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.
Keywords Digital image watermarking - Log-polar mapping - Phase-only filtering - RST invariant