Abstract—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. Index Terms—Fourier–Mellin, rotation, RST, scale, translation, watermarking
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