网格分割的3维网格模型非盲水印算法

目的 信息技术的发展使得面向3维模型版权保护的问题越来越突出，提出一种新的基于网格分割的3维网格模型非盲水印算法。方法 首先使用基于形状直径函数的网格分割算法对3维网格模型进行有意义的网格分割，然后计算每个分块的鲁棒重心并以此为中心将模型由直角坐标系转换到球面坐标系，最后通过调制每个顶点范数的分布来嵌入水印，在水印检测阶段使用非盲检测的方法提取水印。结果 针对目前基于网格分块的水印算法的网格分割不一致以及对分割边界依赖性过强等问题，引入基于形状直径函数的网格分割算法并在重对齐、重采样过程中加入待检测模型与原始模型分块匹配过程以保证网格分割的一致性，并且选取分块的顶点范数的分布作为水印嵌入基元，使得算法能够有效地减弱对分割边界的依赖性。结论 实验结果表明，该算法可以有效抵抗平移、旋转、缩放、噪声、细分、简化、剪切等常见的攻击以及多种攻击的联合攻击。

Non-blind watermarking algorithm for 3D mesh models based on mesh segmentation

Objective The issue of copyright protection for 3D models is increasing prominently with the development of information technology. A non-blind watermarking algorithm for 3D mesh models based on mesh segmentation is presented. Method Firstly, meaningful mesh segmentation on 3D mesh model is conduct using the mesh segmentation algorithm based on shape diameter function. Then, the robust center of gravity for each sub-block is calculated and which is used as the center to transform model to the spherical coordinate system from the Cartesian coordinate system. Finally, watermark sequence is embedded by modulating the distribution of vertex norms for each sub-block. In watermarking detection, a non-blind method is used to detect the watermarking sequence. Result Aiming at the problems of inconsistent mesh segmentation and the strong dependence on the patch boundary in current watermarking algorithms based on mesh patching, a mesh segmentation algorithm is introduced in and a block matching process with original model is added to register and resample process to ensure the consistency of mesh segmentation. Furthermore, the distribution of vertex norms for each sub-block is chosen to be the watermarking embedding primitive, which can weaken the dependence on the patch boundary. Conclusion Experimental results show that the proposed algorithm can resist a variety of common attacks including translating, rotating, uniform scaling, noise adding, mesh subdivision, mesh simplification, mesh cropping and their combined attacks.