Advertisement

Functional Extensions of a Raster Representation for Topological Relations

  • Stephan Winter
  • Andrew U. Frank
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1580)

Abstract

Topological relations are not well defined for raster representations. In particular the widely used classification of topological relations based on the nine-intersection [8,5] cannot be applied to raster representations [9]. But a raster representation can be completed with edges and corners [14] to become a cell complex with the usual topological relations [16]. Although it is fascinating to abolish some conceptual differences between vector and raster, such a model appeared as of theoretical interest only.

In this paper definitions for topological relations on a raster – using the extended model – are given and systematically transformed to functions which can be applied to a regular raster representation. The extended model is used only as a concept; it need not to be stored. It becomes thus possible to determine the topological relation between two regions, given in raster representation, with the same reasoning as in vector representations. This contributes to the merging of raster and vector operations. It demonstrates how the same conceptual operations can be used for both representations, thus hiding in one more instance the difference between them.

Keywords

Vector Representation Spatial Database Vertical Edge Topological Relation Indexing Schema 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bird, R., Wadler, P.: Introduction to Functional Programming. Series in Computer Science. Prentice Hall International, New York (1988)Google Scholar
  2. 2.
    Bittner, T., Frank, A.U.: On representing geometries of geographic space. In: Poiker, T.K., Chrisman, N. (eds.) 8th International Symposium on Spatial Data Handling, International Geographical Union, Vancouver, vol. 2774, pp. 111–122 (1998)Google Scholar
  3. 3.
    Dorenbeck, C., Egenhofer, M.J.: Algebraic optimization of combined overlay operations. In: Mark, D.M., White, D. (eds.) Auto-Carto 10, ACSM-ASPRS, Baltimore, pp. 296–312 (1991)Google Scholar
  4. 4.
    Egenhofer, M.J.: Reasoning about binary topological relations. In: Günther, O., Schek, H.-J. (eds.) Advances in Spatial Databases (SSD 1991), pp. 143–160. Springer, Heidelberg (1991)Google Scholar
  5. 5.
    Egenhofer, M.J., Clementini, E., di Felice, P.: Topological relations between regions with holes. International Journal of Geographical Information Systems 8, 129–142 (1994)CrossRefGoogle Scholar
  6. 6.
    Egenhofer, M.J., Frank, A.U., Jackson, J.P.: A topological data model for spatial databases. In: Buchmann, A., Smith, T.R., Wang, Y.-F., Günther, O. (eds.) SSD 1989. LNCS, vol. 409, pp. 271–286. Springer, Heidelberg (1990)Google Scholar
  7. 7.
    Egenhofer, M.J., Franzosa, R.D.: Point-set topological spatial relations. International Journal of Geographical Information Systems 5, 161–174 (1991)CrossRefGoogle Scholar
  8. 8.
    Egenhofer, M.J., Herring, J.R.: A mathematical framework for the definition of topological relationships. In: 4th International Symposium on Spatial Data Handling, Zürich, International Geographical Union, pp. 803–813 (1990)Google Scholar
  9. 9.
    Egenhofer, M.J., Sharma, J.: Topological relations between regions in IR2 and ℤ2. In: Abel, D.J., Ooi, B.-C. (eds.) SSD 1993. LNCS, vol. 692, pp. 316–336. Springer, Heidelberg (1993)Google Scholar
  10. 10.
    Frank, A.U., Kuhn, W.: A specification language for interoperable GIS. In: Goodchild, M.F., Egenhofer, M., Fegeas, R., Kottman, C. (eds.): Interoperating Geographic Information Systems. Kluwer, Norwell (to appear)Google Scholar
  11. 11.
    Frank, A.U., Kuhn, W., Hölbling, W., Schachinger, H., Haunold, P. (eds.): Gofer as used at Geolnfo/TU Vienna, Dept. of Geoinformation, TU Vienna, Vienna, Austria. GeoInfo Series, vol. 12 (1997)Google Scholar
  12. 12.
    Hernández, D.: Qualitative Representation of Spatial Knowledge. Springer, Berlin (1994)Google Scholar
  13. 13.
    Kong, T.Y., Rosenfeld, A.: Digital topology: Introduction and survey. CVGIP 48, 357–393 (1989)Google Scholar
  14. 14.
    Kovalevsky, V.A.: Finite topology as applied to image analysis. Computer Vision, Graphics, and Image Processing 46, 141–161 (1989)CrossRefGoogle Scholar
  15. 15.
    Samet, H.: The Design and Analysis of Spatial Data Structures. Addison-Wesley, Reading (1990)Google Scholar
  16. 16.
    Winter, S.: Topological relations between discrete regions. In: Egenhofer, M.J., Herring, J.R. (eds.) SSD 1995. LNCS, vol. 951, pp. 310–327. Springer, Heidelberg (1995)Google Scholar
  17. 17.
    Winter, S.: Location-based similarity measures for regions. In: ISPRS Commission IV Symposium, Stuttgart, Germany (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Stephan Winter
    • 1
  • Andrew U. Frank
    • 1
  1. 1.Dept. of GeoinformationTechnical University ViennaViennaAustria

Personalised recommendations