A Formalization Of Topological Relations Between Simple Spatial Objects

This paper presents a new framework for modeling topological relations among objects of type point, line, and region. The main contributions are in two directions: First, the formalism proposed allows specifying all possible relations by means of symmetric matrices (whereas the usual formulation of such relations does not have this property). Symmetric matrices enable the efficient and automatic verification of valid matrices associated only with the possible topological relations. Second, it allows the specification of cases where two objects are spatially related in more than one way (e.g., a line that crosses a given region in one part and is adjacent to the same region region in another part). This increases the flexibility that users are offered to model queries on spatial databases using topological relations. © Springer-Verlag Berlin Heidelberg 2013.6175Alboody, A., Inglada, J., Sedes, F., Enriching the spatial reasoning system RCC8 (2009) SIGSPATIAL Spec, 1 (1), pp. 14-20Alexandroff, P., (1961) Elementary Concepts of Topology, , Dover Publications, Inc., New YorkClementini, E., Felice, P.D., Acomparison ofmethods for representing topological relationships (1995) Inf Sci Appl, 3 (3), pp. 149-178Clementini, E., Felice, P.D., Van Oosterom, P., (1992) A Small Set of Formal Topological Relationships Suitable for End-user Interaction, , Technical Report, University of L'Aquilla, ItalyClementini, E., Sharma, J., Egenhofer, M., Modelling topological spatial relations: Strategies for query processing (1994) Comput Graph, 18 (6), pp. 815-822Deng, M., Cheng, T., Chen, X., Li, Z., Multi-level topological relations between spatial regions based upon topological invariants (2007) GeoInformatica, 11 (2), pp. 239-267Egenhofer, M., ExtendingSQLfor cartographic display (1991) Cartogr Geogr Inf Syst, 18 (4), pp. 230-245Egenhofer, M., Al-Taha, K., Reasoning about gradual changes of topological relationships (1992) Theories and Methods of Spatio-temporal Reasoning in Geographic Space, pp. 196-219. , Frank ICA, Formentini U (eds), Springer, PisaEgenhofer, M., Franzosa, R., Point-set topological spatial relations (1991) Int J Geogr Inf Syst, 5 (2), pp. 161-174Egenhofer, M., Herring, J., Amathematical framework for the definition of topological relationships (1990) Proceedings Fourth International Symposium on Spatial Data Handling, 2, pp. 803-813. , Brassel K, Kishimoto H (eds) International geographical union, Zurich, SwitzerlandEgenhofer, M., Herring, J., (1991) Categorizing Binary Topological Relationships between Regions, Lines, and Points in Geographic Databases, , Technical report, Department of Surveying Engineering, University of Maine, OronoEgenhofer, M., Herring, J., (1991) Categorizing Topological Spatial Relations between Point, Line, and Area Objects, , Technical Report, University of MaineEgenhofer, M., Mark, D., Modelling conceptual neighbourhoods of topological line-region relations (1995) Int J Geogr Inf Syst, 9 (5), pp. 555-565Frank, A., Mapquery-database query language for retrieval of geometric data and its graphical representation (1982) ACM Comput Graph, 16 (3), pp. 199-207Freksa, C., Temporal reasoning based on semi-intervals (1992) Artif Intell, 54, pp. 199-227Herring, J., The mathematical modeling of spatial and non-spatial information in geographic information systems (1991) Cognitive and Linguistic Aspects of Geographic Space, pp. 313-350. , Mark D, Frank A (eds) Kluwer Academic Publishers, DordrechtHerring, J., Larsen, R., Shivakumar, J., Extensions to the SQLlanguage to support spatial analysis in a topological database (1988) Proceedings GIS/LIS'88, pp. 741-750. , San Antonio, TXKurata, Y., Semi-automated derivation of conceptual neighborhood graphs of topological relations (2009) Proceedings of the International Conference on Spatial Information TheoryKurata, Y., Egenhofer, M., The 9+-intersection for topological relations between a directed line segment and a region (2007) Proceedings of the Workshop on Behavioral Monitoring and Interpretation, 42, pp. 62-76McKenney, M., Pauly, A., Praing, R., Schneider, M., Dimension-refined topological predicates (2005) Proceedings GIS'05, , Bremen, GermanyPapadias, D., Egenhofer, M., Sharma, J., Hierarchical reasoning about direction relations (1996) Proccedings 4th ACM Workshop on Advances In, GIS, pp. 107-114Pigot, S., Topological models for 3d spatial information systems (1991) Proceedings of Autocarto 10 (Falls Church: American Society for Photogrammetry and Remote Sensing, pp. 368-392. , Mark D, White D (eds)Raper, J., Bundock, M., UGIX: A layer-based model for a GIS user interface (1991) Cognitive and Linguistic Aspects of Geographic Space, pp. 449-476. , Mark D, FrankA(eds) Kluwer Academic Publishers, DordrechtRoussopoulos, N., Faloutsos, C., Sellis, T., An efficient pictorial database system for PSQL (1988) IEEE Trans Software Eng, 14 (5), pp. 630-63