A Watermarking Framework for Subdivision Surfaces

  • Guillaume Lavoué
  • Florence Denis
  • Florent Dupont
  • Atilla Baskurt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4105)


This paper presents a robust watermarking scheme for 3D subdivision surfaces. Our proposal is based on a frequency domain decomposition of the subdivision control mesh and on spectral coefficients modulation. The compactness of the cover object (the coarse control mesh) has led us to optimize the trade-off between watermarking redundancy (which insures robustness) and imperceptibility by introducing two contributions: (1) Spectral coefficients are perturbed according to a new modulation scheme analyzing the spectrum shape and (2) the redundancy is optimized by using error correcting codes. Since the watermarked surface can be attacked in a subdivided version, we have introduced a so-called synchronization algorithm to retrieve the control polyhedron, starting from a subdivided, attacked version. Through the experiments, we have demonstrated the high robustness of our scheme against both geometry and connectivity alterations.


Error Correct Code Convolutional Code Polygonal Mesh Subdivision Surface Repetition Code 
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  1. 1.
    Benedens, O.: Geometry-based watermarking of 3d models. IEEE Computer Graphics and Application 19, 46–55 (1999)CrossRefGoogle Scholar
  2. 2.
    Cayre, F., Macq, B.: Data hiding on 3-d triangle meshes. IEEE Transactions on Signal Processing 51, 939–949 (2003)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Kanai, S., Date, H., Kishinami, T.: Digital watermarking for 3d polygons using multi-resolution wavelet decomposition. In: IFIP WG 5.2 International Workshop on Geometric Modeling: Fundamental and Application (GEO-6), pp. 296–307 (1998)Google Scholar
  4. 4.
    Praun, E., Hoppe, H., Finkelstein, H.: Robust mesh watermarking. In: Siggraph, pp. 69–76 (1999)Google Scholar
  5. 5.
    Yin, K., Pan, Z., Shi, J., hang, D.: Robust mesh watermarking based on multiresolution processing. Computers and Graphics 25, 409–420 (2001)CrossRefGoogle Scholar
  6. 6.
    Ohbuchi, R., Takahashi, S., Miyazawa, T., Mukaiyama, A.: Watermarking 3d polygonal meshes in the mesh spectral domain. In: Graphic interface, pp. 9–17 (2001)Google Scholar
  7. 7.
    Ohbuchi, R., Mukaiyama, A., Takahashi, S.: A frequency-domain approach to watermarking 3d shapes. Computer Graphic Forum 21, 373–382 (2002)CrossRefGoogle Scholar
  8. 8.
    Wu, J., Kobbelt, L.: Efficient spectral watermarking of large meshes with orthogonal basis functions. The Visual Computers 21, 848–857 (2005)CrossRefGoogle Scholar
  9. 9.
    Catmull, E., Clark, J.: Recursively generated b-spline surfaces on arbitrary topological meshes. Computer-Aided Design 10, 350–355 (1978)CrossRefGoogle Scholar
  10. 10.
    Marinov, M., Kobbelt, L.: Optimization methods for scattered data approximation with subdivision surfaces. Graphical Models 67, 452–473 (2005)CrossRefGoogle Scholar
  11. 11.
    Lavoué, G., Dupont, F., Baskurt, A.: A framework for quad/triangle subdivision surface fitting: Application to mechanical objects. Computer Graphics Forum 25 (2006)Google Scholar
  12. 12.
    Bollabás, B.: Modern graph theory. Springer, Heidelberg (1998)Google Scholar
  13. 13.
    Baudry, S., Delaigle, J.F., Sankur, B., Macq, B., Maitre, H.: Analyses of error correction strategies for typical communication channels in watermarking. Signal Processing 81, 1239–1250 (2001)MATHCrossRefGoogle Scholar
  14. 14.
    Pottmann, H., Leopoldseder, S.: A concept for parametric surface fitting which avoids the parametrization problem. Computer Aided Geometric Design 20, 343–362 (2003)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Lavoué, G., Drelie Gelasca, E., Dupont, F., Baskurt, A., Ebrahimi, T.: Perceptually driven 3d distance metrics with application to watermarking. In: SPIE Applications of Digital Image Processing XXIX (2006)Google Scholar
  16. 16.
    Benedens, O., Dittmann, J., Petitcolas, F.: 3d watermarking design evaluation. In: SPIE Security and Watermarking of Multimedia Contents V, vol. 5020, pp. 337–348 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Guillaume Lavoué
    • 1
  • Florence Denis
    • 1
  • Florent Dupont
    • 1
  • Atilla Baskurt
    • 1
  1. 1.INSA de Lyon, Laboratoire LIRIS UMR 5205Université Claude Bernard Lyon 1VilleurbanneFrance

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