Skip to main content
SpringerLink
Log in

Hierarchical topology-preserving simplification of terrains

  • original article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

We present an algorithm for simplifying terrain data that preserves topology. We use a decimation algorithm that simplifies the given data set using hierarchical clustering. Topology constraints, along with local error metrics, are used to ensure topology-preserving simplification and to compute precise error bounds in the simplified data. The earth’s mover distance is used as a global metric to compute the degradation in topology as the simplification proceeds. Experiments with both analytic and real terrain data are presented. Results indicate that one can obtain significant simplification with low errors without losing topology information.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bajaj CL, Pascucci V, Schikore DR (1999) Visualization of scalar topology for structural enhancement. In: Proc Visualization ’98. IEEE Computer Society, New Jersey, pp 51–58

  2. Bajaj CL, Schikore DR (1998) Topology preserving data simplification with error bounds. J Comput Graphics 22(1): 3–12

    Article  Google Scholar 

  3. de Leeuw WC, van Liere R (1999) Collapsing flow topology using area metrics. In: Proc Visualization ’99. IEEE Computer Society, New York, pp 349–354

  4. Fowler RJ, Little JJ (1979) Automatic extraction of irregular network digital terrain models. In: Proc SIGGRAPH. ACM, New York, pp 199–207

  5. Gerstner T (1999) Adaptive hierarchical methods for landscape representation and analysis. In: S. Hergarten, H.J. Neugebauer (eds) Process modelling and landform evolution (Lecture notes in earth sciences 78). Springer, Berlin, pp 75–92

  6. Gerstner T, Hannappel M (2000) Error measurement in multiresolution digital elevation models. In: G.B.M. Heuvelink, M.J.P.M. Lemmens (eds) Accuracy 2000 (Proc 4th Int Symp Spatial Accuracy Assessment in Natural Resources and Environmental Sciences). Delft University Press, Delft, pp 245–252

  7. Gerstner T, Pajarola R (2000) Topology preserving and controlled topology simplifying multiresolution isosurface extraction. In: IEEE Visualization 2000. IEEE Computer Society Press, New Jersey, pp 259–266

  8. Heckbert PS, Garland M (1997) Survey of surface approximation algorithms. Carnegie Mellon University Technical Report

  9. Helman JL, Hesselink L (1991) Visualizing vector field topology in fluid flows. IEEE Comput Graphics Appl 11(3): 36–46

    Article  Google Scholar 

  10. Interrante V, Fuchs H, Pfizer S (1995) Enhancing transparent skin surfaces with ridge and valley lines. In: IEEE Visualization ’95. IEEE Computer Society Press, New Jersey, pp 52–59

  11. Lavin Y, Batra RK, Hesselink L (1998) Feature comparisons of vector fields using earth mover’s distance. In: Proc Visualization ’98. IEEE Computer Society, New Jersey, pp 103–109

  12. Lodha SK, Renteria JC, Roskin KM (2000) Topology preserving compression of 2D vector fields. In: Proc IEEE Visualization. IEEE Computer Society Press, New Jersey, pp 343–350

  13. McCormack JE, Gahegan MN, Roberts SA, Hogg J, Hoyle BS (1993) Feature-based derivation of drainage networks. Int J Geograph Inf Syst 7(3): 263–279

    Google Scholar 

  14. Puppo E, Scopigno R (1997) LOD and multiresolution principles and applications. Eurographics ’97 tutorial notes. Eurographics association, Switzerland

  15. Rubner Y, Tomasi C (1998) The earth mover’s distance as a metric for image retrieval. Tech Report STAN-CS-TN-98-86. Department of Computer Science, Stanford University

  16. Telea A, van Wijk JJ (1999) Simplified representation of vector fields. In: Proc Visualization ’99. IEEE Computer Society, New Jersey, pp 35–42

  17. Tricoche X, Schewuermann G, Hagen H (2000) A topology simplification method for 2d vector fields. In: IEEE Visualization 2000. IEEE Computer Society Press, New Jersey, pp 359–366

  18. Wilhelms J, van Gelder A (1994) Multi-dimensional trees for controlled volumetric rendering and compression. In: ACM Symp Volume Visualization ’94. New York, pp 27–34

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, 95064, Santa Cruz, CA, USA

    Suresh K. Lodha, Krishna M. Roskin & Jose C. Renteria

Authors
  1. Suresh K. Lodha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Krishna M. Roskin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jose C. Renteria
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suresh K. Lodha.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lodha, S., Roskin, K. & Renteria, J. Hierarchical topology-preserving simplification of terrains. Vis Comput 19, 493–504 (2003). https://doi.org/10.1007/s00371-003-0214-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-003-0214-2

Keywords

Search

Navigation