基于最小均方差下的3D模型数字水印算法

A 3-D Model Watermarking Algorithm Based on Minimum Mean Square Error

使得三维模型变换带来的误差能量,最小影射到嵌入水印上.为使嵌入的水印对于三维模型的拓扑变换和几何变换都具有鲁棒性,提出一种基于最小均方差的3D几何模型算法,算法首先通过对三维网格顶点排序和挑选,排序和挑选的原则是使得被挑选的顶点具有最小的边距和,即通过对3D模型网格顶点优化选择,使得选择后的顶点受到拓扑攻击影响最小;然后,计算选择后顶点扰动均方误差能量,将水印嵌入到受误差能量影响最小的空间,使得嵌入的水印受到几何攻击影响最小.实验结果表明,算法对几何攻击和拓扑攻击具有好的抵御能力.

In this paper, the basic idea is to lead to the embedding watermark that has the least value of error energy, which is caused by various transforms of 3D model. In order to the embedding watermark that has the robustness to the topological and geometrical attacks, we firstly choose the vertexes of 3D mesh, and the principle of chosen vertexes has the shortest edge among vertexes. Namely, those chosen vertexes have the least influenced to topology transform of the 3D geometry model. Then, resisting to the geometrical transforms, we calculate the Mean Square Error of triangle mesh vertexes, and project them to the space that has the least mean square error value. So, we obtain that the robustness of the approach lies in hiding a watermark in the space that is least susceptible to the 3D model potential modification. AS a result, our algorithm is able to resist the topological and geometrical attaeks, The robustness of our method is demonstrated by various attacks through computer simulation.