为了提高数字水印算法的鲁棒性, 提出了一种基于矢量长度比的三维网格零水印算法. 首先, 将三维网格模型由直角坐标系转化为球坐标系. 其次, 对网格模型的顶点进行分块并计算每个块质心. 然后, 计算每个顶点到块质心的距离以及邻域顶点到块质心的平均距离的比值, 并将比值序列与比值的平均值进行比较, 根据比较的大小记为0和1; 统计每个分块0、1数量的多数, 以此构成模型的特征序列. 最后, 将版权信息的二值序列与特征序列进行异或, 得到最终的零水印序列. 实验结果表明, 本文算法能够抵抗平移、旋转、均匀缩放、噪声、平滑、简化和剪切等常见的攻击, 也能够对三维网格模型进行版权保护.
To improve the robustness of the digital watermarking algorithm, this study proposes a zero-watermarking algorithm for three-dimensional (3D) mesh based on the vector length ratio. First, the 3D mesh model is converted from a rectangular coordinate system to a spherical coordinate system. Second, we divide the vertices of the mesh model into blocks and calculate the centroid of each block. Then, we calculate the ratio of the distance between each vertex and the centroid of the block to the average distance between its neighbor vertex and the centroid and compare the ratio sequence with the average of the ratios. We record the comparison results as 0 or 1 according to the size relation and perform statistics of the majority of the numbers of 0 and 1 in each block. In this way, the characteristic sequence of the model can be constituted. Finally, the binary sequence of the copyright information and the characteristic sequence are XORed to obtain the final zero-watermark sequence. Experimental results show that the algorithm in this study can resist common attacks such as translation, rotation, uniform scaling, noise, smoothing, simplification, and cropping, and can protect the copyright of the 3D mesh model.