Watermarking 3D Polygonal Meshes Using the Singular Spectrum Analysis

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.

[1]  Andreas Galka,et al.  Topics in Nonlinear Time Series Analysis, with Implications for Eeg Analysis , 2000 .

[2]  Boon-Lock Yeo,et al.  Watermarking 3D Objects for Verification , 1999, IEEE Computer Graphics and Applications.

[3]  Michael G. Wagner,et al.  Robust watermarking of polygonal meshes , 2000, Proceedings Geometric Modeling and Processing 2000. Theory and Applications.

[4]  Hiroshi Masuda,et al.  Watermarking three-dimensional polygonal models through geometric and topological modifications , 1998, IEEE J. Sel. Areas Commun..

[5]  Andrew L. Rukhin,et al.  Analysis of Time Series Structure SSA and Related Techniques , 2002, Technometrics.

[6]  Hiroshi Masuda,et al.  Data embedding algorithms for geometrical and non-geometrical targets in three-dimensional polygonal models , 1998, Comput. Commun..

[7]  Hiroshi Masuda,et al.  Watermaking three-dimensional polygonal models , 1997, MULTIMEDIA '97.

[8]  Adam Finkelstein,et al.  Robust mesh watermarking , 1999, SIGGRAPH.

[9]  Oliver Benedens,et al.  Geometry-Based Watermarking of 3D Models , 1999, IEEE Computer Graphics and Applications.

[10]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[11]  Hiroshi Masuda,et al.  A shape-preserving data embedding algorithm for NURBS curves and surfaces , 1999, 1999 Proceedings Computer Graphics International.

[12]  Ryutarou Ohbuchi,et al.  Watermarking 3D Polygonal Meshes in the Mesh Spectral Domain , 2001, Graphics Interface.

[13]  S. Kanai,et al.  Digital Watermarking for 3D Polygons using Multiresolution Wavelet Decomposition , 1998 .