中文摘要：

为了扩展三维模型数字水印抵抗攻击的种类,提高水印对抗简化、剪切及联合攻击的鲁棒性,基于顶点范数提出一种新的三维模型空域非盲数字水印算法.在水印嵌入阶段,建立规格化的三维模型顶点集,通过修改顶点集中的顶点范数,改变符合给定条件的顶点比例来嵌入水印;在水印检测阶段,分别统计待检测模型和原始模型中符合给定条件顶点的数目,根据顶点数目的变化提取水印,并利用相关性验证原始水印的存在性.算法基于VC＋＋实现,并使用Stanford的bunny、horse模型进行了透明性、鲁棒性试验分析.结果表明：该算法嵌入的水印具有较好的透明性,不受平移、旋转、均匀缩放等几何变换和顶点重排序的影响,能够有效抵抗噪声、简化、剪切、量化、平滑、细分等攻击,并且对联合攻击也具有一定的鲁棒性.

英文摘要：

In order to extend attack resistance types of digital watermark in three-dimensional models and improve the robustness against simplification,cropping and combination attacks,a new non-blind watermarking scheme based on vertex norm in spatial domain was proposed.During watermark embedding,the normalized vertex sets of 3D models were built,and the vertex norms in these vertex sets were modified to embed watermark by changing the proportion of vertices satisfying specified conditions.During watermark detecting,the number of vertices satisfying the given conditions in detected model and original model were counted respectively and compared to extract watermark.The existence of original watermark was verified by correlation test.The algorithm was implemented based on VC＋ ＋,and experimental analysis on transparency and robustness were completed by bunny and horse model of Stanford.The results show that the watermark embedded by the scheme has enough imperceptibility,and is not affected by translation,rotation,uniform scaling and vertex re-ordering.The good robustness against noise,simplification,cropping,quantization,smoothing,subdivision and combination attacks is also achieved.