2D and 3D image localization,compression and reconstruction using new hybrid moments

In this article, we will present a new set of hybrid polynomials and their corresponding moments, with a view to using them for the localization, compression and reconstruction of 2D and 3D images. These polynomials are formed from the Hahn and Krawtchouk polynomials. The process of calculating these is successfully stabilized using the modified recurrence relations with respect to the n order, the variable x and the symmetry property. The hybrid polynomial generation process is carried out in two forms: the first form contains the separable discrete orthogonal polynomials of Krawtchouk–Hahn (DKHP) and Hahn–Krawtchouk (DHKP). The latter are generated as the product of the discrete orthogonal Hahn and Krawtchouk polynomials, while the second form is the square equivalent of the first form, it consists of discrete squared Krawtchouk–Hahn polynomials (SKHP) and discrete polynomials of Hahn–Krawtchouk squared (SHKP). The experimental results clearly show the efficiency of hybrid moments based on hybrid polynomials in terms of localization property and computation time of 2D and 3D images compared to other types of moments; on the other hand, encouraging results have also been shown in terms of reconstruction quality and compression despite the superiority of classical polynomials.