Nowadays, nobody doubts about the huge economical benefits the watermarking solutions will one day bring. The paper
is devoted to the theoretical evaluation of the watermarking capacity, i.e. devoted to find out with mathematical rigour
the maximum amount of information which can be inserted into the DWT of natural video, for prescribed constraints of
transparency and robustness. The starting point is the accurate statistical model for the watermarking attacks the authors
already reported. In this paper, in addition to the classical Shannon solutions, the capacity is evaluated by two
approaches: (1) a method developed in order to increase speed and precision for watermarking evaluations and (2) the
general Blahut-Arimoto algorithm, adapted by Justin Dauwels for the discrete case. The experiments are run on a video
corpus of 10 video sequences of about 25 minutes each.
The main issue this paper addresses is to obtain the information sources characterising the video sequences represented in
DWT domain and to discuss their relevance for practical applications. From the statistical point of view, this means to
establish whether the DWT coefficients can be approximated by random variables and, if so, to compute the
corresponding probability density functions (pdf). The corpus considered in experiments is composed of 10 video
sequences, belonging to different movies, each of them about 25 minutes long, DivX coded at a very low rate.
Regardless the final targeted application (compression, watermarking, texture analysis, indexation, ...), image/video modelling in the DCT domain is generally approached by tests of concordance with some well known pdfs (like Gaussian, generalised Gaussian, Laplace, Rayleigh ...). Instead of forcing the images/videos to stick to such theoretical models, our study aims at estimating the true pdf characterising their behaviour. In this respect, we considered three intensively used ways of applying DCT, namely on whole frames, on 4x4 blocks, and on 8x8 blocks. In each case, we first prove that a law modelling the corresponding coefficients exists. Then, we estimate this law by Gaussian mixtures and finally we identify the generality of such model with respect to the data on which it was computed and to the estimation method it relies on.
Defined as the maximum amount of information which can be inserted in an original media for prescribed transparency
and robustness, watermarking capacity has been a challenging research topic in the last years. The present paper allows
several current limitations in this respect to be overcame. As the capacity strongly depends on the attack statistical
behaviour, the first part of our paper is devoted to their in-depth investigation. By advancing an original statistical
approach, it is pointed out that we may speak about probability density functions modelling several types of attacks
(filtering, small rotation, StirMark). Then, these new accurate models are considered as the starting points in the
probability evaluation. The experimental study is based on the watermarking methods inserting the mark in the hierarchy
of the coefficients corresponding to three types of wavelets transforms, namely the (2,2), (4,4) and (9,7). The video
corpus consisted in 10 video sequences of about 25 minutes each, with heterogeneous content.
Video watermarking enforces property right for digital video: a mark is transparently embedded into original data. The
true owner is identified by detecting this mark. The robust watermarking techniques allow the mark detection even when
the protected video is attacked. Generally, the better the transparency and robustness, the smaller the mark size. We
evaluate the maximum theoretical quantity of information which can be inserted into the 2D-DWT coefficient hierarchy,
for prescribed transparency and robustness constraints. In order to ensure the accuracy in capacity evaluation, our paper
do not relay on any assumption concerning the noise model. Instead, it carries out an in-depth analysis on the statistical
behaviour of the real life attacks (StirMark, Gaussian filtering, sharpening, rotation). The experiments are performed on
10 low rate video sequences of 30 minutes each and compares among them three types of bi-orthogonal DWT, namely
the (2,2), (4,4), and (9,7). The overall results (theoretical and experimental) are discussed not only for conventional
watermarking applications, but for hidden channel, indexing and retrieval applications, as well.
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