摘要：

现有彩色图像水印算法存在各通道间彼此独立、忽视了通道间的内在关联问题。为了实现在彩色图像中嵌入鲁棒可逆水印, 提出一种基于三元数指数傅里叶矩(TEFM)的彩色图像鲁棒可逆水印算法。首先, 结合三元数理论与指数傅里叶矩构造了TEFM变换; 然后, 利用两阶段鲁棒可逆水印算法在TEFM域嵌入水印信息。第一阶段通过量化索引调制(QIM)方法, 对标准化后的TEFM变换系数进行修改来嵌入水印; 第二阶段通过预测误差扩展的方法将嵌入鲁棒水印引起的失真作为补偿信息可逆地嵌入到鲁棒水印图像中。实验结果表明, 所提算法在最终水印图像中的平均峰值信噪比(PSNR)在44 dB以上, 并且在未受攻击下可以无损恢复原始图像, 与现有算法相比, 在对图像进行中值滤波、均值滤波、椒盐噪声等常规攻击下的误码率(BER)有不同程度的降低, 其中在受到中值滤波3×3的攻击下, 比其他三种先进方法的平均BER分别降低了16.7%、7.6%、6.8%。因此, 所提的水印算法具有不可见性、高容量、可逆性和较高的鲁棒性。

关键词: 彩色图像, 鲁棒可逆水印, 指数傅里叶矩, 三元数变换, 量化索引调制

Abstract:

Existing color image watermarking algorithms are applied between channels that are independent of each other, ignoring the intrinsic correlation between the channels. To achieve the embedding of robust reversible watermarking in color images, a color image robust reversible watermarking algorithm based on the Trinion of Exponential Fourier Moments (TEFM) is proposed. First, the trinion theory and exponential Fourier moments are used to construct the TEFM transform, and then, a two-stage robust reversible watermarking algorithm is used to embed the watermark information in the TEFM domain. In the first stage, the standardized TEFM transform coefficients are modified through Quantization Index Modulation (QIM) to embed the watermark; in the second stage, the distortions caused by embedding robust watermarks are embedded into the robust watermarked image as compensatory information through the prediction error expansion method. Experimental results show that the average Peak Signal-to-Noise Ratio (PSNR) of the final watermarked image obtained using this algorithm is greater than 44 dB. The original image can be recovered losslessly under unattacked conditions. The Bit Error Rate (BER) is reduced to different degrees compared with that for existing algorithms under regular attacks on the image, such as median filtering, mean filtering, and salt-and-pepper noise. Under the attack of 3×3 median filtering, average BER reductions of 16.7%, 7.6%, and 6.8% are achieved compared with other three state-of-the-art methods, respectively. These results confirm that the proposed watermarking algorithm offers invisibility, high capacity, reversibility, and high robustness.

Key words: color image, robust reversible watermarking, exponential Fourier moments, trinion transform, Quantization Index Modulation (QIM)