A Rectification Scheme for RST Invariant Image Watermarking

Rotation, Shifting, and Translation (RST) invariant image watermarking is a very important research topic. In this letter, we report a new filtering method in the log-polar mapping (LPM), and a novel rectification method that can be used in any RST invariant image watermarking algorithms. We get a log-polar mapping of an image by calculating the Fourier transform of the image and resampling the Fourier transform magnitudes into log-polar coordinates. Rotation and scaling in the spatial domain result in translational shifts in the LPM domain. Translation in the spatial domain has no effect in the LPM domain. We cut a small block as a template from the LPM domain during watermark embedding process, then calculate the cross-correlation between this template and the LPM spectrum of the watermarked image by using the new filtering method. As we will discuss later, the new filtering method is the only choice. From the location of its peak value, we can get the shift parameters for rotation and scaling. Thus, we can obtain the rotation and scaling parameters from the relationship between the two domains. We employ the same strategy to the image in the spatial domain and get the translational parameters. After obtaining RST parameters, we re-synchronize the transformed image for the watermark detection.