Abstract: To improve the robustness of spatial watermarking schemes for three-dimensional models against various attacks especially the simplification, cropping and their combined attacks, a new watermarking scheme combined with tendency detection of vertices for three-dimensional models was proposed. In the scheme, the spherical coordinates of vertices were used to construct the ordered vertex sets and the vertex norms representing the model shape approximately were selected to be modified to embed watermark. Watermark was extracted based on the tendency of vertices variations achieved by comparing and counting the variations between the vertex norms of detected model and original model. The negative effect on watermark detection caused by cropping was reduced further by introducing the analysis on the rate of deleted vertices. The experiments show the scheme is robust enough against the common single attacks including translation, rotation, uniform scaling, vertex re-ordering, noise, simplification, cropping, quantization and subdivision and combination attacks. The smoothing attack also can be resisted to some extent. Thereby, the watermarking scheme can be applied to the copyright protection of three-dimensional models.

Key words: digital watermarking, three-dimensional model, spatial watermarking, copyright protection, non-blind watermarking, tendency of vertices

摘要： 为了提高三维模型空域数字水印算法对抗各类攻击尤其是简化、剪切及其联合攻击的鲁棒性,提出一种新的结合顶点趋势检测的三维模型数字水印算法。利用三维模型顶点的球面坐标构建有序顶点集,选择体现三维模型整体形状信息的顶点范数嵌入水印;通过比较和统计待检测模型和原始模型顶点范数的变化关系,以变化趋势为依据实现水印检测,并分析顶点缺失率进一步弱化剪切对水印检测的影响。实验表明,该算法对各种常见的单一类型攻击如平移、旋转、均匀缩放、顶点重排序、噪声、简化、剪切、量化和细分以及联合攻击都具有较好的鲁棒性,对平滑攻击也有一定的抵抗能力,能够较好地应用于三维模型的版权保护。

关键词: 数字水印, 三维模型, 空域水印, 版权保护, 非盲水印, 顶点趋势