基于几何校正与非下采样Shearlet变换的图像水印算法

为了解决当前图像水印技术难以抵御几何失真，使其鲁棒性较低与误检率较高的问题，提出了几何校正与非下采样Shearlet变换的图像水印算法.首先，引入Cat映射，对水印信息图像进行置乱；随后，借助非下采样Shearlet变换机制，对载体图像进行处理，获取低通子带和高通子带，并将低通子带分割为尺寸相同的小块；通过修改低通子带的Shearlet系数，建立水印嵌入机制，将水印信息植入到载体图像中，获取水印密文；构建几何失真图像训练样本，基于极谐变换，计算水印图像的极谐变换系数模，充分描述其鲁棒特征；基于模糊支持向量机，预测几何失真参数，对水印图像进行几何校正；最后，再次利用非下采样Shearlet变换处理校正水印图像，获取低通子带小块，设计水印提取方法，复原其水印信息.实验结果显示：与当前图像水印算法相比，所提算法具有更高的不可感知能力与鲁棒性，对于各种几何攻击，所提取技术的复原水印与初始水印的相关系数均要高于0.95.

Image Watermarking Algorithm Based on Geometric Correction and Non-subsampled Shearlet Transform

To solve the defects in current image watermarking technology, including poor robustness and the high false-detection rate induced by the difficulty of resisting geometric distortion, we propose an image watermarking algorithm based on geometric correction and the non-subsample Shearlet transform. First, we use Cat mapping to permute the watermark information image. Then, we use a non-subsampled Shearlet transform to embed the watermarking information in the permutated image, output the low-pass subband and a series of high-pass subbands, and segment the low-pass subband into small blocks of the same size. To embed the information into a carrier image, we construct a watermark-embedding mechanism by modifying the non-subsampling Shearlet transform coefficients of the low-pass subband. Then, to fully describe the robust features, we construct geometric-distortion image-training samples and calculate the modulus of the polar harmonic transform coefficients of the watermark image based on the polar harmonic transformation. Then, we introduce a fuzzy support vector machine to predict the geometric-distortion parameter for correcting the watermark image. Lastly, we process the corrected watermark image using a non-sub-sampled Shearlet transform to obtain the low-pass subband, and design a watermark detection method for restoring the watermark information. The experimental results show that this algorithm has higher perceptual ability and better robustness than existing image watermarking algorithms, and for all kinds of geometric attacks, the correlation coefficients between the recovered and original watermarks are higher than 0.95.