Lin C Y, Wu M, Bloom J A, Cox I J, Miller M L, Lui Y M
IBM Thomas J. Watson Res. Center, Yorktown Heights, NY 10598, USA.
IEEE Trans Image Process. 2001;10(5):767-82. doi: 10.1109/83.918569.
Many electronic watermarks for still images and video content are sensitive to geometric distortions. For example, simple rotation, scaling, and/or translation (RST) of an image can prevent blind detection of a public watermark. In this paper, we propose a watermarking algorithm that is robust to RST distortions. The watermark is embedded into a one-dimensional (1-D) signal obtained by taking the Fourier transform of the image, resampling the Fourier magnitudes into log-polar coordinates, and then summing a function of those magnitudes along the log-radius axis. Rotation of the image results in a cyclical shift of the extracted signal. Scaling of the image results in amplification of the extracted signal, and translation of the image has no effect on the extracted signal. We can therefore compensate for rotation with a simple search, and compensate for scaling by using the correlation coefficient as the detection measure. False positive results on a database of 10,000 images are reported. Robustness results on a database of 2000 images are described. It is shown that the watermark is robust to rotation, scale, and translation. In addition, we describe tests examining the watermarks resistance to cropping and JPEG compression.
许多用于静止图像和视频内容的电子水印对几何失真很敏感。例如，图像的简单旋转、缩放和/或平移（RST）会妨碍对公共水印的盲检测。在本文中，我们提出了一种对RST失真具有鲁棒性的水印算法。水印被嵌入到通过对图像进行傅里叶变换、将傅里叶幅度重采样到对数极坐标，然后沿对数半径轴对这些幅度的函数求和而获得的一维（1-D）信号中。图像的旋转会导致提取信号的周期性移位。图像的缩放会导致提取信号的放大，而图像的平移对提取信号没有影响。因此，我们可以通过简单搜索来补偿旋转，并通过使用相关系数作为检测度量来补偿缩放。报告了在10000幅图像数据库上的误报结果。描述了在2000幅图像数据库上的鲁棒性结果。结果表明，该水印对旋转、缩放和平移具有鲁棒性。此外，我们还描述了检验水印对裁剪和JPEG压缩抗性的测试。
