<title>Rotation-, scale-, and translation-resilient public watermarking for images</title>

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 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 1-dimensional signal obtained by first 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. If the image is rotated, the resulting signal is cyclically shifted. If it is scaled, the signal is multiplied by some value. And if the image is translated, the signal is unaffected. We can therefore compensate for rotation with a simple search, and for scaling by using the correlation coefficient for the detection metric. False positive results on a database of 10,000 images are reported. Robustness results on a database of 2,000 images are described. It is shown that the watermark is robust to rotation, scale and translation. In addition, the algorithm shows resistance to cropping.