Abstract: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.