The 2D-DCT coefficient statistical behaviour: A comparative analysis on different types of image sequences

This paper presents a method designed to analyse the distribution of the 2D-DCT (bi-Dimensional Discrete Cosine Transform) coefficient hierarchy computed over three types of image sequences: colour video, grey-level X-ray CT (computerised tomography) images and computer simulated noise images. This method is a statistical approach which combines in a new way the following four tests: (1) the χ² (Chi-square) test on concordance between experimental data and a theoretical probability density function, (2) the ρ (Ro) test on correlation, (3) the Fisher F test on equality between two variances, and (4) the Student T test on equality between two means. Such an approach was compulsory so as to mathematically overcome the dependency existing among successive images in the considered sequences. The results obtained on natural sequences (either video or medical images) are compared to those corresponding to computer simulated sequences, interesting differences being pointed out and discussed. The overall results may play a central role in a large variety of image/video processing applications: compression, segmentation, retrieval, protection (e.g. cryptography and watermarking). For instance, we successfully applied them to the design of a new robust watermarking method for colour video.