Performance enhancement of high order Hahn polynomials using multithreading

Abstract

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 various values of DHaPs parameters, sizes, and different values of threads. In comparison to the unthreaded situation, the results demonstrate an improvement in the processing time which increases as the polynomial size increases, reaching its maximum of 5.8 in the case of polynomial size and order of 8000 × 8000 (matrix size). Furthermore, the trend of continuously raising the number of threads to enhance performance is inconsistent and becomes invalid at some point when the performance improvement falls below the maximum. The number of threads that achieve the highest improvement differs according to the size, being in the range of 8 to 16 threads in 1000 × 1000 matrix size, whereas at 8000 × 8000 case it ranges from 32 to 160 threads.

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“…The variables F, G, and H are given in Table 3. It should be noted that after computing the coefficient using (23) at n = x − 1, Equation ( 24) can be applied directly to compute coefficients at n = x.…”

“…Moreover, recent developments in algorithms for computing Krawtchouk polynomial coefficients have been proposed to address instability issues associated with the computation of high-order polynomials [19,22,23]. One such approach involves the use of the three-term recurrence relation, which expresses each coefficient of the Krawtchouk polynomial in terms of the previous two coefficients.…”

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