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Single-Holed Regions: Their Relations and Inferences

  • Maria Vasardani
  • Max J. Egenhofer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5266)

Abstract

The discontinuities in boundaries and exteriors that regions with holes expose offer opportunities for inferences that are impossible for regions without holes. A systematic study of the binary relations between single-holed regions shows not only an increase in the number of feasible relations (from eight between two regions without holes to 152 for two single-holed regions), but also identifies the increased reasoning power enabled by the holes. A set of quantitative measures is introduced to compare various composition tables over regions with and without holes. These measures reveal that inferences over relations for holed regions are overall crisper and yield more unique results than relations over regions without holes. Likewise, compositions that involve more holed regions than regions without holes provide crisper inferences, which supports the need for relation models that capture holes explicitly.

Keywords

Cumulative Frequency Topological Relation Spatial Reasoning Composition Result Converse Relation 
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. Ahmed, N., Kanhere, S., Jha, S.: The Holes Problem in Wireless Sensor Networks: A Survey. Mobile Computing and Communications Review 9(2), 4–18 (2005)CrossRefGoogle Scholar
  2. Cassati, R., Varzi, A.: Holes and Other Superficialities. MIT Press, Cambridge (1994)Google Scholar
  3. Cohn, A., Gotts, N.: The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries. In: Burrough, P., Frank, A. (eds.) Geographic Objects with Indeterminate Boundaries, pp. 171–187. Taylor & Francis, Bristol (1996)Google Scholar
  4. Clementini, E., Di Felice, P.: An Algebraic Model for Spatial Objects with Indeterminate Boundaries. In: Burrough, P., Frank, A. (eds.) Geographic Objects with Indeterminate Boundaries, pp. 155–170. Taylor & Francis, Bristol (1996)Google Scholar
  5. Egenhofer, M.: Deriving the Composition of Binary Topological Relations. Journal of Visual Languages and Computing 5(1), 133–149 (1994)CrossRefGoogle Scholar
  6. Egenhofer, M., Clementini, E., Di Felice, P.: Topological Relations Between Regions With Holes. International Journal of Geographical Information Systems 8(2), 129–144 (1994)CrossRefGoogle Scholar
  7. Egenhofer, M., Franzosa, R.: Point-Set Topological Spatial Relations. International Journal of Geographical Information Systems 5(2), 161–174 (1991)CrossRefGoogle Scholar
  8. Egenhofer, M., Herring, J.: 1994, Categorizing Binary Topological Relations Between Regions, Lines, and Points in Geographic Databases. Technical Report, Department of Surveying Engineering, University of Maine (1990)Google Scholar
  9. Egenhofer, M., Vasardani, M.: Spatial Reasoning with a Hole. In: Winter, S., Duckham, M., Kulik, L., Kuipers, B. (eds.) COSIT 2007. LNCS, vol. 4736, pp. 303–320. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. Lewis, D., Lewis, S.: Holes. Australasian Journal of Philosophy 48, 206–212 (1970)CrossRefGoogle Scholar
  11. Li, S., Ying, M.: Region Connection Calculus: Its Models and Composition Table. Artificial Intelligence 145(1-2), 121–146 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  12. Mackworth, A.: Consistency in Networks of Relations. Artificial Intelligence 8(1), 99–118 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  13. Papadias, D., Theodoridis, Y., Selis, T., Egenhofer, M.: Topological Relations in the World of Minimum Bounding Rectangles: A Study with R-trees. SIGMOD Record 24(2), 92–103 (1995)CrossRefGoogle Scholar
  14. Randell, D., Cohn, A., Cui, Z.: A Spatial Logic Based on Regions and Connection. In: Proceedings of the 3rd International Conference on Knowledge Representation and Reasoning, pp. 165–176. Morgan Kaufmann, San Mateo (1992)Google Scholar
  15. Schneider, M., Behr, T.: Topological Relationships between Complex Spatial Objects. ACM Transactions on Database Systems 31(1), 39–81 (2006)CrossRefGoogle Scholar
  16. Stefanidis, A., Nittel, S.: Geosensor Networks. CRC Press, Boca Raton (2004)Google Scholar
  17. Varzi, A.: Reasoning about Space: The Hole Story. Logic and Logical Philosophy 4, 3–39 (1996)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Maria Vasardani
    • 1
  • Max J. Egenhofer
    • 1
  1. 1.National Center for Geographic Information and Analysis and Department of Spatial Information Science and EngineeringUniversity of MaineBoardman HallUSA

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