New Algorithm for Large-Sized 2D and 3D Image Reconstruction using Higher-Order Hahn Moments

Discrete orthogonal moments such as Hahn moments are powerful tools for image analysis, especially for the reconstruction of 2D and 3D images. Several methods have been proposed to calculate Hahn moments, but the computation of the kernel polynomials of these latter is limited by the problem of the numerical fluctuation of higher-order polynomial values (overflow). In this paper, we propose an efficient method for the exact computation of Hahn polynomials using the modified Gram–Schmidt orthonormalization processes. This method greatly reduces the propagation of numerical errors involved in the computation of Hahn polynomials by the conventional methods. The method thus proposed is used for reconstructing large-sized 2D and 3D images. A comparison with other kinds of discrete orthogonal moments is also established in order to validate the stability and superiority of the proposed method when reconstructing large-sized 2D and 3D images. The results obtained show the reliability and effectiveness of the proposed method in terms of computation accuracy and numerical stability of high-order Hahn moments.