Digital Watermarking for 3D Polygons using Multiresolution Wavelet Decomposition

Recently, much interest is being taken in methods to protect the copyright of digital data and preventing illegal duplication of it. However, in the area of CAD/CAM and CG, there are no effective ways to protect the copyright of 3D geometric models. As a first step to solve this problem, a new digital watermarking method for 3D polygonal models is introduced in this paper. Watermarking is one of the copyright protection methods where an invisible watermark is secretly embedded into the original data. The proposed watermarking method is based on wavelet transform (WT) and multiresolution representation (MRR) of the polygonal model. The watermark can be embedded in the large wavelet coefficient vectors at various resolution levels of the MRR. This makes the embedded watermark imperceptible and invariant to the affine transformation. And also makes the control of the geometric error caused by the watermarking reliable. First the requirements and features of the proposed watermarking method are discussed. Second the mathematical formulations of WT and MRR of the polygonal model are shown. Third the algorithm of embedding and extracting the watermark is proposed. Finally, the effectiveness of the proposed watermarking method is shown through several simulation results.