Some theoretical bounds on the capacity of watermarking channels with geometrical distortions

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 compute the expression of capacity for a channel with shift and for a channel with jitter. We also compare the theoretic bounds obtained to the rate achieved by some watermarking methods