Fast computation of Charlier moments and its inverses using Clenshaw's recurrence formula for image analysis

In this paper, we propose a new fast way to compute both the image Charlier moments and its inverses using Clenshaw's recurrence formula. Firstly, we present recursive polynomials of Charlier with respect to the order n and with respect to the variable x and then we define Clenshaw's recurrence formula to improve the consuming time of the proposed algorithm. So, to show the robustness of the proposed method, a comparative study with the classical method is carried out. In fact, the results of the simulations carried out on binary and gray-scale images show the effectiveness of the proposed method in terms of the calculation time of Charlier moments and in terms of image reconstruction capacity with respect to Krawtchouk moments.