An image rectification scheme and its applications in RST invariant digital image watermarking

This paper presents an image rectification scheme that can be used by any image watermarking algorithm to provide robustness against rotation, scaling and translation (RST) transformations. Rotation and scaling transformations in the spatial domain result in cyclically translational shifts in the log-polar mapping (LPM) of the magnitude of the Fourier transform spectrum of an image. We cut a small block from the LPM domain as a matching template. A new filtering method is proposed to compute the cross-correlation between this template and the magnitude of the LPM of the image having undergone RST transformations to detect the rotation and scaling parameters. We employ the same strategy in the spatial domain to detect the translational parameters in the spatial domain. The scheme can also be used to detect image flipping. The cost of the templates is low and the templates can even be compressed. The detection accuracy for rotation, scaling and translation is also presented. We compare the matching results for the different filters and their performance by the three criteria: signal-to-noise ratio (SNR), peak-to-correlation energy (PCE), and Horner efficiency. We demonstrate that our phase-only filtering method is the only one that can be used in the LPM domain. We also introduce three applications for this rectification scheme and give their experimental results.