基于Clifford代数的3D点云模型数字水印算法

引入Clifford代数，在G3空间中建立了不依赖于特定坐标系的、多维统一的3D点云数据几何表征与计算模型.介绍了Clifford代数空间中的Fourier变换及其计算公式，进而提出了基于Clifford-Fourier变换的3D点云模型数字水印算法.该方法将点云模型映射为相应的Clifford几何空间域系数，并对其进行水印信息的嵌入和提取.实验分析表明，所提出的方法对平移、旋转、均匀缩放、重排序、简化和噪声等各种攻击均具有较好的鲁棒性.

Digital Watermarking Algorithm for 3D Point Cloud Model Based on Clifford Algebra

In this paper, the generalized geometric representation of the 3D Point Cloud data was proposed based on Clifford algebra, where the expressions of 3D Point Cloud data were unified without losing their geometric meaning, and the geometric operation was coordinate-free for different dimensional spaces. The Clifford Fourier Transform was introduced into the digital watermarking algorithm for the 3D Point Cloud model, where point cloud models were mapped to the corresponding domain coefficients in space G3. Then the watermark was embedded or extracted based on these coefficients. The experimental results show that the algorithm has very good performance in affine transformation, reordering, simplification and noise, and is robust against attacks.