The first method is Dimensionally Extended Nine-Intersection Model Based on Components (DE-9IMBC) that extends Dimensionally Extended Nine-Intersection Model (DE-9IM) and takes into account the topological relationships between components of these complex features. The advantage of DE-9IMBC is that, a large number of different topological relationships can be checked. The second method extends the definitions of topological relationships in Open Geodata Interoperability Specification (OpenGIS), and redefines the seven named topological relationships: {Disjoint, Touches, Within, Crosses, Overlaps, Contains and Equal}, to represent the topological relationships between heterogeneous geometrycollection features. It is proven that the seven extended topological relationships are complete and mutually exclusive, and they are suitable for being embedded in spatial query languages.