Preferred Language
Articles
/
1xYFBYcBVTCNdQwCMC3d
Reliable Recurrence Algorithm for High-Order Krawtchouk Polynomials

Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the initial value of the KP parameter. In addition, a new diagonal recurrence relation is introduced and used in the proposed algorithm. The diagonal recurrence algorithm was derived from the existing n direction and x direction recurrence algorithms. The diagonal and existing recurrence algorithms were subsequently exploited to compute the KP coefficients. First, the KP coefficients were computed for one partition after dividing the KP plane into four. To compute the KP coefficients in the other partitions, the symmetry relations were exploited. The performance evaluation of the proposed recurrence algorithm was determined through different comparisons which were carried out in state-of-the-art works in terms of reconstruction error, polynomial size, and computation cost. The obtained results indicate that the proposed algorithm is reliable and computes lesser coefficients when compared to the existing algorithms across wide ranges of parameter values of p and polynomial sizes N. The results also show that the improvement ratio of the computed coefficients ranges from 18.64% to 81.55% in comparison to the existing algorithms. Besides this, the proposed algorithm can generate polynomials of an order ∼8.5 times larger than those generated using state-of-the-art algorithms.

Scopus Clarivate Crossref
View Publication
Publication Date
Tue Jun 04 2024
Journal Name
Computation
High-Performance Krawtchouk Polynomials of High Order Based on Multithreading

Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parall

... Show More
View Publication
Scopus Clarivate Crossref
Publication Date
Thu Aug 13 2020
Journal Name
Journal Of Imaging
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 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 app

... Show More
View Publication Preview PDF
Scopus (28)
Crossref (27)
Scopus Clarivate Crossref
Publication Date
Sat Jan 01 2022
Journal Name
Ieee Access
Fast Computation of Hahn Polynomials for High Order Moments

View Publication
Scopus (36)
Crossref (36)
Scopus Clarivate Crossref
Publication Date
Mon Sep 11 2017
Journal Name
Journal Of Mathematical Imaging And Vision
Fast Recursive Computation of Krawtchouk Polynomials

View Publication
Scopus (40)
Crossref (41)
Scopus Clarivate Crossref
Publication Date
Sun Sep 11 2022
Journal Name
Concurrency And Computation: Practice And Experience
Fast and accurate computation of high‐order Tchebichef polynomials

View Publication
Scopus (20)
Crossref (20)
Scopus Clarivate Crossref
Publication Date
Wed Oct 25 2023
Journal Name
Plos One
Performance enhancement of high order Hahn polynomials using multithreading

Orthogonal polynomials and their moments have significant role in image processing and computer vision field. One of the polynomials is discrete Hahn polynomials (DHaPs), which are used for compression, and feature extraction. However, when the moment order becomes high, they suffer from numerical instability. This paper proposes a fast approach for computing the high orders DHaPs. This work takes advantage of the multithread for the calculation of Hahn polynomials coefficients. To take advantage of the available processing capabilities, independent calculations are divided among threads. The research provides a distribution method to achieve a more balanced processing burden among the threads. The proposed methods are tested for va

... Show More
View Publication
Scopus (1)
Crossref (1)
Scopus Clarivate Crossref
Publication Date
Thu Feb 01 2024
Journal Name
Ain Shams Engineering Journal
Performance enhancement of high degree Charlier polynomials using multithreaded algorithm

View Publication
Scopus Clarivate Crossref
Publication Date
Wed Jan 01 2020
Journal Name
Ieee Access
A New Separable Moments Based on Tchebichef-Krawtchouk Polynomials

View Publication
Scopus (18)
Crossref (17)
Scopus Clarivate Crossref
Publication Date
Mon Mar 01 2021
Journal Name
Iop Conference Series: Materials Science And Engineering
An efficient multistage CBIR based on Squared Krawtchouk-Tchebichef polynomials
Abstract<p>Image databases are increasing exponentially because of rapid developments in social networking and digital technologies. To search these databases, an efficient search technique is required. CBIR is considered one of these techniques. This paper presents a multistage CBIR to address the computational cost issues while reasonably preserving accuracy. In the presented work, the first stage acts as a filter that passes images to the next stage based on SKTP, which is the first time used in the CBIR domain. While in the second stage, LBP and Canny edge detectors are employed for extracting texture and shape features from the query image and images in the newly constructed database. The p</p> ... Show More
View Publication
Crossref (4)
Crossref
Publication Date
Thu Nov 15 2018
Journal Name
Journal Of Mathematical Imaging And Vision
A New Hybrid form of Krawtchouk and Tchebichef Polynomials: Design and Application

View Publication
Scopus (31)
Crossref (27)
Scopus Clarivate Crossref