, Volume 4, Issue 4, pp 349–373 | Cite as

Terrain Reconstruction from Contours by Skeleton Construction

  • David Thibault
  • Christopher M. Gold


Generating terrain models from contour input is still an important process. Most methods have been unsatisfactory, as they either do not preserve the form of minor ridges and valleys, or else they are poor at modeling slopes. A method is described here, based on curve extraction and generalization techniques, that is guaranteed to preserve the topological relationships between curve segments. The skeleton, or Medial Axis Transform, can be extracted from the Voronoi diagram of a well-sampled contour map and used to extract additional points that eliminate cases of “flat triangles” in a triangulation. Elevation estimates may be made at these points. Based on this approach it is possible to make reasonable estimates of slopes for terrain models, and to extract meaningful intermediate points for triangulated irregular networks (TINs).

terrain modeling Delaunay/Voronoi diagrams contour lines skeleton generalization 


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  1. 1.
    H. Alt and O. Schwarzkopf. “The Voronoi diagram of curved objects,” Proceedings, 11th Annual ACM Symposium on Computational Geometry, 89–97, 1995.Google Scholar
  2. 2.
    N. Amenta, M. Bern, and D. Eppstein. “The crust and the beta-skeleton: combinatorial curve reconstruction,” Graphical Models and Image Processing, Vol. 60:125–135, 1998.Google Scholar
  3. 3.
    G. Aumann, H. Ebner, and L. Tang. “Automatic derivation of skeleton lines from digitized contours,” ISPRS Journal of Photogrammetry and Remote Sensing, Vol. 46:259–268, Elsevier Science Publishers B.V.: Amsterdam, 1991.Google Scholar
  4. 4.
    H. Blum. “A transformation for extracting new descriptors of shape,” in W. Whaten Dunn (Ed.), Models for the Perception of Speech and Visual Form. MIT Press: Cambridge, Mass., 153–171, 1967.Google Scholar
  5. 5.
    A. Carrara, G. Bitelli, and R. Carla. “Comparison of techniques for generating digital terrain models from contour lines,” International Journal of Geographical Information Science, Vol. 11:451–473, 1997.Google Scholar
  6. 6.
    A.B. Garcia, C.G. Nicieza, J.B.O. Meréé, and A.M. Diaz. “A contour line based triangulating algorithm,” Proceedings, 5th International Symposium on Spatial Data Handling, 273–284, 1990.Google Scholar
  7. 7.
    C.M. Gold. “Chapter 3—Surface interpolation, spatial adjacency and G.I.S,” in Three Dimensional Applications in Geographic Information Systems (J. Raper, Ed.), Taylor and Francis, Ltd.: London, 21-35, 1989.Google Scholar
  8. 8.
    C.M. Gold. “Simple topology generation from scanned maps,” Proceedings, Auto-Carto 13, ACM/ASPRS, Seattle, April, 337–346, 1997.Google Scholar
  9. 9.
    C.M. Gold. “The Quad-Arc data structure,” in Poiker, T.K. and Chrisman, N.R. (Eds.). Proceedings, 8th International Symposium on Spatial Data Handling, Vancouver, BC, 713–724, 1998.Google Scholar
  10. 10.
    C.M. Gold. “Crust and anticrust: a one-step boundary and skeleton extraction algorithm,” in Proceedings of the ACM Conference on Computational Geometry, Miami, Florida, 189–196, 1999.Google Scholar
  11. 11.
    C.M. Gold, J. Nantel, and W. Yang. “Outside-in: An alternative approach to forest map digitizing,” International Journal of Geographical Information Systems, Vol. 10:291–310, 1996.Google Scholar
  12. 12.
    C.M. Gold and J. Snoeyink. “A one-step crust and skeleton extraction algorithm,” Algorithmica, (in press).Google Scholar
  13. 13.
    L. Guibas and J. Stolfi. “Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams,” Transactions on Graphics, Vol. 4:74–123, 1985.Google Scholar
  14. 14.
    R.L. Ogniewicz. “Skeleton-space: a multiscale shape description combining region and boundary information,” Proceedings on Computer Vision and Pattern Recognition, 746–751, 1994.Google Scholar
  15. 15.
    R. Ogniewicz and M. Ilg. “Skeletons with euclidian metric and correct topology and their application in object recognition and document analysis,” Proceedings of the 4th International Symposium on Spatial Data Handling, Vol. 1:15–24, 1990.Google Scholar
  16. 16.
    A. Okabe, B. Boots, and K. Sugihara. Spatial Tessellations—Concepts and Applications of Voronoi Diagrams. John Wiley and Sons: Chichester. 1992.Google Scholar
  17. 17.
    G.J. Robinson. “The accuracy of digital elevation models derived from digitised contour data,” Photogrammetric Record, Vol. 14:805–814, 1994.Google Scholar
  18. 18.
    R. Weibel, M. Heller. “Digital terrain Modelling,” in Maguire, D.J., M.F. Goodchild, and D.W. Rhind, (Eds.) Geographical Information Systems: Principles and applications. Longman: London, 1990.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • David Thibault
    • 1
  • Christopher M. Gold
    • 2
    • 3
  1. 1.Center for Research in GeomaticsLaval UniversityQuebec City, QcCanada
  2. 2.Center for Research in GeomaticsLaval UniversityQuebec City, QcCanada
  3. 3.Department of Land Surveying and Geo-InformaticsHong Kong Polytechnic University, Hung HomKowloonHong Kong

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