Abstract: A zero watermarking scheme for 3D point model has been researched.Based on shape analysis of 3D models and combined with data analysis theory，the global geometry property that is more stable than the other geometry properties is selected as the basis of producing watermark.The vertex norms are calculated and the vertex sets are built where vertices are ordered by vertex norms.Then watermark is constructed by analyzing the distribution of the number of vertices in each vertex set.Experiments show the scheme executes rapidly and can resist translation，rotation，uniform scaling，vertex re-ordering，noise，simplification，quantization，smoothing，subdivision and shows some robustness against cropping attack.The scheme can be applied to 3D point models directly and satisfies the requests for copyright protection of 3D models.

Key words: 3D point model, digital watermarking, zero watermarking, copyright protection, vertex norm

摘要： 对三维点云模型零水印技术开展研究，基于三维模型形状分析、结合数据分析理论，选择具有较高稳定性的三维模型全局几何特征作为水印构造的基础，通过计算三维模型顶点范数，以顶点范数为依据建立三维模型有序顶点集，分析顶点集中顶点数目的分布情况构造水印。实验结果表明，该方法执行速度较快，可以直接应用于三维点云数据，能够很好地抵抗平移、旋转、均匀缩放、顶点重排序、噪声、简化、量化、平滑和细分等常见攻击，对剪切攻击也有一定的鲁棒性，能够满足三维模型版权保护的要求。

关键词: 三维点云模型, 数字水印, 零水印, 版权保护, 顶点范数