Skip to main content
SpringerLink
Log in

Probabilistic composition of cone-based cardinal direction relations

  • Published:
Science in China Series E: Technological Sciences Aims and scope Submit manuscript

Abstract

Composition tables play a significant role in qualitative spatial reasoning (QSR). At present, a couple of composition tables focusing on various spatial relations have been developed in a qualitative approach. However, the spatial reasoning processes are usually not purely qualitative in everyday life, where probability is one important issue that should be considered. In this paper, the probabilistic compositions of cone-based cardinal direction relations (CDR) are discussed and estimated by making some assumptions. Consequently, the form of composition result turns to be {(R 1,P 1), (R 2,P 2), ..., (R n ,P n )}, where P i is the probability associated with relation R i . Employing the area integral method, the probabilities in each composition case can be computed with the assumption that the target object is uniformly distributed in the corresponding cone regions.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cohn A G, Hazarika SM. Qualitative spatial representation and reasoning: An overview. Fund Inform, 2001, 46: 1–29

    MATH  MathSciNet  Google Scholar 

  2. Freksa C. Using orientation information for qualitative spatial reasoning. In: Proceeding of the International Conference GIS-From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning in Geographic Space. Berlin: Springer-Verlag, 1992. 162–178

    Google Scholar 

  3. Duckham M, Worboys M. Computational structure in three-valued nearness relations. Proc COSIT, 2001. 76–91

  4. Renz J. Qualitative Spatial Reasoning with Topological Information. Berlin: Springer-Verlag, 2002

    MATH  Google Scholar 

  5. Ligozat G, Renz J. What is a qualitative calculus? A general framework. Proc PRICAI, 2004. 53–64

  6. Bennett B, Isli A, Cohn A G. When does a composition table provide a complete and tractable proof procedure for a relational constraint language? Proc IJCAI-97, 1997

  7. Randell D A, Cohn A G, Cui Z. Computing transitivity tables: A challenge for automated theorem provers. Proc 11th CADE, 1992. 786–790

  8. Skiadopoulos S, Koubarakis M. Composing cardinal direction relations. Proc SSTD, 2001. 299–317

  9. Frank A U. Qualitative spatial reasoning about distances and directions in geographic space. J Visual Lang Comput, 1992, 3: 343–371

    Article  Google Scholar 

  10. Russell S, Norvig P. Artificial Intelligence: A Modern Approach. New Jersey: Prentice Hall, 2003

    Google Scholar 

  11. Zadeh L A. Making computers think like people. IEEE Spectrum, 1984, 8: 26–32

    Google Scholar 

  12. Ryabov V, Trudel A. Probabilistic temporal interval networks. Proc TIME’04, 2004. 64–67

  13. Dehak S M R, Bloch I, Maître H. Spatial reasoning with incomplete information on relative positioning. IEEE T Pattern Anal, 2005, 27(9): 1473–1484

    Article  Google Scholar 

  14. Frank A U. Qualitative spatial reasoning about distances and directions in geographic space. J Visual Lang Comput, 1992, 3: 343–371

    Article  Google Scholar 

  15. Goyal R K, Egenhofer M J. Similarity of cardinal directions. Proc SSTD, 2001. 36–58

  16. Frank A U. Qualitative spatial reasoning about cardinal directions. In: Proceeding of the 7th Austrian Conference on Artificial Intelligence, 1991. 157–167

  17. Frank A U. Qualitative spatial reasoning: Cardinal directions as an example. Int J Geogr Inf Syst, 1996, 10(3): 269–290

    Article  Google Scholar 

  18. Ligozat G. Categorical methods in qualitative reasoning: The case for weak representations. Proc COSIT 2005, 2005. 265–282

  19. Cussens J. Parameter estimation in stochastic logic programs. Mach Learn, 2001, 43(3): 245–271

    Article  Google Scholar 

  20. Flach P A, Gyftodimos E. Probabilistic reasoning with terms. Comput Inf Sci, 2002, 7(11): 1–10

    Google Scholar 

  21. Wang X, Liu Y, Gao Z, et al. Landmark-based qualitative reference system. Proc IGARSS, 2005, 2: 932–935

    Google Scholar 

  22. Montello D R, Frank A U. Modeling directional knowledge and reasoning in environmental space: testing qualitative metrics. In: The Construction of Cognitive Maps. Dordrecht: Kluwer Academic Publishers, 1996. 321–344

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Remote Sensing and Geographical Information Systems, Peking University, Beijing, 100871, China

    Yu Liu & Yuan Tian

  2. College of Software, Beihang University, Beijing, 100083, China

    JingNong Weng

Authors
  1. Yu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuan Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. JingNong Weng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuan Tian.

Additional information

Supported by the National Hi-Tech Research and Development Program of China (Grant No. 2007AA12Z216) and the National Natural Science Foundation of China (Grant No. 40701134)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Y., Tian, Y. & Weng, J. Probabilistic composition of cone-based cardinal direction relations. Sci. China Ser. E-Technol. Sci. 51 (Suppl 1), 81–90 (2008). https://doi.org/10.1007/s11431-008-5007-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-008-5007-4

Key words

Search

Navigation