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Linearized Terrain: Languages for Silhouette Representations

  • Lars Kulik
  • Max J. Egenhofer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2825)

Abstract

The scope of this paper is a qualitative description of terrain features that can be characterized using the silhouette of a terrain. The silhouette is a profile of a landform seen from a particular observer’s perspective. We develop a terrain language as a formal framework to capture terrain features. The horizon of a terrain silhouette is represented as a string. The alphabet of the terrain language comprises straight-line segments. These line primitives are classified according to three criteria: (1) the alignment of their slope, (2) their relative lengths, characterized by orders of magnitude, and (3) their differences in elevation, described by an order relation. We employ term rewriting rules to identify terrain features at different granularity levels. There are three kinds of rules: aggregation, generalization, and simplification rules. The aggregation rules generate a description of the terrain features at a given granularity level. For a terrain description the generalization and simplification rules specify the transi- tion from a finer granularity level to a coarser one. An example shows how the three kinds of rules lead to a terrain description at different granularity levels.

Keywords

Formal languages granularity qualitative spatial reasoning terrain 

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References

  1. Cinque, L., Lombardi, L.: Shape description and recognition by a multiresolution approach. Image and Vision Computing 13(8), 599–607 (1995)CrossRefGoogle Scholar
  2. Clementini, E., Di Felice, P.: A global framework for qualitative shape description. GeoInformatica 1, 11–27 (1997)CrossRefGoogle Scholar
  3. Davis, E.: Order of magnitude comparisons of distance. Journal of Artificial Intelligence Research 10, 1–38 (1999)Google Scholar
  4. de Berg, M.T., Dobrindt, K.T.G.: On levels of detail in terrains. Graphical Models & Image Processing 60(1), 1–12 (1998)CrossRefGoogle Scholar
  5. De Floriani, L., Magillo, P.: Horizon computation on a hierarchical triangulated terrain model. The Visual Computer 11(3), 134–149 (1995)Google Scholar
  6. De Floriani, L., Magillo, P.: Intervisibility on terrains. In: Longley, P., Goodchild, M., Maguire, D., Rhind, D. (eds.) Geographical information systems, pp. 543–556. Wiley, New York (1999)Google Scholar
  7. De Floriani, L., Magillo, P.: Multiresolution mesh representation: Models and data structures. In: Iske, A., Ewald, Q., Floater, M.S. (eds.) Tutorials on Multiresolution in Geometric Modelling, pp. 363–418. Springer, Berlin (2002)Google Scholar
  8. Department of the Army: Field Manual No. 3-25.26: Map reading and land navigation, Washington, DC (2001)Google Scholar
  9. Dershowitz, N.: A taste of rewrite systems. In: Lauer, P.E. (ed.) Functional Programming, Concurrency, Simulation and Automated Reasoning. LNCS, vol. 693, pp. 199–228. Springer, Heidelberg (1993)Google Scholar
  10. Egenhofer, M.J., Kuhn, W.: Beyond desktop GIS. In: GIS PlaNET, Lisbon, Portugal (1998)Google Scholar
  11. Egenhofer, M.J., Mark, D.M.: Naive geography. In: Kuhn, W., Frank, A.U. (eds.) COSIT 1995. LNCS, vol. 988, pp. 1–15. Springer, Heidelberg (1995)Google Scholar
  12. Frank, A., Palmer, B., Robinson, V.: Formal methods of the accurate definition of some fundamental terms in physical geography. In: Proceedings, 2nd International Symposium on Spatial Data Handling, Seattle, Washington, pp. 583–599 (1986)Google Scholar
  13. Frank, A.U.: Qualitative spatial reasoning: Cardinal directions as an example. International Journal of Geographical Information Science 10(3), 269–290 (1996)CrossRefGoogle Scholar
  14. Galton, A.P., Meathrel, R.C.: Qualitative outline theory. In: Dean, T. (ed.) Proceedings of the 16th International Joint Conference on Artificial Intelligence, IJCAI 1999, Stockholm, Sweden, vol. 2, pp. 1061–1066. Morgan Kaufmann, San Francisco (1999)Google Scholar
  15. Garland, M.: Multiresolution Modeling: Survey & Future Opportunities. In: Eurographics 1999 – State of the Art Reports, Milan, Italy, pp. 111–131 (1999)Google Scholar
  16. Hobbs, J.R.: Granularity. In: Joshi, A.K. (ed.) Proceedings of the 9th International Joint Conference on Artificial Intelligence, Los Angeles, CA, USA, vol. 1, pp. 432–435. Morgan Kaufmann, San Francisco (1985)Google Scholar
  17. Latecki, L.J., Lakämper, R.: Shape similarity measure based on correspondence of visual parts. IEEE Transaction Pattern Analysis and Machine Intelligence 22(10), 1185–1190 (2000)CrossRefGoogle Scholar
  18. Leyton, M.: A process-grammar for shape. Artificial Intelligence 34(2), 213–247 (1988)CrossRefGoogle Scholar
  19. Nayak, P.P.: Order of magnitude reasoning using logarithms. In: Nebel, B., Rich, C., Swartout, W.R. (eds.) Proceedings of the 3rd International Conference on Principles of Knowledge Representation and Reasoning (KR 1992), Cambridge, MA, USA, pp. 201–210. Morgan Kaufmann, San Francisco (1992)Google Scholar
  20. O’Rourke, J.: Computational Geometry in C. Cambridge University Press, New York (1998)zbMATHGoogle Scholar
  21. Raiman, O.: Order of magnitude reasoning. In: Proceedings of AAAI 1988, pp. 100–104 (1986)Google Scholar
  22. Strahler, A.H., Strahler, A.N.: Modern physical geography. John Wiley & Sons, New York (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Lars Kulik
    • 1
  • Max J. Egenhofer
    • 1
  1. 1.National Center for Geographic Information and AnalysisUniversity of MaineOronoUSA

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