Skip to main content

A Discrete Approach to Compute Terrain Morphology

  • Conference paper

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 21))

Abstract

We consider the problem of extracting morphology of a terrain represented as a Triangulated Irregular Network (TIN). We propose a new algorithm and compare it with representative algorithms of the main approaches existing in the literature to this problem. The new algorithm has the advantage of being simple, using only comparisons (and no floating-point computations), and of being suitable for an extension to higher dimensions. Our experiments consider both real data and artificial test data. We evaluate the difference in the results produced on the same terrain data, as well as the impact of resolution level on such a difference, by considering representations of the same terrain at different resolutions.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bajaj, C.L., Pascucci, V., Shikore, D.R.: Visualization of scalar topology for structural enhancement. In: Proceedings IEEE Visualization, pp. 51–58. IEEE Computer Society, Los Alamitos (1998)

    Google Scholar 

  2. Bajaj, C.L., Shikore, D.R.: Topology preserving data simplification with error bounds. Computers and Graphics 22(1), 3–12 (1998)

    Article  Google Scholar 

  3. Bremer, P.-T., Edelsbrunner, H., Hamann, B., Pascucci, V.: A multi-resolution data structure for two-dimensional Morse functions. In: Turk, G., van Wijk, J., Moorhead, R. (eds.) Proceedings IEEE Visualization, pp. 139–146. IEEE Computer Society, Los Alamitos (2003)

    Google Scholar 

  4. Comic, L., De Floriani, L., Papaleo, L.: Morse-Smale decomposition for modeling terrain knowledge. In: Cohn, A., Mark, D. (eds.) COSIT 2005. LNCS, vol. 3693, pp. 426–444. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Danovaro, E., De Floriani, L., Magillo, P., Mesmoudi, M.M., Puppo, E.: Morphology-driven simplification and multi-resolution modeling of terrains. In: Hoel, E., Rigaux, P. (eds.) Proceedings ACM-GIS - International Symposium on Advances in Geographic Information Systems, pp. 63–70. ACM Press, New York (2003)

    Google Scholar 

  6. Danovaro, E., De Floriani, L., Mesmoudi, M.M.: Topological analysis and characterization of discrete scalar fields. In: Asano, T., Klette, R., Ronse, C. (eds.) Geometry, Morphology, and Computational Imaging. LNCS, vol. 2616, pp. 386–402. Springer, Heidelberg (2003b)

    Chapter  Google Scholar 

  7. Edelsbrunner, H., Harer, J., Zomorodian, A.: Hierarchical Morse complexes for piecewise linear 2-manifolds. In: Proceedings ACM Symposium on Computational Geometry, pp. 70–79. ACM Press, New York (2001)

    Google Scholar 

  8. Mangan, A., Whitaker, R.: Partitioning 3D surface meshes using watershed segmentation. IEEE Transaction on Visualization and Computer Graphics 5(4), 308–321 (1999)

    Article  Google Scholar 

  9. Meyer, F.: Topographic distance and watershed lines. Signal Processing 38, 113–125 (1994)

    Article  MATH  Google Scholar 

  10. Pascucci, V.: Topology diagrams of scalar fields in scientific visualization. In: Rana, S. (ed.) Topological Data Structures for Surfaces, pp. 121–129. John Wiley and Sons Ltd., Chichester (2004)

    Google Scholar 

  11. Pfaltz, J.L.: Surface networks. Geographical Analysis 8, 77–93 (1976)

    Article  Google Scholar 

  12. Roerdink, J., Meijster, A.: The watershed transform: definitions, algorithms, and parallelization strategies. Fundamenta Informaticae 41, 187–228 (2000)

    MathSciNet  MATH  Google Scholar 

  13. Schneider, B.: Extraction of hierarchical surface networks from bilinear surface patches. Geographical Analysis 37, 244–263 (2005)

    Article  Google Scholar 

  14. Schneider, B., Wood, J.: Construction of metric surface networks from raster-based DEMs. In: Rana, S. (ed.) Topological Data Structures for Surfaces. John Wiley and Sons Ltd., Chichester (2004)

    Google Scholar 

  15. Smale, S.: Morse inequalities for a dynamical system. Bulletin of American Mathematical Society 66, 43–49 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  16. Stoev, S.L., Strasser, W.: Extracting regions of interest applying a local watershed transformation. In: Proceedings IEEE Visualization, pp. 21–28. IEEE Computer Society, Los Alamitos (2000)

    Google Scholar 

  17. Takahashi, S., Ikeda, T., Kunii, T.L., Ueda, M.: Algorithms for extracting correct critical points and constructing topological graphs from discrete geographic elevation data. Computer Graphics Forum 14(3), 181–192 (1995)

    Article  Google Scholar 

  18. Vincent, L., Soille, P.: Watershed in digital spaces: an efficient algorithm based on immersion simulation. IEEE Transactions on Pattern Analysis and Machine Intelligence 13(6), 583–598 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Magillo, P., Danovaro, E., De Floriani, L., Papaleo, L., Vitali, M. (2008). A Discrete Approach to Compute Terrain Morphology. In: Braz, J., Ranchordas, A., Araújo, H.J., Pereira, J.M. (eds) Computer Vision and Computer Graphics. Theory and Applications. VISIGRAPP 2007. Communications in Computer and Information Science, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89682-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89682-1_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89681-4

  • Online ISBN: 978-3-540-89682-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics