Image analysis using separable discrete moments of Charlier-Tchebichef
Mhamed Sayyouri, Abdeslam Hmimid, Hassan Qjidaa · 2014
In this paper, we propose a new set of separable two- dimensional discrete orthogonal moments called Charlier- Tchebichef's moments. This set of moments is based on the bivariate discrete orthogonal polynomials defined from the product of Charlier and Tchebichef discrete orthogonal polynomials with one variable. We also present an approach for fast computation of Charlier- Tchebichef's moments by using the image slice representation. In this approach the image is decomposes into series of non-overlapped binary slices and each slice is described by a number of homogenous rectangular blocks. Once the image is partitioned into slices and blocks, the computation of Charlier-Tchebichef's moments can be accelerated, as the moments can be computed from the blocks of each slice. A novel set of Charlier-Tchebichef invariant moments is also presented. These invariant moments are derived algebraically from the geometric invariant moments and their computation is accelerated using an image representation scheme. The presented approaches are tested in several well known computer vision datasets including computational time, image reconstruction, moment's invariability and classification of objects. The performance of these invariant moments used as pattern features for a pattern classification is compared with Tchebichef-Krawtchouk, Tchebichef-Hahn and Krawtchouk-Hahn invariant moments Keywords—Charlier-Tchebichef's invariant moments, Image reconstruction, Pattern recognition, Classification.