基于几何特征的三维网格数字水印算法

首先把网格上的点到网格中心的距离看成一维的空域数字信号，并用一维DCT变化到频域；然后在频域信号上加入水印，再通过逆向DCT转回空域信号；最后根据新的空域信号的值修改网格上点的坐标得到加入数字水印的网格．实验结果表明：该算法实现简单，在简化攻击、噪音攻击、二次水印攻击和剪切攻击情况下具有良好的鲁棒性．

A Geometry Property Based Watermarking Scheme for Three Dimensional Meshes

In this article, we propose a robust watermarking scheme for three-dimensional triangle meshes. First, we calculate the distance of each vertex in the mesh to the center of the mesh. And we get a sequence of real numbers which are the values of distances. Second, we consider the real number sequence as a digital signal in spatial domain and transform it to a signal in frequency domain using one-dimensional discrete cosine transform (DCT). Third, we embed a watermark into the signal in frequency domain, and then transform it back to a digital signal in spatial domain. This new spatial-domain signal represents the new values of the distances after embedding a watermark. Finally, we modify the coordinates of the vertices making their distances to the mesh center satisfy these new values. Experiments show that this scheme is both simple to implement and fairly robust against common mesh attacks such as mesh simplification, mesh cropping, random noise added to the vertex coordinates etc.