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On Computational Aspects of Krawtchouk Polynomials for High Orders

Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we prese...

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Autores principales: Mahmmod, Basheera M., Abdul-Hadi, Alaa M., Abdulhussain, Sadiq H., Hussien, Aseel
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8321075/
https://www.ncbi.nlm.nih.gov/pubmed/34460696
http://dx.doi.org/10.3390/jimaging6080081
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author Mahmmod, Basheera M.
Abdul-Hadi, Alaa M.
Abdulhussain, Sadiq H.
Hussien, Aseel
author_facet Mahmmod, Basheera M.
Abdul-Hadi, Alaa M.
Abdulhussain, Sadiq H.
Hussien, Aseel
author_sort Mahmmod, Basheera M.
collection PubMed
description Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes approximately 12.5% of the polynomial coefficients, and then symmetry relations are employed to compute the rest of the polynomial coefficients. The proposed method is evaluated against existing methods in terms of computational cost and maximum size can be generated. In addition, a reconstruction error analysis for image is performed using the proposed method for large signal sizes. The evaluation shows that the proposed method outperforms other existing methods.
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spelling pubmed-83210752021-08-26 On Computational Aspects of Krawtchouk Polynomials for High Orders Mahmmod, Basheera M. Abdul-Hadi, Alaa M. Abdulhussain, Sadiq H. Hussien, Aseel J Imaging Article Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes approximately 12.5% of the polynomial coefficients, and then symmetry relations are employed to compute the rest of the polynomial coefficients. The proposed method is evaluated against existing methods in terms of computational cost and maximum size can be generated. In addition, a reconstruction error analysis for image is performed using the proposed method for large signal sizes. The evaluation shows that the proposed method outperforms other existing methods. MDPI 2020-08-13 /pmc/articles/PMC8321075/ /pubmed/34460696 http://dx.doi.org/10.3390/jimaging6080081 Text en © 2020 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Mahmmod, Basheera M.
Abdul-Hadi, Alaa M.
Abdulhussain, Sadiq H.
Hussien, Aseel
On Computational Aspects of Krawtchouk Polynomials for High Orders
title On Computational Aspects of Krawtchouk Polynomials for High Orders
title_full On Computational Aspects of Krawtchouk Polynomials for High Orders
title_fullStr On Computational Aspects of Krawtchouk Polynomials for High Orders
title_full_unstemmed On Computational Aspects of Krawtchouk Polynomials for High Orders
title_short On Computational Aspects of Krawtchouk Polynomials for High Orders
title_sort on computational aspects of krawtchouk polynomials for high orders
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8321075/
https://www.ncbi.nlm.nih.gov/pubmed/34460696
http://dx.doi.org/10.3390/jimaging6080081
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