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Algorithms for Hierarchical Spatial Reasoning

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Abstract

In several applications, there is the need to reason about spatial relations using multiple local frames of reference that are hierarchically organized. This paper focuses on hierarchical reasoning about direction relations, a special class of spatial relations that describe order in space (e.g., north or northeast). We assume a spatial database of points and regions. Points belong to regions, which may recursively be parts of larger regions. The direction relations between points in the same region are explicitly represented (and not calculated from coordinates). Inference mechanisms are applied to extract direction relations between points located in different regions and to detect inconsistencies. We study two complementary types of inference. The first one derives the direction relation between points from the relations of their ancestor regions. The second type derives the relation through chains of common points using path consistency. We present algorithms for both types of inference and discuss their computational complexity.

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References

  1. J.F. Allen. “Maintaining Knowledge about Temporal Intervals,” CACM 26(11):832–843, 1983.

    Google Scholar 

  2. A. Car and A. Frank. “General Principles of Hierarchical Spatial Reasoning: The Case of Wayfinding,” In the Proceedings of the 6th International Symposium on Spatial Data Handling, 1994.

  3. S.K. Chang, Q.Y. Shi, and C.W. Yan. “Iconic Indexing by 2-D String,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-9,No. 3, pp. 413–428, 1987.

    Google Scholar 

  4. E. Clementini, J. Sharma, and M. Egenhofer. “Modeling Topological Spatial Relations: Strategies for Query Processing.” International Journal of Computer and Graphics, 18(6):815–822, 1994.

    Google Scholar 

  5. Z. Cui, A.G. Cohn, and D.A. Randell. “Qualitative and Topological Relationships in Spatial Databases,” Proceedings of the 3 rd Symposium on Large Spatial Databases (SSD), 1993.

  6. E. Davis. Representing and Acquiring Geographic Knowledge, Morgan Kaufmann, 1986.

  7. J. De Kleer and J. Brown. “Qualitative Physics based on Confluences,” Artificial Intelligence, 24:7–83, 1984.

    Google Scholar 

  8. S. Dutta. “Qualitative Spatial Reasoning: A Semi-Qualitative Approach using Fuzzy Logic,” Proceedings of the First Symposium on the Design and Implementation of Large Spatial Databases 1989.

  9. M. Egenhofer and R. Franzosa. “Point Set Topological Relations,” International Journal of Geographic Information Systems, 5:161–174, 1991.

    Google Scholar 

  10. M. Egenhofer and J. Sharma. “Assessing the Consistency of Complete and Incomplete Topological Information,” Geographical Systems, 1(1):47–68, 1993.

    Google Scholar 

  11. M. Egenhofer. “Spatial SQL: A Query and Presentation Language,” IEEE Transactions on Knowledge and Data Engineering, 6(1):86–95, 1994.

    Google Scholar 

  12. C. Faloutsos and I. Kamel. “Beyond Uniformity and Independence: Analysis of R-trees Using the Concept of Fractal Dimension,” Proceedings of the 13th ACM PODS Symposium on Principles of Database Systems, 1994.

  13. B. Faltings. “Qualitative Kinematics in Mechanisms,” Artificial Intelligence, 44(1):89–119, 1990.

    Google Scholar 

  14. A.U. Frank. “Applications of DBMS to Land Information Systems,” In Proceedings of the 7 th International Conference on Very Large Data Bases (VLDB), 1981.

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

    Google Scholar 

  16. A.U. Frank. “Qualitative Spatial Reasoning: Cardinal Directions as an Example,” International Journal of Geographic Information Systems, 10(3):269–290, 1996.

    Google Scholar 

  17. C. Freksa. “Using Orientation Information for Qualitative Spatial Reasoning,” Proceedings of the International Conference GIS — From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, Pisa, Italy. Springer Verlag LNCS, 1992.

    Google Scholar 

  18. H. Fujihara and A. Mukerjee. Qualitative Reasoning about Document Structures, TR 91-010, Computer Science Department, TAMU, 1991.

  19. K-P. Gapp. “Basic Meaning of spatial Relations: Computation and Evaluation in 3D Space,” Proceedings of the National Conference on Artificial Intelligence, 1994.

  20. J.I. Glasgow. “Spatial Reasoning in Indeterminate Worlds,” Proceedings of the National Conference on Artificial Intelligence, 1994.

  21. J.I. Glasgow and D. Papadias. “Computational Imagery,” In Diagrammatic Reasoning. AAAI/MIT Press, 1995.

  22. M. Grigni, D. Papadias, and C. Papadimitriou. “Topological Inference,” Proceedings of the International Joint Conference of Artificial Intelligence, 1995.

  23. A. Guttman. “R-trees: a Dynamic Index Structure for Spatial Searching,” Proceedings of ACM SIGMOD International Conference on Management of Data, 1984.

  24. D. Hernandez. Qualitative Representation of Spatial Knowledge, Springer Verlag LNAI, 1994.

  25. A. Herskovits. Language and Spatial Cognition, Cambridge University Press, 1986.

  26. S. Hirtle and J. Jonides. “Evidence of Hierarchies in Cognitive Maps,” Memory and Cognition, 13:208–217, 1985.

    Google Scholar 

  27. P.D. Holmes and E. Jungert. “Symbolic and Geometric Connectivity Graph Methods for Route Planning In Digitized Maps,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-14,No. 5, pp. 549–565, 1993.

    Google Scholar 

  28. S-Y. Lee and F-J. Hsu. “Spatial reasoning and similarity retrieval of images using 2D C-string knowledge representation,” Pattern Recognition, 25(3):305–318, 1992.

    Google Scholar 

  29. A, Mackworth and E. Freuder. “The Complexity of some Polynomial Network Consistency Algorithms for Constraint Satisfaction Problems,” Artificial Intelligence, 25:65–74, 1985.

    Google Scholar 

  30. D. Mark. “Counter-Intuitive Geographic Facts: Clues for Spatial Reasoning at Geographic Scale,” Proceedings of the International Conference GIS — From Space to Territory: Theories and Methods of Spatio-Temporal Reasoning in Geographic Space, Pisa, Italy. Springer Verlag LNCS, 1992.

    Google Scholar 

  31. A. Mukerjee and G. Joe. “A Qualitative Model for Space,” Proceedings of the National Conference on Artificial Intelligence, 1991.

  32. M. Nabil, A. Ngu, and J. Shepherd. Picture similarity retrieval using 2d projection interval representation, IEEE TKDE, 8(4), 1996.

  33. D. Papadias and T. Scllis. “Qualitative Representation of Spatial Knowledge in Two-Dimensional Space,” Very Large Data Bases Journal, Special Issue on Spatial Databases, 3(4):479–516, 1994.

    Google Scholar 

  34. D. Papadias and T. Sellis. “A Pictorial Query-By-Example Language,” Journal of Visual Languages and Computing, Special Issue on Visual Query Systems, 6(1):53–72, 1995.

    Google Scholar 

  35. D. Papadias, Y. Theodoridis, T. Sellis, and M. Egenhofer. “Topological Relations in the World of Minimum Bounding Rectangles: a Study with R-trees,” Proceedings of ACM SIGMOD International Conference on Management of Data, 1995.

  36. D. Papadias, M.J. Egenhofer, and J. Sharma. “Hierarchical Reasoning about Direction Relations,” Proceedings of the 4 th ACM Workshop on GIS, 1996.

  37. D. Papadias and Y. Theodoridis. “Spatial Relations, Minimum Bounding Rectangles, and Spatial Data Structures,” International Journal of Geographic Information Systems, 11(2):111–138, 1997.

    Google Scholar 

  38. D. Peuquet and Z. Ci-Xiang. “An Algorithm to Determine the Directional Relationship between Arbitrarily-Shaped Polygons in the Plane,” Pattern Recognition, 20(1):65–74, 1987.

    Google Scholar 

  39. R. Rohrig. “A Theory of Qualitative Spatial Reasoning Based on Order Relations,” Proceedings of the National Conference on Artificial Intelligence, 1994.

  40. N. Roussopoulos, C. Faloutsos, and T. Sellis. “An Efficient Pictorial Database System for PSQL”. IEEE Transactions on Software Engineering, Special issue on Image Databases, pp. 639–650, 1988.

  41. J. Sharma and D. Flewelling. “Inferences from Combined Knowledge of Topology and Directions,” Proceedings of the 4 th Symposium on Large Spatial Databases (SSD), 1995.

  42. J. Sharma. “Heterogeneous Spatial Reasoning in Geographic Information Systems,” Ph.D. Thesis, Department of Spatial Information Science and Engineering, University of Maine, 1996.

  43. P. Sistla, C. Yu, and R. Haddad. “Reasoning about Spatial Relationships in Picture Retrieval Systems,” In the Proceedings of the 20th VLDB Conference, 1994.

  44. T. Smith and K. Park. “Algebraic Approach to Spatial Reasoning,” International Journal of Geographic Information Systems, 6(3):177–192, 1992.

    Google Scholar 

  45. T. Topaloglou. (1996) “Spatial Databases with Partial Information: Representation and Reasoning,” Ph.D. Thesis, Dept. of Computer Science, University of Toronto, Canada, 1996.

    Google Scholar 

  46. T. Topaloglou. “Qualitative Reasoning about Imprecise Spatial information,” Proceedings of the 2nd ACM Workshop on GIS, 1994.

  47. P. van Beek and R. Cohen. “Exact and Approximate Reasoning about Temporal Relations,” Computational Intelligence, 6:132–144, 1990.

    Google Scholar 

  48. P. van Beek. “Reasoning About Qualitative Temporal Information,” Artificial Intelligence, 58:297–326, 1992.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Hong Kong University of Science and Technology, Clearwater Bay, Hong Kong

    Dimitris Papadias

  2. National Center for Geographic Information and Analysis and Department of Spatial Information Science and Engineering, Department of Computer Science, University of Maine, Orono, ME, 04469-5711, USA

    Max J. Egenhofer

Authors
  1. Dimitris Papadias
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  2. Max J. Egenhofer
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Papadias, D., Egenhofer, M.J. Algorithms for Hierarchical Spatial Reasoning. GeoInformatica 1, 251–273 (1997). https://doi.org/10.1023/A:1009760430440

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