Abstract
Current spatial database systems offer limited querying capabilities beyond topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane in five regions that are obtained from projective properties of two reference objects: then, by considering the empty/non empty intersections of a primary object with these five regions, the model is able to distinguish between 31 different projective relations.
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References
Clementini, E., Di Felice, P.: Spatial Operators. ACM SIGMOD Record 29(3), 31–38 (2000)
Clementini, E., Di Felice, P., Hernández, D.: Qualitative representation of positional information. Artificial Intelligence 95, 317–356 (1997)
Clementini, E., Di Felice, P., van Oosterom, P.: A Small Set of Formal Topological Relationships Suitable for End-User Interaction. In: Abel, D.J., Ooi, B.-C. (eds.) SSD 1993. LNCS, vol. 692, pp. 277–295. Springer, Heidelberg (1993)
Dugat, V., Gambarotto, P., Larvor, Y.: Qualitative Theory of Shape and Orientation. In: Proc. of the 16th Int. Joint Conference on Artificial Intelligence (IJCAI 1999), pp. 45–53. Morgan Kaufmann Publishers, Stockolm (1999)
Egenhofer, M.J.: Deriving the composition of binary topological relations. Journal of Visual Languages and Computing 5(1), 133–149 (1994)
Egenhofer, M.J., Herring, J.R.: Categorizing Binary Topological Relationships Between Regions, Lines, and Points in Geographic Databases. In: Department of Surveying Engineering, University of Maine, Orono (1991)
Freksa, C.: Using Orientation Information for Qualitative Spatial Reasoning. In: Frank, A.U., Campari, I., Formentini, U. (eds.) Theories and Models of Spatio-Temporal Reasoning in Geographic Space, pp. 162–178. Springer, Berlin (1992)
Gapp, K.-P.: Angle, Distance, Shape, and their Relationship to Projective Relations. In: Proceedings of the 17th Conference of the Cognitive Science Society, Pittsburgh, PA (1995)
Gapp, K.-P.: From Vision to Language: A Cognitive Approach to the Computation of Spatial Relations in 3D Space. In: Proc. of the First European Conference on Cognitive Science in Industry, Luxembourg, pp. 339–357 (1994)
Goyal, R., Egenhofer, M.J.: Cardinal directions between extended spatial objects. IEEE Transactions on Knowledge and Data Engineering (2003) (in press)
Hernández, D.: Qualitative Representation of Spatial Knowledge. LNCS (LNAI), vol. 804. Springer, Heidelberg (1994)
Isli, A.: Combining Cardinal Direction Relations and other Orientation Relations in QSR. In: AI&M 14-2004, Eighth International Symposium on Artificial Intelligence and Mathematics, Fort Lauderdale, Florida, January 4-6 (2004)
Kray, C., Blocher, A.: Modeling the Basic Meanings of Path Relations. In: Proc. of the 16th International Joint Conference on Artificial Intelligence (IJCAI 1999), pp. 384–389. Morgan Kaufmann Publishers, Stockolm (1999)
Kulik, L., et al.: A graded approach to directions between extended objects. In: Proc. of the 2nd Int. Conf. on Geographic Information Science, pp. 119–131. Springer, Boulder (2002)
Kulik, L., Klippel, A.: Reasoning about Cardinal Directions Using Grids as Qualitative Geographic Coordinates. In: Freksa, C., Mark, D.M. (eds.) COSIT 1999. LNCS, vol. 1661, pp. 205–220. Springer, Heidelberg (1999)
Moratz, R., Fischer, K.: Cognitively Adequate Modelling of Spatial Reference in Human-Robot Interaction. In: Proc. of the 12th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2000, Vancouver, BC, Canada, pp. 222–228 (2000)
OpenGIS Consortium, OpenGIS Simple Features Specification for SQL (1998)
Retz-Schmidt, G.: Various Views on Spatial Prepositions. AI Magazine 9(2), 95–105 (1988)
Schlieder, C.: Reasoning about ordering. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 341–349. Springer, Heidelberg (1995)
Schmidtke, H.R.: The house is north of the river: Relative localization of extended objects. In: Montello, D.R. (ed.) COSIT 2001. LNCS, vol. 2205, pp. 415–430. Springer, Heidelberg (2001)
Scivos, A., Nebel, B.: Double-Crossing: Decidability and Computational Complexity of a Qualitative Calculus for Navigation. In: Montello, D.R. (ed.) COSIT 2001. LNCS, vol. 2205, pp. 431–446. Springer, Heidelberg (2001)
Struik, D.J.: Projective Geometry. Addison-Wesley, London (1953)
Vorwerg, C., et al.: Projective relations for 3D space: Computational model, application, and psychological evaluation. In: Proc. of the 14th National Conference on Artificial Intelligence and 9th Innovative Applications of Artificial Intelligence Conference, AAAI 1997, IAAI 1997, pp. 159–164. AAAI Press / The MIT Press, Providence, Rhode Island (1997)
Waller, D., et al.: Place learning in humans: The role of distance and direction information. Spatial Cognition and Computation 2, 333–354 (2000)
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Billen, R., Clementini, E. (2004). A Model for Ternary Projective Relations between Regions. In: Bertino, E., et al. Advances in Database Technology - EDBT 2004. EDBT 2004. Lecture Notes in Computer Science, vol 2992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24741-8_19
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DOI: https://doi.org/10.1007/978-3-540-24741-8_19
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