Multimedia Tools and Applications

, Volume 78, Issue 22, pp 31245–31265 | Cite as

Fast computation of inverse Meixner moments transform using Clenshaw’s formula

  • Hicham KarmouniEmail author
  • Tarik Jahid
  • Abdeslam Hmimid
  • Mhamed Sayyouri
  • Hassan Qjidaa


Orthogonal moments are recognized as useful tools for object representation and image analysis. It was shown that they have better image representation capability than the continuous orthogonal moments. One problem concerning the use of moments is the high computational cost, which may limit where the online computation is required. In this paper, we propose a recursive method based on Clenshaw’s recurrence formula that can be implemented to transform kernels of Meixner moments and its inverse for fast computation. There is no need for the proposed method to compute the Meixner polynomial values of various orders on various data points, where the computational complexity is reduced. Experimental results show that the proposed method performs better than the existing methods in term of computation speed and the effectiveness of image reconstruction capability in both noise-free and noisy conditions.


Clenshaw’s formula Meixner moments Fast computation Inverse transform, image reconstruction 



The authors would like to thank the anonymous referees whose careful reviews and detailed comments helped improve the readability of this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.CED-ST, STIC, Laboratory of Electronic Signals and Systems of Information LESSI, Faculty of Science Dhar El MahrezUniversity Sidi Mohamed Ben AbdellahFezMorocco
  2. 2.Engineering, Systems and Applications Laboratory, National School of Applied SciencesSidi Mohamed Ben Abdellah UniversityFezMorocco

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