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Performance enhancement of high order Hahn polynomials using multithreading.

Basheera M Mahmmod1, Wameedh Nazar Flayyih1, Zainab Hassan Fakhri1

  • 1Department of Computer Engineering, University of Baghdad, Baghdad, Iraq.

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|October 25, 2023
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Summary
This summary is machine-generated.

This study introduces a fast multithreaded approach for computing high-order discrete Hahn polynomials (DHaPs), crucial for image processing. The method significantly reduces computation time, especially for large polynomial sizes, improving efficiency in computer vision applications.

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Area of Science:

  • Computer Vision
  • Numerical Analysis
  • Computational Mathematics

Background:

  • Orthogonal polynomials, including discrete Hahn polynomials (DHaPs), are vital in image processing and computer vision for tasks like compression and feature extraction.
  • High-order calculations of DHaPs can lead to numerical instability, posing a challenge for practical applications.

Purpose of the Study:

  • To propose a fast, multithreaded approach for computing high-order discrete Hahn polynomials.
  • To address the numerical instability issues associated with high-order DHaPs.
  • To optimize the computational performance of DHaPs using parallel processing.

Main Methods:

  • Leveraging multithreading to parallelize the computation of Hahn polynomial coefficients.
  • Implementing a distribution method for balanced processing load across threads.
  • Testing the proposed method with various DHaPs parameters, matrix sizes, and thread counts.

Main Results:

  • Demonstrated significant improvement in processing time compared to unthreaded computations, with gains increasing proportionally to polynomial size.
  • Achieved a maximum speedup factor of 5.8 for polynomial sizes and orders of 8000x8000.
  • Identified an optimal range of threads for maximum performance, noting that excessive threads can lead to diminishing returns or performance degradation.

Conclusions:

  • The proposed multithreaded approach offers an efficient solution for computing high-order discrete Hahn polynomials.
  • Parallel processing effectively mitigates computational bottlenecks and improves performance in image processing and computer vision tasks.
  • Careful consideration of thread count is necessary to maximize performance benefits, as scalability is not linear beyond a certain point.