Use of synchronisation patterns to estimate geometric distortions in digital watermarking

Watermarking can be modeled as a transmission through a steganographic channel. Most of the channel studied up to now in the literature were additive or substitutive channels where the noise modifies the data values. But other modifications occur frequently during the watermark life, namely geometric distortions: images may be cropped, scaled and even non-linearly distorted by digital/analog conversion or by an attacker. We model here the 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 the jitter attack, and describe an optimal estimation algorithm, named Forward-Backward.