Fast computation of inverse Meixner moments transform using Clenshaw's formula

Orthogonal moments are recognized as useful tools for object representation and image analysis. It was shown that they have better image representation capability than the continuous orthogonal moments. One problem concerning the use of moments is the high computational cost, which may limit where the online computation is required. In this paper, we propose a recursive method based on Clenshaw's recurrence formula that can be implemented to transform kernels of Meixner moments and its inverse for fast computation. There is no need for the proposed method to compute the Meixner polynomial values of various orders on various data points, where the computational complexity is reduced. Experimental results show that the proposed method performs better than the existing methods in term of computation speed and the effectiveness of image reconstruction capability in both noise-free and noisy conditions.