Abstract: In order to make the image watermarking algorithm have authentication function, this paper proposes a semi-fragile image watermarking authentication algorithm based on Sobel edge detection and Zernike invariant moments. The normalized carrier image is third-level decomposed based on discrete wavelet transform (DWT) to get 10 sub-bands LL₃,HL₃,LH₃,HH₃,HH₂,HL₂,LH₂,HL₁,LH₁,HH₁. Then the sub-band LL₃ is processed by using the Sobel operator and Zernike moments. And the watermark embedding mechanism is designed to embed the watermark information into DWT coefficients of sub-band LL₃ for forming the initial watermark image. And the Sobel operator is used again to detect the initial watermark image for obtaining the edge map to determine the embedded position, so that the final watermark image is got by embedding the watermark information into Zernike moment of edge map. Meanwhile, the watermark restoration method is established to extract the complete watermark information. Finally, the watermark authentication method is designed based on weighted Euclidean distance to determine the authenticity of the watermark information. The experimental results show that this algorithm has higher robust and lower tamper rate.

Key words: semi-fragile image watermarking, watermark authentication, Sobel edge detection, Zernike invariant moments, disceret wavelet transform (DWT), weighted Euclidean distance

摘要： 为了提高半脆弱图像水印算法的认证能力，提出了基于边缘检测与Zernike不变矩的半脆弱图像水印认证算法。引入离散小波变换（disceret wavelet transform，DWT）机制，对归一化后的载体图像进行三级分解，获取10个子带LL₃、HL₃、LH₃、  HH₃、HH₂、HL₂、 LH₂、 HL₁、LH₁、HH₁；再利用Sobel算子与Zernike矩方法对LL₃子带进行处理，输出边缘映射与量化特征的Zernike矩，将二者视为水印信息；随后，设计水印嵌入机制，将Sobel边缘映射嵌入到载体图像的LL₃子带对应的DWT系数中，形成初始水印图像；并再次利用Sobel算子对初始水印图像进行检测，获取边缘映射，确定嵌入位置，将Zernike矩隐藏到这些位置，获取最终的水印图像；建立水印复原方法，提取完整的水印信息。最后，基于权重欧式距离，设计了水印认证方法，以认证图像与定位篡改区域。实验结果显示，与当前水印技术相比，所提算法具有更强的鲁棒性与更低的篡改率。

关键词: 半脆弱图像水印, 水印认证, Sobel边缘检测, Zernike不变矩, 离散小波变换（DWT）, 权重欧式距离