Advertisement

Watermarking 3D Polygonal Meshes Using the Singular Spectrum Analysis

  • Kohei Murotani
  • Kokichi Sugihara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2768)

Abstract

Watermarking is to embed a structure called a watermark into the target data such as images. The watermark can be used, for example, in order to secure the copyright and detect tampering. This paper presents a new robust watermarking method that adds a watermark into a 3D polygonal mesh in the spectral domain. In this algorithm, a shape of a 3D polygonal model is regarded as a sequence of vertices called a vertex series. The spectrum of the vertex series is computed using the singular spectrum analysis (SSA) for the trajectory matrix derived from the vertex series. Watermarks embedded by this method are resistant to similarity transformations and random noises.

Keywords

Singular Value Decomposition Singular Spectrum Analysis Hankel Matrix Voronoi Region Chip Rate 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Benedens, O.: Geometry-Based Watermarking of 3D Models. IEEE CG&A, pp. 46-55 (January/February 1999) Google Scholar
  2. 2.
    Galka, A.: Topics in Nonlinear Time Series Analysis, pp. 49–71. World Scientific, Singapore (2001)Google Scholar
  3. 3.
    Golyandina, N., Nekrutkin, V., Zhigljavsky, A.: Analysis of Time Series Structure–SSA and Related Techniques. Chapman & Hall/CRC (2001)Google Scholar
  4. 4.
    Kanai, S., Date, H., Kishinami, T.: Digital Watermarking for 3D Polygons Using Multiresolution Wavelet Decomposition. In: Proceedings of the Sixth IFIP WG 5.2 International Workshop on Geometric Modeling: Fundamentals and Applications (GEO-6), Tokyo, Japan, pp. 296–307 (December 1998)Google Scholar
  5. 5.
    Ohbuchi, R., Masuda, H., Aono, M.: Watermarking Three-Dimensional Polygonal Models. In: Proceedings of the ACM International Conference on Multimedia 1997, Seattle, USA, pp. 261–272 (November 1997)Google Scholar
  6. 6.
    Ohbuchi, R., Masuda, H., Aono, M.: Watermarking Three-Dimensional Polygonal Models Through Geometric and Topological Modifications. IEEE Journal on Selected Areas in Communication 16(4), 551–560 (1998)CrossRefGoogle Scholar
  7. 7.
    Ohbuchi, R., Masuda, H., Aono, M.: Targeting Geometrical and Non-Geometrical Components for Data Embedding in Three-Dimensional Polygonal Models. Computer Communications 21, 1344–1354 (1998)CrossRefGoogle Scholar
  8. 8.
    Ohbuchi, R., Masuda, H., Aono, M.: A Shape-Preserving Data Embedding Algorithm for NURBS Curves and Surfaces. In: Proceedings of the Computer Graphics International 1999, Canmore, Canada, June 7-11, pp. 180–177 (1999)Google Scholar
  9. 9.
    Ohbuchi, O., Takahashi, S., Miyazawa, T., Mukaiyama, A.: Watermarking 3D Polygonal Meshes in the Mesh Spectral Domain. In: Proceedings of the Graphics Interface 2001, Ontario, Canada, pp. 9–17 (June 2001)Google Scholar
  10. 10.
    Praun, E., Hoppe, H., Finkelstein, A.: Robust Mesh Watermarking. ACM SIGGRAPH 1999, pp. 69–76 (1999)Google Scholar
  11. 11.
    Wagner, M.G.: Robust Watermarking of Polygonal Meshes. In: Proceedings of Geometric Modeling & Processing 2000, Hong Kong, April 10-12, pp. 201–208 (2000)Google Scholar
  12. 12.
    Yeo, B-L., Yeung, M.M.: Watermarking 3D Objects for Verification. IEEE CG&A, pp. 36-45 (January/February 1999) Google Scholar
  13. 13.
    Matsui, K.: Basic of watermarks (in Japanese). Morikita Shuppan Publishers, Tokyo (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Kohei Murotani
    • 1
  • Kokichi Sugihara
    • 1
  1. 1.Department of Mathematical Informatics Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan

Personalised recommendations