A fast computation of charlier moments for binary and gray-scale images

The discrete orthogonal moments have been shown that they represent the image better than the continuous orthogonal moments. A problem concerning the use of moments as descriptors is the highest cost of calculation. In this paper, we present the reconstruction of binary and gray-scale images by Charlier moments. The calculations of these discrete orthogonal polynomials discussed in this task, including the recurrence relation with respect to variable x and order n, we propose an efficient computation of Charlier moments for binary and gray-scale images by using image block representation IBR for binary image and PIBR for gray-scale image. The moments of image can be obtained from the moments of all blocks, thus, it can accelerate the computational efficiency since the number of blocks is less than the size of the image. Finally, the performances of Charlier moments in describing images were measured in terms of the image reconstruction error.