Skip to main content

Topological Relationships Between Maps

  • Chapter
  • First Online:
Map Framework
  • 397 Accesses

Abstract

The study of topological relationships between objects in space has received much attention from a variety of research disciplines including robotics, geography, cartography, artificial intelligence, cognitive science, computer vision, image databases, spatial database systems, and geographical information systems (GIS).

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  1. Clementini, E., Di Felice, P.: A comparison of methods for representing topological relationships. Information Sciences-Applications 3(3), 149–178 (1995)

    Article  Google Scholar 

  2. Clementini, E., Di Felice, P.: A model for representing topological relationships between complex geometric features in spatial databases. Information sciences 90(1), 121–136 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Clementini, E., Di Felice, P., Van Oosterom, P.: A small set of formal topological relationships suitable for end-user interaction. In: Advances in Spatial Databases, pp. 277–295. Springer (1993)

    Google Scholar 

  4. Clementini, E., Di Felice, P., Califano, G.: Composite regions in topological queries. Information Systems 20(7), 579–594 (1995)

    Article  Google Scholar 

  5. Cohn, A.G.: Qualitative spatial representations. In: Proc. IJCAI-99 Workshop on Adaptative Spatial Representations of Dynamic Environments. Citeseer (1999)

    Google Scholar 

  6. Cohn, A.G., Hazarika, S.M.: Qualitative spatial representation and reasoning: An overview. Fundamenta informaticae 46(1-2), 1–29 (2001)

    MathSciNet  MATH  Google Scholar 

  7. Cohn, A.G., Bennett, B., Gooday, J., Gotts, N.M.: Qualitative spatial representation and reasoning with the region connection calculus. GeoInformatica 1(3), 275–316 (1997)

    Article  Google Scholar 

  8. Cui, Z., Cohn, A.G., Randell, D.A.: Qualitative and topological relationships in spatial databases. In: Advances in Spatial Databases, pp. 296–315. Springer (1993)

    Google Scholar 

  9. Egenhofer, M.J., Herring, J.: Categorizing binary topological relations between regions, lines, and points in geographic databases. Tech. rep., The National Center for Geographic Information and Analysis, University of California (1990)

    Google Scholar 

  10. Egenhofer, M.J., Herring, J.: A mathematical framework for the definition of topological relationships. In: Fourth international symposium on spatial data handling, pp. 803–813. Zurich, Switzerland (1990)

    Google Scholar 

  11. Egenhofer, M.J., Franzosa, R.D.: Point-set topological spatial relations. International Journal of Geographical Information System 5(2), 161–174 (1991)

    Article  Google Scholar 

  12. Egenhofer, M.J., Franzosa, R.D.: On the equivalence of topological relations. International Journal of Geographical Information Systems 9(2), 133–152 (1995)

    Article  Google Scholar 

  13. Egenhofer, M.J., Sharma, J., Mark, D.M.: A critical comparison of the 4-intersection and 9-intersection models for spatial relations: formal analysis. In: AUTOCARTO-CONFERENCE-, pp. 1–1. ASPRS AMERICAN SOCIETY FOR PHOTOGRAMMETRY AND (1993)

    Google Scholar 

  14. Egenhofer, M.J., Clementini, E., Di Felice, P.: Topological relations between regions with holes. International Journal of Geographical Information Science 8(2), 129–142 (1994)

    Article  Google Scholar 

  15. McKenney, M., Schneider, M.: Topological relationships between map geometries. In: Database Systems for Advanced Applications, pp. 110–125. Springer (2008)

    Google Scholar 

  16. McKenney, M., Pauly, A., Praing, R., Schneider, M.: Dimension-refined topological predicates. In: Proceedings of the 13th annual ACM international workshop on Geographic information systems, pp. 240–249. ACM (2005)

    Google Scholar 

  17. McKenney, M., Pauly, A., Praing, R., Schneider, M.: Preserving local topological relationships. In: Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems, pp. 123–130. ACM (2006)

    Google Scholar 

  18. McKenney, M., Pauly, A., Praing, R., Schneider, M.: Local topological relationships for complex regions. In: Advances in Spatial and Temporal Databases, pp. 203–220. Springer (2007)

    Google Scholar 

  19. McKenney, M., Praing, R., Schneider, M.: Deriving topological relationships between simple regions with holes. In: Headway in Spatial Data Handling, pp. 521–531. Springer (2008)

    Google Scholar 

  20. Schneider, M.: Spatial Data Types for Database Systems - Finite Resolution Geometry for Geographic Information Systems, vol. LNCS 1288. Springer-Verlag, Berlin Heidelberg (1997)

    Google Scholar 

  21. Schneider, M., Behr, T.: Topological relationships between complex spatial objects. ACM Transactions on Database Systems (TODS) 31(1), 39–81 (2006)

    Article  Google Scholar 

  22. Worboys, M.F., Bofakos, P.: A canonical model for a class of areal spatial objects. In: Advances in Spatial Databases, pp. 36–52. Springer (1993)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mark McKenney .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this chapter

Cite this chapter

McKenney, M., Schneider, M. (2016). Topological Relationships Between Maps. In: Map Framework. Springer, Cham. https://doi.org/10.1007/978-3-319-46766-5_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46766-5_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46764-1

  • Online ISBN: 978-3-319-46766-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics