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Composing Cardinal Direction Relations

  • Spiros Skiadopoulos
  • Manolis Koubarakis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2121)

Abstract

We study the recent proposal of Goyal and Egenhofer who presented a model for qualitative spatial reasoning about cardinal directions. Our approach is formal and complements the presentation of Goyal and Egenhofer. We focus our efforts on the operation of composition for two cardinal direction relations. We point out that the only published method to compute the composition does not always work correctly. Then we consider progressively more expressive classes of cardinal direction relations and give composition algorithms for these classes. Our theoretical framework allows us to prove formally that our algorithms are correct. Finally, we demonstrate that in some cases, the binary relation resulting from the composition of two cardinal direction relations cannot be expressed using the relations defined by Goyal and Egenhofer.

Keywords

Binary Relation Spatial Relation Reference Region Geographic Information System Cardinal Direction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    B. Bennett. Logical Representations for Automated Reasoning About Spatial Relations. PhD thesis, School of Computer Studies, University of Leeds, 1997.Google Scholar
  2. 2.
    Z. Cui, A.G. Cohn, and D.A. Randell. Qualitative and Topological Relationships in Spatial Databases. In Proceedings of SSD-93, pages 296–315, 1993.Google Scholar
  3. 3.
    M.J. Egenhofer. Reasoning about Binary Topological Relationships. In Proceedings of SSD-91, pages 143–160, 1991.Google Scholar
  4. 4.
    B. Faltings. Qualitative Spatial Reasoning Using Algebraic Topology. In Proceedings of COSIT-95, volume 988 of LNCS, 1995.Google Scholar
  5. 5.
    A.U. Frank. Qualitative Spatial Reasoning about Distances and Directions in Geographic Space. Journal of Visual Languages and Computing, 3:343–371, 1992.CrossRefGoogle Scholar
  6. 6.
    R. Goyal and M.J. Egenhofer. The Direction-Relation Matrix: A Representation for Directions Relations Between Extended Spatial Objects. In the annual assembly and the summer retreat of University Consortium for Geographic Information Systems Science, June 1997.Google Scholar
  7. 7.
    R. Goyal and M.J. Egenhofer. Cardinal Directions Between Extended Spatial Objects. IEEE Transactions on Data and Knowledge Engineering, (in press), 2000. Available at http://www.spatial.maine.edu/max/RJ36.html.
  8. 8.
    P.C. Kanellakis, G.M. Kuper, and P.Z. Revesz. Constraint Query Languages. Journal of Computer and System Sciences, 51:26–52, 1995.CrossRefMathSciNetGoogle Scholar
  9. 9.
    M. Koubarakis. The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases. Theoretical Computer Science, 171:25–60, January 1997. Special Issue on Uncertainty in Databases and Deductive Systems, Editor: L.V.S. Lakshmanan.Google Scholar
  10. 10.
    G. Ligozat. Reasoning About Cardinal Directions. Journal of Visual Languages and Computing, 9:23–44, 1998.CrossRefGoogle Scholar
  11. 11.
    S. Lipschutz. Set Theory and Related Topics. McGraw Hill, 1998.Google Scholar
  12. 12.
    D. Papadias. Relation-Based Representation of Spatial Knowledge. PhD thesis, Dept. of Electrical and Computer Engineering, National Technical University of Athens, 1994.Google Scholar
  13. 13.
    D. Papadias, N. Arkoumanis, and N. Karacapilidis. On The Retrieval of Similar Configurations. In Proceedings of 8th International Symposium on Spatial Data Handling (SDH), 1998.Google Scholar
  14. 14.
    D. Papadias, Y. Theodoridis, T. Sellis, and M.J. Egenhofer. Topological Relations in the World of Minimum Bounding Rectangles: A Study with R-trees. In Proceedings of ACM SIGMOD-95, pages 92–103, 1995.Google Scholar
  15. 15.
    C.H. Papadimitriou, D. Suciu, and V. Vianu. Topological Queries in Spatial Databases. Journal of Computer and System Sciences, 58(1):29–53, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    D.A. Randell, Z. Cui, and A. Cohn. A Spatial Logic Based on Regions and Connection. In Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference (KR’92). Morgan Kaufmann, October 1992.Google Scholar
  17. 17.
    J. Renz and B. Nebel. On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus. Artificial Intelligence, 1–2:95–149, 1999.MathSciNetGoogle Scholar
  18. 18.
    A.P. Sistla, C. Yu, and R. Haddad. Reasoning About Spatial Relationships in Picture Retrieval Systems. In Proceedings of VLDB-94, pages 570–581, 1994.Google Scholar
  19. 19.
    S. Skiadopoulos and M. Koubarakis. Qualitative Spatial Reasoning with Cardinal Directions. Submitted for publication, 2001.Google Scholar
  20. 20.
    K. Zimmermann. Enhancing Qualitative Spatial Reasoning-Combining Orientation and Distance. In Proceedings of COSIT-93, volume 716 of LNCS, pages 69–76, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Spiros Skiadopoulos
    • 1
  • Manolis Koubarakis
    • 2
  1. 1.Dept. of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece
  2. 2.Dept. of Electronic and Computer EngineeringTechnical University of CreteCreteGreece

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