Skip to main content

On Internal Cardinal Direction Relations

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3693))

Abstract

Internal Cardinal Direction (ICD) relations can be considered as the refinement to the contains/within topological relation. It is widely used to describe the position of an object in a region. In this paper, three ICD models with varying degrees of details are presented – ICD-5, ICD-9 and ICD-13. In each of these, the notion of a “middle part” is defined using Minimum Bounding Rectangles (MBR). Then focusing on ICD-9, three representation methods are discussed. They are major portion, point set of intersections and proportions of intersections respectively. The ICD-9 model is validated by a cognitive experiment, which helped to determine the size of the middle part in ICD-9 and validate the MBR-based partition method. Based on a psychological theory about vague predicates, conceptual neighborhood and intersection of ICD relations are also discussed briefly.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bennett, B.: Logical Representations for Automated Reasoning about Spatial Relations. PhD thesis, School of Computer Studies, University of Leeds (1997)

    Google Scholar 

  2. Bonini, N., Osherson, D., Viale, R., Williamson, T.: On the Psychology of Vague Predicates. Mind and Language 14, 373–393 (1999)

    Article  Google Scholar 

  3. Car, A., Frank, A.: Modeling of the Hierarchy of Space Applied to Large Road Networks. In: Nievergelt, J., Widmayer, P., Roos, T., Schek, H.-J. (eds.) IGIS 1994. LNCS, vol. 884, pp. 15–24. Springer, Heidelberg (1994)

    Google Scholar 

  4. Clementini, E., Felice, P., Hernández, D.: Qualitative Representation of Positional Information. Artifical Intelligence 95, 317–356 (1997)

    Article  MATH  Google Scholar 

  5. Cohn, A.G., Hazarika, S.M.: Qualitative Spatial Representation and Reasoning: An Overview. Fundamenta Informaticae 46, 1–29 (2001)

    MATH  MathSciNet  Google Scholar 

  6. Cui, Z., Cohn, A.G., Randell, D.A.: Qualitative and Topological Relationships in Spatial Databases. In: Abel, D.J., Ooi, B.-C. (eds.) SSD 1993. LNCS, vol. 692, pp. 296–315. Springer, Heidelberg (1993)

    Google Scholar 

  7. Duckham, M., Worboys, M.: Computational Structure in Three-valued Nearness Relations. In: Montello, D.R. (ed.) Spatial Information Theory: Foundations of Geograpic Information Science. LNCS, vol. 2005, pp. 76–91. Springer, Berlin (2001)

    Google Scholar 

  8. Egenhofer, M.J.: Reasoning about Binary Topological Relationships. In: Switzerland, Z., Gunther, O., Schek, H.J. (eds.) SSD 1991. LNCS, vol. 525, pp. 143–160. Springer, Heidelberg (1991)

    Google Scholar 

  9. Faltings, B.: Qualitative Spatial Reasoning Using Algebraic Topology. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 17–30. Springer, Heidelberg (1995)

    Google Scholar 

  10. Frank, A.U.: Qualitative Spatial Reasoning about Distances and Directions in Geographic Space. Journal of Visual Languages and Computing 3, 343–371 (1992)

    Article  Google Scholar 

  11. Gahegan, M.: Proximity Operators for Qualitative Spatial Reasoning. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 31–44. Springer, Heidelberg (1995)

    Google Scholar 

  12. Goyal, R., Egenhofer, M.J.: 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 Science (June 1997)

    Google Scholar 

  13. Goyal, R., Egenhofer, M.J.: Cardinal Directions between Extended Spatial Objects. In: IEEE Transactions on Data and Knowledge Engineering (2000) (in press) Available at http://www.spatial.maine.edu/~max/RJ36.html

  14. Goyal, R., Egenhofer, M.J.: Similarity of Cardinal Directions. In: Jensen, C.S., Schneider, M., Seeger, B., Tsotras, V.J. (eds.) SSTD 2001. LNCS, vol. 2121, pp. 36–55. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  15. Hernández, D., Clementini, E., Felice, P.D.: Qualitative Distance. In: Frank, A.U., Kuhn, W. (eds.) COSIT 1995. LNCS, vol. 988, pp. 45–57. Springer, Heidelberg (1995)

    Google Scholar 

  16. Hernández, D.: Qualitative vs. Fuzzy Representation of Spatial Distance. In: Freksa, C., Jantzen, M., Valk, R. (eds.) Foundations of Computer Science. LNCS, vol. 1337, pp. 389–398. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  17. Hernández, D.: Qualitative Representation of Spatial Knowledge. LNCS, vol. 804. Springer, Heidelberg (1994)

    Book  MATH  Google Scholar 

  18. Hirtle, S.C., Jonides, J.: Evidence of hierarchies in Cognitive Maps. Memory & Cognition 13, 208–217 (1985)

    Article  Google Scholar 

  19. Leung, Y., Keung, K.S., He, J.Z.: A Generic Concept-based Object-oriented Geographical Information System. International Journal of Geographical Information Science 13, 475–498 (1999)

    Article  Google Scholar 

  20. Ligozat, G.: Reasoning About Cardinal Directions. Journal of Visual Languages and Computing 9, 23–44 (1998)

    Article  Google Scholar 

  21. Longley, P.A., Goodchild, M.F., Maguire, D., Rhind, D.W.: Geographic Information Systems and Science, pp. 79–96. John Wiley & Sons, Ltd., Chichester (2001)

    Google Scholar 

  22. Mark, D., Comos, D., Egenhofer, M., Freundschuh, S., Gould, M., Nunes, J.: Evaluating and Refining Computational Models of Spatial Relations through Cross-linguistic Human-subjects Testing. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 553–568. Springer, Heidelberg (1995)

    Google Scholar 

  23. Mark, D.M.: Spatial Representation: A Cognitive View. In: Maguire, D.J., Goodchild, M.F., Rhind, D.W., Longley, P. (eds.) Geographical Information Systems: Principles and Applications, 2nd edn., vol. 1, pp. 81–89. John Wiley & Sons, New York (1999)

    Google Scholar 

  24. Mennis, L.M., Peuquet, D.J., Qian, L.: A Conceptual Framework for Incorporating Cognitive Principles into Geographical Database Representation. International Journal of Geographical Information Science 14, 501–520 (2000)

    Article  Google Scholar 

  25. Montello, D.: Scale and Multiple Psychologies of Space. In: Campari, I., Frank, A.U. (eds.) COSIT 1993. LNCS, vol. 716, pp. 312–321. Springer, Heidelberg (1993)

    Google Scholar 

  26. Papadias, D., Theodoridis, Y., Sellis, T., Egenhofer, M.: Topological Relations in the World of Minimum Bounding Rectangles: A Study with R-trees. In: Carey, M., Schneider, D. (eds.) Proceedings of ACM SIGMOD, San Jose, CA, pp. 92–103 (1995)

    Google Scholar 

  27. Papadias, D., Egenhofer, M.: Algorithms for Hierarchical Spatial Reasoning. Geoinformatica 1, 251–273 (1997)

    Article  Google Scholar 

  28. Randell, D., Cui, Z., Cohn, A.: A Spatial Logic Based on Regions and Connection. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference (KR 1992), pp. 165–176. Morgan Kaufmann, San Francisco (1992)

    Google Scholar 

  29. Renz, J., Nebel, B.: On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus. Artificial Intelligence 12, 95–149 (1999)

    MathSciNet  Google Scholar 

  30. Renz, J., Mitra, D.: Qualitative Direction Calculi with Arbitrary Granularity. In: Zhang, C., Guesgen, H.W., Yeap, W.-K. (eds.) PRICAI 2004. LNCS (LNAI), vol. 3157, pp. 65–74. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  31. Schamber, L., Eisenberg, M.B., Nilan, M.S.: A re-examination of relevance: toward a dynamic, situational definition. Information Processing & Management 26, 755–776 (1990)

    Article  Google Scholar 

  32. Sistla, A.P., Yu, C., Haddad, R.: Reasoning About Spatial Relationships in Picture Retrieval Systems. In: Jorge, B., Jarke, M., Zaniolo, C. (eds.) Proceedings of VLDB, pp. 570–581. Morgan Kaufmann, San Francisco (1994)

    Google Scholar 

  33. Skiadopoulos, S., Koubarakis, M.: Composing Cardinal Direction Relations. In: Jensen, C.S., et al. (eds.) SSTD 2001. LNCS, vol. 2121, pp. 299–317. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  34. Smith, B., Varzi, A.C.: Fiat and Bona Fide Boundaries. Philosophy and Phenomenological Research 60, 401–420 (2000)

    Article  Google Scholar 

  35. Stevens, A., Coupe, P.: Distortions in Judged Spatial Relations. Cognitive Psychology 10, 422–437 (1978)

    Article  Google Scholar 

  36. Timpf, S., Volta, G.S., Pollock, D.W., Egenhofer, M.J.: A Conceptual Model of Wayfinding Using Multiple Levels of Abstraction. In: Frank, A.U., Formentini, U., Campari, I. (eds.) GIS 1992. LNCS, vol. 639, pp. 348–367. Springer, Heidelberg (1992)

    Google Scholar 

  37. Timpf, S., Frank, A.U.: Using Hierarchical Spatial Data Structures for Hierarchical Spatial Reasoning. In: Frank, A.U. (ed.) COSIT 1997. LNCS, vol. 1329, pp. 69–83. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  38. Worboys, M.F.: Nearness Relations in Environmental Space. International Journal of Geographical Information Science 15, 633–651 (2001)

    Article  Google Scholar 

  39. Yashino, R.: A Note on Cognitive Map: An Optimal Spatial Knowledge Representation. Journal of Mathematical Psychology 35, 371–393 (1991)

    Article  MathSciNet  Google Scholar 

  40. Zimmermann, K.: Enhancing Qualitative Spatial Reasoning- Combining Orientation and Distance. In: Campari, I., Frank, A.U. (eds.) COSIT 1993. LNCS, vol. 716, pp. 69–76. Springer, Heidelberg (1993)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Liu, Y., Wang, X., Jin, X., Wu, L. (2005). On Internal Cardinal Direction Relations. In: Cohn, A.G., Mark, D.M. (eds) Spatial Information Theory. COSIT 2005. Lecture Notes in Computer Science, vol 3693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556114_18

Download citation

  • DOI: https://doi.org/10.1007/11556114_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28964-7

  • Online ISBN: 978-3-540-32020-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics