Estimation of geometric distortions in digital watermarking

Watermarking can be modeled as transmission through a steganographic channel. Up to now, most of the channels studied in the literature have been additive or substitutive channels where noise modifies the data values. However, other modifications occur frequently during the life of a watermark, namely geometric distortions: images may be cropped, scaled and even non-linearly distorted by digital/analog conversion or by an attacker. We model geometric transformations by a geometric channel and introduce a random variable, the index variable, to model geometric deformations. We propose to use a synchronisation pattern to estimate geometric distortions caused by jitter attack, and describe two estimation algorithms (Viterbi and forward-backward).