一种基于Ridgelet变换和抑制式FCM聚类的数字水印算法

Robust Digital Watermarking Based on Ridgelet Transform and s-FCM

利用人类视觉系统的掩蔽效应和脊波变换(ridgelet transform,RT),提出了一种新颖的自适应乘性数字水印算法。由于脊波具有方向敏感性和各向异性的特点,具有自然纹理和曲线边缘的图像首先进行分块脊波变换,使脊波变换系数能够分段线状表示图像中的边缘奇异性。然后根据不同纹理程度的图像块提取脊波方向能量特征,结合人眼接受信号具有近似对数的特性对此特征进行非线性调整;并将其作为抑制式模糊聚类(suppressed fuzzy C-means algorithm,s-FCM)的特征向量,将图像块分成两类:较平坦区域、强纹理和边缘区域。最后将数字水印自适应嵌入到属于第二类的图像块的能量最大方向的中频脊波系数,并由该图像块的脊波方向能量特征控制嵌入强度。水印通过相关检测器判断存在与否。实验结果表明水印算法具有较高的不可见性和稳健性。

A muhiplicative watermarking method operating in the Ridgelet domain （RT） was proposed, using the masking effect of the human visual system. Since the ridgelet transform has directional sensitivity and anisotropy, the image was first partitioned into small pieces and the RT was applied for each piece to obtain a sparse representation of the image, especially for straight edge singularity. Based on the characteristic of ridgelet coefficients in representation of different texture features, these image pieces were classified into frat regions and texture regions by suppressed Fuzzy C-Mean （s-FCM） clustering algorithm. The watermarking was embedded into the middle ridgelet subband in the highest energy directions of texture pieces, where the embedding strength was also adjusted by the ridgelet coefficients of each piece based on the feature of luminance masking and texture masking. Then the embedded watermark could be detected by correlation detector. Experimental results prove robustness and transparency of the proposed watermarking scheme.