Shape Compression using Spherical Geometry Images

  • Hugues Hoppe
  • Emil Praun
Part of the Mathematics and Visualization book series (MATHVISUAL)


We recently introduced an algorithm for spherical parametrization and remeshing, which allows resampling of a genus-zero surface onto a regular 2D grid, a spherical geometry image. These geometry images offer several advantages for shape compression. First, simple extension rules extend the square image domain to cover the infinite plane, thereby providing a globally smooth surface parametrization. The 2D grid structure permits use of ordinary image wavelets, including higher-order wavelets with polynomial precision. The coarsest wavelets span the entire surface and thus encode the lowest frequencies of the shape. Finally, the compression and decompression algorithms operate on ordinary 2D arrays, and are thus ideally suited for hardware acceleration. In this paper, we detail two wavelet-based approaches for shape compression using spherical geometry images, and provide comparisons with previous compression schemes.


Coarse Level Triangle Mesh Original Mesh Geometry Image Normal Mesh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alliez, P., and Desbrun, M.: Progressive encoding for lossless transmission of 3D meshes. Proc. ACM SIGGRAPH 2001.Google Scholar
  2. 2.
    Alliez, P., and Desbrun, M.: Valence-driven connectivity encoding for 3D meshes. Proc. Eurographics 2001.Google Scholar
  3. 3.
    Alliez, P., and Gotsman, C.: Recent advances in compression of 3D meshes. Advances in Multiresolution for Geometric Modelling, N. A. Dodgson, M. S. Floater, and M. A. Sabin (eds.), Springer, 2004, pp. 3–26 (this book).Google Scholar
  4. 4.
    Antonini, M., Barlaud, M., Mathieu, P., and Daubechies, I.: Image coding using wavelet transform. IEEE Transactions on Image Processing, 205–220, 1992.Google Scholar
  5. 5.
    Attene, M., Falcidieno, B., Spagnuolo, M., and Rossignac, J.: SwingWrapper: Retiling triangle meshes for better EdgeBreaker compression. ACM Transactions on Graphics, to appear.Google Scholar
  6. 6.
    Briceño, H., Sander, P., McMillan, L., Gortler, S., and Hoppe, H.: Geometry videos. Symposium on Computer Animation 2003.Google Scholar
  7. 7.
    Davis, G.: Wavelet image compression construction kit. (1996).Google Scholar
  8. 8.
    Deering, M.: Geometry compression. Proc. ACM SIGGRAPH 1995, 13–20.Google Scholar
  9. 9.
    Eck, M., DeRose, T., Duchamp, T., Hoppe, H., Lounsbery, M., and Stuetzle, W.: Multiresolution analysis of arbitrary meshes. Proc. ACM SIGGRAPH 1995, 173–182.Google Scholar
  10. 10.
    Gotsman, C., Gumhold, S., and Kobbelt, L.: Simplification and compression of 3D meshes. In Tutorials on Multiresolution in Geometric Modelling, A. Iske, E. Quak, M. S. Floater (eds.), Springer, 2002, pp. 319–361.Google Scholar
  11. 11.
    Gu, X., Gortler, S., and Hoppe, H.: Geometry images. Proc. ACM SIGGRAPH 2002, 355–361.Google Scholar
  12. 12.
    Gumhold, S., and Strasser, W.: Real time compression of triangle mesh connectivity. Proc. ACM SIGGRAPH 1998, 133–140.Google Scholar
  13. 13.
    Guskov, I., Vidimce, K., Sweldens, W., and Schröder, P.: Normal meshes. Proc. ACM SIGGRAPH 2000, 95–102.Google Scholar
  14. 14.
    Hoppe, H.: Progressive meshes. Proc. ACM SIGGRAPH 1996, 99–108.Google Scholar
  15. 15.
    Karni, Z., and Gotsman, C.: Spectral compression of mesh geometry. Proc. ACM SIGGRAPH 2000, 279–286.Google Scholar
  16. 16.
    Khodakovsky, A., Schröder, P., and Sweldens, W.: Progressive geometry compression. Proc. ACM SIGGRAPH 2000.Google Scholar
  17. 17.
    Khodakovsky, A., and Guskov, I.: Normal mesh compression. Geometric Modeling for Scientific Visualization, Springer-Verlag, Heidelberg, Germany (2002).Google Scholar
  18. 18.
    Khodakovsky, A., Litke, N., and Schröder, P.: Globally smooth parameterizations with low distortion. Proc. ACM SIGGRAPH 2003.Google Scholar
  19. 19.
    Lounsbery, M., DeRose, T., and Warren, J.: Multiresolution analysis for surfaces of arbitrary topological type. ACM Transactions on Graphics, 16(1), 34–73 (1997).CrossRefGoogle Scholar
  20. 20.
    Praun, E., and Hoppe, H.: Spherical parametrization and remeshing. Proc. ACM SIGGRAPH 2003, 340–349.Google Scholar
  21. 21.
    Rossignac, J.: EdgeBreaker: Connectivity compression for triangle meshes. IEEE Trans. on Visualization and Computer Graphics, 5(1), 47–61 (1999).CrossRefGoogle Scholar
  22. 22.
    Rossignac, J.: 3D mesh compression. Chapter in The Visualization Handbook, C. Johnson and C. Hanson, (eds.), Academic Press, to appear (2003).Google Scholar
  23. 23.
    Sander, P., Wood, Z., Gortler, S., Snyder J., and Hoppe, H.: Multi-chart geometry images. Symposium on Geometry Processing 2003, 157–166.Google Scholar
  24. 24.
    Schröder, P., and Sweldens, W.: Spherical wavelets: Efficiently representing functions on the sphere. Proc. ACM SIGGRAPH 1995, 161–172.Google Scholar
  25. 25.
    Shapiro, A., and Tal, A.: Polygon realization for shape transformation. The Visual Computer, 14(8–9), 429–444 (1998).CrossRefGoogle Scholar
  26. 26.
    Sorkine, O., Cohen-Or, D., and Toledo, S.: High-pass quantization for mesh encoding. Symposium on Geometry Processing, 2003.Google Scholar
  27. 27.
    Taubin, G., Gueziec, A., Horn, W., and Lazarus, F.: Progressive forest split compression. Proc. ACM SIGGRAPH 1998.Google Scholar
  28. 28.
    Touma, C., and Gotsman, C.: Triangle mesh compression. Graphics Interface 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hugues Hoppe
    • 1
  • Emil Praun
    • 2
  1. 1.Microsoft ResearchRedmondUSA
  2. 2.University of UtahSalt Lake CityUSA

Personalised recommendations