许多现有的适用于图像的数字水印对几何失真都是很敏感的。尤其是此类失真会严重妨碍对水印的盲提取。为此，提出了一种基于奇异值分解的数字水印算法，它对常见的几何失真是稳健的。此水印是被嵌入到图像分解后的奇异值之中。根据奇异值分解的代数性质，严格证明了嵌入了水印的图像在受到转置、镜像、旋转、放大和平移等几何失真后，其奇异值是不变的。在经过了上述的几何失真、一般的信号处理操作或JPEG压缩以后，嵌入的水印能够被可靠地提取和检测。实验结果表明本算法具有很好的稳健性。

Many digital watermarks now available for images are sensitive to geometric distortions, which particularly prevent blind detection of a public watermark. In this paper, a watermarking algorithm based on singular value decomposition (SVD) is proposed, which is robust to common geometric distortions. The watermark is embedded into image's singular values. By the algebraic properties of SVD, it is proved rigorously that singular values of the watermarked image are invariant when it goes through the geometric distortions of transpose, mirror reflection, rotation, scale, and translation. Experimental results show that the watermarking algorithm performs well in robustness. The embedded watermark can be detected reliably, following these geometric distortions, usual signal processing, or JPEG compression.