Digital Watermarking for 3D Polygons using Multiresolution Wavelet Decomposition
Digital Watermarking for 3D Polygons using Multiresolution Wavelet Decomposition
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发表时间：
1998
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通讯作者：
S. Kanai;T. Kishinami
中科院分区：
文献类型：
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作者：
S. Kanai;T. Kishinami
最近，人们对保护数字数据版权和防止非法复制的方法产生了很大兴趣。然而，在CAD/CAM和CG领域，还没有有效的方法来保护3D几何模型的版权。作为解决这一问题的第一步，本文介绍了一种新的 3D 多边形模型数字水印方法。水印是将不可见的水印秘密地嵌入到原始数据中的版权保护方法之一。所提出的水印方法基于小波变换（WT）和多边形模型的多分辨率表示（MRR）。水印可以嵌入到 MRR 的各种分辨率级别的大小波系数向量中。这使得嵌入的水印难以察觉并且对于仿射变换具有不变性。并且也使得水印引起的几何误差的控制变得可靠。首先讨论所提出的水印方法的要求和特征。其次显示了多边形模型的 WT 和 MRR 的数学公式。第三，提出了水印的嵌入和提取算法。最后，通过多个仿真结果证明了所提出的水印方法的有效性。
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.