基于概率密度梯度值估计与圆谐傅里叶变换的鲁棒图像水印算法  

Robust image watermarking algorithm based on probability density gradient estimation and radial harmonic Fourier transformation

作　　者：张森[1,2] 曹再辉 施进发 

机构地区：[1]郑州航空工业管理学院计算机学院 [2]航空经济发展河南省协同创新中心 [3]华北水利水电大学

出　　处：《电子测量与仪器学报》2018年第10期126-137,共12页Journal of Electronic Measurement and Instrumentation

基　　金：国家自然科学基金青年科学基金(51705472);国家自然科学基金(71371172);河南省科技攻关计划(162102210152);河南省教育厅重点研究项目(15A520123);河南省高等学校重点科研项目(18A520051)资助

摘　　要：为了解决当前基于图像特征点的水印技术存在的问题,设计了基于概率密度梯度值估计与圆谐傅里叶变换的鲁棒图像水印算法。首先,基于载体图像的强度概率密度,构建概率密度梯度估计函数;利用概率密度梯度值替代强度梯度,计算载体图像的二阶自相关矩阵,以改进Harris-Laplace检测算子,充分提取载体的鲁棒特征点;然后,基于LOG(Laplacian-of-Gaussians)算子,计算每个点的特征尺度,构建了圆形局部特征区域;引入圆谐傅里叶变换,对所有局部特征区域进行处理,输出相应的傅里叶系数;定义鲁棒系数选择规则,从所有的傅里叶系数中确定合适的系数作为水印隐藏位置;根据选择的鲁棒系数,设计水印嵌入方法,将加密后的二值水印隐藏到这些系数中,形成水印图像;最后,建立水印检测机制,从水印图像中复原二值水印。测试结果显示,与当前图像水印方案相比,面对几何变换攻击,所提算法具有更高的不可感知性,所输出的水印图像与载体的相似度为0.994;另外,所提技术也具备更强的鲁棒性,复原水印失真度最小,在中心裁剪攻击下,所提算法的复原水印对应的峰值信噪比(PSNR)、归一化系数(NC)值最大,分别达到了41.91dB、0.901。In order to solve the defects as watermarking technology based on image feature points, a robust image watermarking algorithm based on probability density gradient estimation and radial harmonic Fourier transformation is designed. Firstly, probability density gradient estimation function was built based on intensity probability density of carrier image. Then the two-order autocorrelation matrix of the carrier image was calculated by using the probability density gradient instead of the intensity gradient, which for improving the Harris-Laplace detection operator to extract the robust feature points of the carrier image. The feature scale of each point was calculated based on the LOG operator to construct the circular local feature area. And the corresponding transformation coefficients were output by using the radial harmonic Fourier transformation to process each local feature area. A robust coefficient selection rule is defined to select the appropriate coefficients from all the Fourier transformation coefficients as watermark embedding locations. The watermark embedding method was designed according to the chosen robust coefficients to hiding the encrypted binary watermarking into these coefficients for forming the watermark image. Finally, the watermark detection method was established to extract binary watermarking from watermark image. The test results show that this algorithm has a higher uncertainty, which the similarity between the output watermark image and the carrier is 0.994; in addition, this algorithm also has a stronger robustness against the geometric transform attack, as well as the least distortion of the watermark compared with the current image watermarking scheme. The corresponding peak signal to noise ratio and the normalized coefficient value of the restored watermark with this algorithm are the largest, which is up to 41.91 dB and 0.901 respectively under the center clipping attack.

关 键 词：图像水印 概率密度梯度估计 二阶自相关矩阵 Harris-Laplace检测算子 特征尺度 圆谐傅里叶变换 特征点 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]