Image analysis by Meixner moments and a digital filter

In this paper, we propose a new method for the rapid calculation of Meixner's discrete orthogonal moments and its inverses. In this method, we have used the notion of digital filters based on the Z transform both to accelerate the computation time of Meixner and to reduce the reconstruction error of the images. To guarantee the numerical stability and robustness with respect to the noise, we propose two algorithms that treat the images as a set of blocks where each block will be treated independently. In fact, through the first algorithm, the moments of Meixner are computed from a set of geometric blocks of fixed size. On the other hand, in the second algorithm, the images are represented by a slice set where each slice contains several homogeneous blocks of different sizes. The moments of Meixner, in this case, are calculated from each block in each slice. The application of these two algorithms allowed us to deduce a significant reduction in processed information and image space, that permits the use of Meixner moments of low order for a better description of the fine details of the images. The performances of the proposed method are demonstrated through several simulations on different image bases.