A Constructive and Unifying Framework for Zero-Bit Watermarking

Abstract

Abstract-In the watermark detection scenario, also known as zero-bit watermarking, a watermark, carrying no hidden message, is inserted in a piece of content. The watermark detector checks for the presence of this particular weak signal in received contents. The article looks at this problem from a classical detection theory point of view, but with side information enabled at the embedding side. This means that the watermark signal is a function of the host content. Our study is twofold. The first step is to design the best embedding function for a given detection function, and the best detection function for a given embedding function. This yields two conditions, which are mixed into one 'fundamental' partial differential equation. It appears that many famous watermarking schemes are indeed solution to this 'fundamental' equation. This study thus gives birth to a constructive framework unifying solutions, so far perceived as very different.

Hermite polynomials as provably good functions to watermark white gaussian hosts

“…Last but not least: the higher the 'original' efficiency η(1, 0) = , the less robust is the scheme in the sense that η(γ, σZ )/η(1, 0) = (1 + σ 2 Z ) −η(1,0) decreases faster with the strength of the attack. We have found this feature in other watermarking schemes [7].…”

“…One can show [7] that this detection function is centered under hypothesis H0, as required in subsection 2.2, provided E{ w(s) 2 |H0} < +∞. The constant kt enforces that Var{t(r)|H0} = 1:…”

“…This conference paper is an extract of [7], where we only look at white gaussian hosts. This gives birth to polynomials solutions known as Hermite polynomial, whose extension is the JANIS watermarking scheme, invented heuristically some years ago.…”

Towards robust and secure watermarking

“…This is mostly due to the lack of stationarity and to the wide variety of distribution from a content to another. From the theoretical viewpoint, [8] proposes a unifying theory of zero-bit watermarking, but its main drawback is its lack of universality: the embedder and detector must know the statistical distribution of the host content. More recently, Comesaña et al have found the optimum scheme under the restrictive assumption that the host distribution belongs to the white and Gaussian family [6], whatever its variance.…”

Efficient blind decoders for additive spread spectrum embedding based data hiding

“…To our knowledge, the majority of the current literature has been focused on watermark detection and many algorithms have been proposed. For instance, in [23] a watermark based on the host content is added and the detection is accomplished with the Neyman-Pearson criterion. In [24], a new perceptual masking is proposed and a correlation based detector is studied for watermark detection.…”