0565460 - ÚTIA 2023 RIV US eng J - Journal Article
Mahmmod, B. M. - Abdulhussain, S. H. - Suk, Tomáš - Hussain, A.
Fast Computation of Hahn Polynomials for High Order Moments.
IEEE Access. Roč. 10, č. 1 (2022), s. 48719-48732. ISSN 2169-3536. E-ISSN 2169-3536
R&D Projects: GA ČR GA21-03921S
Grant - others:AV ČR(CZ) StrategieAV21/1
Institutional support: RVO:67985556
Keywords : Hahn polynomials * Hahn moments * propagation error * numerical error
OECD category: Electrical and electronic engineering
Impact factor: 3.9, year: 2022
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2022/ZOI/suk-0565460.pdf https://ieeexplore.ieee.org/document/9764684

Discrete Hahn polynomials (DHPs) and their moments are considered to be one of the efficient orthogonal moments and they are applied in various scientific areas such as image processing and feature extraction. Commonly, DHPs are used as object representation, however, they suffer from the problem of numerical instability when the moment order becomes large. In this paper, an operative method to compute the Hahn orthogonal basis is proposed and applied to high orders. This paper developed a new mathematical model for computing the initial value of the DHP and for different values of DHP parameters (alpha and beta). In addition, the proposed method is composed of two recurrence algorithms with an adaptive threshold to stabilize the generation of the DHP coefficients. It is compared with state-of-the-art algorithms in terms of computational cost and the maximum size that can be correctly generated. The experimental results show that the proposed algorithm performs better in both parameters for wide ranges of parameter values alpha and beta, and polynomial sizes.
Permanent Link: https://hdl.handle.net/11104/0337913