Image analysis by Meixner moments and a digital filter Tarik Jahid 1 & Abdeslam Hmimid 1 & Hicham Karmouni 1 & Mhamed Sayyouri 2 & Hassan Qjidaa 1 & Abdellah Rezzouk 3 Received: 3 April 2017 /Revised: 17 September 2017 /Accepted: 30 October 2017 # Springer Science+Business Media, LLC, part of Springer Nature 2017 Abstract 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. Multimed Tools Appl https://doi.org/10.1007/s11042-017-5371-9 * Tarik Jahid jahidtarik@gmail.com Abdeslam Hmimid abdeslam.hmimid@usmba.ac.ma Hicham Karmouni hicham.karmouni@usmba.ac.ma Mhamed Sayyouri mhamed.sayyouri@usmba.ac.ma Hassan Qjidaa qjidah@yahoo.fr Abdellah Rezzouk rezzouk@yahoo.fr 1 CED-ST, STIC, Laboratory of Electronic Signals and Systems of Information LESSI, Faculty of Science Dhar El Mahrez, University Sidi Mohamed Ben Abdellah- Fez, Fez, Morocco 2 Laboratoire des Sciences de l’Ingénieur pour l’Energie, Ecole Nationale des Sciences Appliquées d’El Jadida, Université Chouaïb Doukkali, BP 1166, 24004 El Jadida Plateau, Morocco 3 CED-ST, SMPI, Laboratory of Solid Physics LPS, Faculty of Science Dhar El Mahrez, University Sidi Mohamed Ben Abdellah- Fez, Fez, Morocco