基于径向基函数的三维网格鲁棒公钥非盲水印

A Robust Public-Key Non-Blind Watermarking Algorithm for 3D Mesh Based on Radial Basis Functions

针对径向基函数水印算法不能抵抗剪切和伪造攻击以及鲁棒性不足等问题,提出一种大规模三维网格鲁棒公钥非盲谱水印算法.首先引入椭圆曲线数字签名算法以抵抗模型伪造;然后提出一种基于二次误差简化的中心点集优化选取算法来降低预基函数的奇异性,提高网格重构质量;为了提高算法的鲁棒性并抵抗剪切攻击,对大规模三维网格进行语义分片,引入嵌入起始位参数调整水印在低频谱系数的绝对嵌入,最终以谱系数扰动量为权值进行水印位提取.与已有非盲谱水印算法进行详细比较的结果证明,采用文中算法生成的水印网格具有更好的视觉质量和鲁棒性.

To resist the cropping and forging attacks,and also improve robustness in 3D mesh watermarking algorithm based on radial basis functions,a robust public-key non-blind watermarking algorithm for large 3D mesh is presented,which is conducted on the spectral space of each segmented patch.Firstly,an elliptic curve digital signature algorithm is adopted so that the proposed algorithm can assert the ownership,resist forging of the mesh.Secondly,with an optimized center point set determination method based on quadric error mesh simplification,our algorithm decreases singularity of pre-basis functions and improves the mesh reconstruction quality.To improve watermark robustness and resist cropping attack,the large 3D mesh is segmented into patches semantically,and the signature bits are embedded into the low-frequency spectral coefficients absolutely starting from a proper position.Then the signature bits are extracted weightedly with regard to their corresponding disturbed spectral coefficients.Finally,through detailed comparisons with other spectral watermarking algorithms,it shows that our algorithm exhibits better visual quality and robustness against to various attacks.