Affine Invariant Watermarks for 3D Polygonal and NURBS Based Models
We present a scheme for embedding secret or public readable watermarks into 3D models consisting of polygonal or NURBS surfaces. The scheme realizes affine invariant watermarks by displacing vertices (control points) and satisfies constraints regarding maximum tolerated vertex movements or, in the NURBS case, differences of original and watermarked surfaces. The algorithm uses the volume of two tetrahedrons as an embedding feature. The scheme described can be stacked on a more robust scheme allowing transmission of labeling information to the user or increasing blind detection capabilities of the underlying scheme. The paper makes two major contributions, both driven by real world requirements: The first one is a technique to cope with reduced precisions of vertex coordinates. Real world modeling applications represent vertex coordinates with single floating point precision. Vertex coordinates in VRML scenes are represented by 6 decimal digits or even less. Mesh compression schemes may quantize vertex coordinates to even below precision of 4 decimal digits. The second contribution of this paper is a general technique for reducing processing time of watermark (label) extraction satisfying impatient users and enhancing robustness with respect to affiine transformations and, in particular, vertex randomization attacks. The technique is based on simplifying the mesh applying edge collapses prior to watermark embedding and retrieval. The technique depends on a consistent order of vertices in embedding and retrieval process. We sketch possible extensions of the proposed scheme.
KeywordsWatermarking 3D Polygonal Model NURBS Surfaces Public readable Watermark Secret Watermark Affine Transformation.
Unable to display preview. Download preview PDF.
- 1.O. Benedens and C. Busch. Towards Blind Detection of Robust Watermarks in Polygonal Models. Eurographics 2000 Conference Proceedings, August 2000.Google Scholar
- 2.H. Hoppe. Progressive Meshes. SIGGRAPH 96 Conference Proceedings, ACM SIGGRAPH, pp. 99–108, 1996.Google Scholar
- 3.G. Nielson and T. Foley. A Survey of Applications of an Affine Invariant Norm. Mathematical Methods in Computer Aided Design, Academic Press, pp. 445–467, 1989.Google Scholar
- 4.R. Ohbuchi, H. Masuda, and M. Aono. Watermarking Three-Dimensional Polygonal Models. ACM Multimedia 97, pp. 261–272, 1997.Google Scholar
- 6.R. Ohbuchi, H. Masuda, and M. Aono. A Shape-Preserving Data Embedding Al-gorithm for NURBS Curves and Surfaces. Computer Graphics International 1999 (CGI’99) Proceedings, pp. 180–177, June 1999.Google Scholar
- 7.L. Piegel and W. Tiller. The NURBS Book. 2nd Edition, Springer, Berlin, 1997.Google Scholar
- 8.E. Praun, H. Hoppe, and A. Finkelstein. Robust Mesh Watermarking. SIGGRAPH 99 Proceedings, pp. 69–76, 1999.Google Scholar
- 9.M. Wagner. Robust Watermarking of Polygonal Meshes. Geometric Modelling and Processing 2000 Proceedings, April 2000.Google Scholar