Probability density function estimation for video in the DCT domain

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 4 × 4 blocks, and on 8 × 8 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 relaies on.