On Digital Image Representation by the Delaunay Triangulation

  • Josef Kohout
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4872)


This paper deals with a transformation of raster grey-scale images into a geometric representation by the Delaunay triangulation. It discusses the influence of image filtering techniques and methods for the evaluation of significance of pixels on the conversion process. Furthermore, it proposes several novel approaches for a compression of the Delaunay triangulation and compares them with existing solutions.


image coding Delaunay triangulation compression 


  1. 1.
    Battiato, S., Gallo, G., Messina, G.: SVG rendering of real Images using data dependent triangulation. In: Proceedings of SCCG 2004, pp. 185–192 (2004)Google Scholar
  2. 2.
    Ciampalini, A., Cignoni, P., Montani, C., Scopigno, R.: Multiresolution decimation based on global error. The Visual Computer 13, 228–246 (1997)CrossRefGoogle Scholar
  3. 3.
    Cooper, O., Campbell, N., Gibson, D.: Automatic augmentation and meshing of sparse 3D scene structure. In: Proceedings of 7th IEEE Workshop on Applications of Computer Vision, Breckenridge, pp. 287–293. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  4. 4.
    Demaret, L., Dyn, N., Floater, M.S., Iske, A.: Adaptive thinning for terrain modelling and image compression. Advances in Multiresolution for Geometric Modelling, 321–340 (2004)Google Scholar
  5. 5.
    Devillers, O.: On deletion in Delaunay triangulations. In: Proceedings of SCG 1999, pp. 181–188. ACM Press, New York (1999)CrossRefGoogle Scholar
  6. 6.
    Floyd, R.W., Steinberg, L.: An adaptive algorithm for spatial grey scale. In: Proceedings of the Society of Information Display, pp. 75–77 (1976)Google Scholar
  7. 7.
    Galic, I., Weickert, J., Welk, M.: Towards PDE-based image compression. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds.) VLSM 2005. LNCS, vol. 3752, pp. 37–48. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    García, M.A., Vintimilla, B.X., Sappa, A.D.: Efficient approximation of grey-scale images through bounded error triangular meshes. In: Proceedings of IEEE International Conference on Image Processing, Kobe, pp. 168–170. IEEE Computer Society, Los Alamitos (1999)Google Scholar
  9. 9.
    Gevers, T., Smeulders, A.W.: Combining region splitting and edge detection through guided Delaunay image subdivision. In: Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition, pp. 1021–1026. IEEE Computer Society Press, Los Alamitos (1997)CrossRefGoogle Scholar
  10. 10.
    Grundland, M., Gibbs, Ch., Dodgson, N.A.: Stylized rendering for multiresolution image representation. Proceedings of SPIE 5666, 280–292 (2005)CrossRefGoogle Scholar
  11. 11.
    Kreylos, O., Hamann, B.: On simulated annealing and the construction of linear spline approximations for scattered data. IEEE Transactions on Visualization and Computer Graphics 7, 17–31 (2001)CrossRefGoogle Scholar
  12. 12.
    Marr, D., Hildreth, E.C.: Theory of edge detection. In: Proceedings of the Royal Society, London B, vol. 207, pp. 187–217 (1980)Google Scholar
  13. 13.
    Prasad, L., Skourikhine, A.N.: Vectorized image segmentation via trixel agglomeration. Pattern Recognition 39, 501–514 (2006)zbMATHCrossRefGoogle Scholar
  14. 14.
    Rila, L.: Image coding using irregular subsampling and Delaunay triangulation. In: Proceedings of SIBGRAPI, pp. 167–173 (1998)Google Scholar
  15. 15.
    Rosignac, J.: Edgebreaker: Connectivity compression for triangle meshes. IEEE Transactions of Visualization and Computer Graphics 5, 47–61 (1999)CrossRefGoogle Scholar
  16. 16.
    Su, D., Willis, P.: Image interpolation by pixel level data-dependent triangulation. Computer Graphics Forum 23, 189–201 (2004)CrossRefGoogle Scholar
  17. 17.
    Yu, X., Morse, B.S., Sederberg, T.W.: Image reconstruction using data-dependent triangulation. IEEE Computer Graphics and Applications 21, 62–68 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Josef Kohout
    • 1
  1. 1.Department of Computer Science and Engineering, University of West Bohemia, Univerzitní 22, 306 14 PlzeňCzech Republic

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