Skip to main content

Point Partitions: A Qualitative Representation for Region-Based Spatial Scenes in \( {\mathbb{R}}^{2} \)

  • Conference paper
  • First Online:
  • 1251 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9927))

Abstract

A complete qualitative scene description should be such that it captures the essential details of a configuration so that a topologically correct depiction can be recreated. This paper models a spatial scene through sequences of point partitions, that is, how embedding space and objects are distributed around the intersections of the boundaries of regions. Twenty-three base patterns are identified, which suffice to capture complex scenes, including configurations with holes. To demonstrate the diagrammatic depiction of a spatial scene from point partition patterns, such a scene is recreated using the developed model. The paper also provides a means of transitioning between these more complex relations and the eight coarse topological relations of the 4-intersection.

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 EPUB and 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

References

  1. Adams, C., Franzosa, R.: Introduction to Topology: Pure and Applied. Pearson Prentice Hall, Upper Saddle River (2008)

    Google Scholar 

  2. Bruns, T., Egenhofer, M.: Similarity of spatial scenes. In: 7th International Symposium on Spatial Data Handling, Delft, The Netherlands, pp. 31–42 (1996)

    Google Scholar 

  3. Clementini, E., Felice, P.D.: Topological invariants for lines. IEEE Trans. Knowl. Data Eng. 10(1), 38–54 (1998)

    Article  Google Scholar 

  4. Dube, M.P., Egenhofer, M.J.: Surrounds in partitions. In: Huang, Y., Schneider, M., Gertz, M., Krumm, J., Sankaranarayanan, J. (eds.) ACM SIGSPATIAL 2014, pp. 233–242. ACM Press, New York (2014)

    Google Scholar 

  5. Dube, M.P., Egenhofer, M.J., Lewis, J.A., Stephen, S., Plummer, M.A.: Swiss Canton Regions: a model for complex objects in geographic partitions. In: Fabrikant, S.I., Raubal, M., Bertolotto, M., Davies, C., Freundschuh, S., Bell, S. (eds.) COSIT 2015. LNCS, vol. 9368, pp. 309–330. Springer, Heidelberg (2015). doi:10.1007/978-3-319-23374-1_15

    Chapter  Google Scholar 

  6. Egenhofer, M.J.: A reference system for topological relations between compound spatial objects. In: Heuser, C.A., Pernul, G. (eds.) ER 2009. LNCS, vol. 5833, pp. 307–316. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Egenhofer, M.J., Franzosa, R.D.: On the equivalence of topological relations. Int. J. Geogr. Inf. Syst. 9(2), 133–152 (1995)

    Article  Google Scholar 

  8. Egenhofer, M.J., Franzosa, R.D.: Point-set topological spatial relations. Int. J. Geogr. Inf. Syst. 5(2), 161–174 (1991)

    Article  Google Scholar 

  9. Egenhofer, M.J., Herring, J.: Categorizing binary topological relationships between regions, lines and points in geographic database. Technical report, University of Maine (1991)

    Google Scholar 

  10. 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)

    Chapter  Google Scholar 

  11. Galton, A.: Modes of overlap. J. Vis. Lang. Comput. 9(1), 61–79 (1998)

    Article  Google Scholar 

  12. Kurata, Y.: The 9+-Intersection: a universal framework for modeling topological relations. In: Cova, T.J., Miller, H.J., Beard, K., Frank, A.U., Goodchild, M.F. (eds.) GIScience 2008. LNCS, vol. 5266, pp. 181–198. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Kurata, Y., Egenhofer, M.J.: The 9+-Intersection for topological relations between a directed line segment and a region. In: Gottfried, B. (eds.) Workshop on Behaviour and Monitoring Interpretation, Technical report 42, Technologie-Zentrum Informatik, University of Bremen, Germany, pp. 62–76 (2007)

    Google Scholar 

  14. Lewis, J.A., Dube, M.P., Egenhofer, M.J.: The topology of spatial scenes in R2. In: Tenbrink, T., Stell, J., Galton, A., Wood, Z. (eds.) COSIT 2013. LNCS, vol. 8116, pp. 495–515. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  15. Lewis, J.A., Egenhofer, M.J.: Oriented regions for linearly conceptualized features. In: Duckham, M., Pebesma, E., Stewart, K., Frank, A.U. (eds.) GIScience 2014. LNCS, vol. 8728, pp. 333–348. Springer, Heidelberg (2014)

    Google Scholar 

  16. Nedas, K.A., Egenhofer, M.J.: Spatial-scene similarity queries. Trans. GIS 12(6), 661–681 (2008)

    Article  Google Scholar 

  17. Papadimitriou, C.H., Suciu, D., Vianu, V.: Topological queries in spatial databases. In: ACM PODS, pp. 81–92 (1996)

    Google Scholar 

  18. Randell, D.A., Cui, Z., Cohn, A.G.: A spatial logic based on regions and connection. In: Nebel, B., Rich, C., Swartout, W.R. (eds.) KR92, pp. 165–176. Morgan Kaufmann, San Francisco (1992)

    Google Scholar 

  19. Schneider, M., Behr, T.: Topological relationships between complex spatial objects. ACM Trans. Database Syst. 31(1), 39–81 (2006)

    Article  Google Scholar 

  20. Vasardani, M., Egenhofer, M.J.: Comparing relations with a multi-holed region. In: Hornsby, K.S., Claramunt, C., Denis, M., Ligozat, G. (eds.) COSIT 2009. LNCS, vol. 5756, pp. 159–176. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Vasardani, M., Timpf, S., Winter, S., Tomko, M.: From descriptions to depictions: a conceptual framework. In: Tenbrink, T., Stell, J., Galton, A., Wood, Z. (eds.) COSIT 2013. LNCS, vol. 8116, pp. 299–319. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  22. Worboys, M.: The maptree: a fine-grained formal representation of space. In: Xiao, N., Kwan, M.-P., Goodchild, M.F., Shekhar, S. (eds.) GIScience 2012. LNCS, vol. 7478, pp. 298–310. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

Download references

Acknowledgments

Joshua Lewis is supported by a teaching assistantship at the University of Maine. Max Egenhofer’s work was partially supported by NSF grants IIS-1016740 and IIS-1527504.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Joshua A. Lewis .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Lewis, J.A., Egenhofer, M.J. (2016). Point Partitions: A Qualitative Representation for Region-Based Spatial Scenes in \( {\mathbb{R}}^{2} \) . In: Miller, J., O'Sullivan, D., Wiegand, N. (eds) Geographic Information Science. GIScience 2016. Lecture Notes in Computer Science(), vol 9927. Springer, Cham. https://doi.org/10.1007/978-3-319-45738-3_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45738-3_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45737-6

  • Online ISBN: 978-3-319-45738-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics