Optimal decoding for watermarks subject to geometrical attacks

摘要

Watermarking can be modeled as a transmission through a steganographic channel. Most of the channels studied up to now in the literature were additive or substitutive channels where the noise modifies the data value. But other modifications may occur, as geometric distortions: images may be cropped, scaled, non-linearly distorted, etc. We model such transformations by a geometric channel, where the noise modifies the geometry of the image rather than the data values. We study the jitter channel which copies and deletes randomly some lines of the image. We use a Markov chain to model the channel, and propose an algorithm to enhance the detection of a watermark embedded by a spread-spectrum technique subject to a jitter attack.