Fast and efficient recursive algorithm of Meixner polynomials

Meixner polynomials (MNPs) and their moments are considered significant feature extraction tools because of their salient representation in signal processing and computer vision. However, the existing recurrence algorithm of MNPs exhibits numerical instabilities of coefficients for high-order polyno...

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Vydané v:Journal of real-time image processing Ročník 18; číslo 6; s. 2225 - 2237
Hlavní autori: Abdulhussain, Sadiq H., Mahmmod, Basheera M.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2021
Springer Nature B.V
Predmet:
Algorithms
Coefficients
Computational efficiency
Computer Graphics
Computer Science
Computer vision
Computing costs
Coordinate transformations
Error analysis
Feature extraction
Image Processing and Computer Vision
Multimedia Information Systems
Original Research Paper
Pattern Recognition
Polynomials
Propagation
Signal,Image and Speech Processing
ISSN:1861-8200, 1861-8219
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Popis
Shrnutí:Meixner polynomials (MNPs) and their moments are considered significant feature extraction tools because of their salient representation in signal processing and computer vision. However, the existing recurrence algorithm of MNPs exhibits numerical instabilities of coefficients for high-order polynomials. This paper proposed a new recurrence algorithm to compute the coefficients of MNPs for high-order polynomials. The proposed algorithm is based on a derived identity for MNPs that reduces the number of the utilized recurrence times and the computed number of MNPs coefficients. To minimize the numerical errors, a new form of the recurrence algorithm is presented. The proposed algorithm computes ∼ 50% of the MNP coefficients. A comparison with different state-of-the-art algorithms is performed to evaluate the performance of the proposed recurrence algorithm in terms of computational cost and reconstruction error. In addition, an investigation is performed to find the maximum generated size. The results show that the proposed algorithm remarkably reduces the computational cost and increases the generated size of the MNPs. The proposed algorithm shows an average improvement of ∼ 77% in terms of computation cost. In addition, the proposed algorithm exhibits an improvement of ∼ 1269% in terms of generated size.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1861-8200
1861-8219
DOI:10.1007/s11554-021-01093-z