Fast computation of inverse Meixner moments transform using Clenshaw’s formula
- 14 Downloads
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.
KeywordsClenshaw’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.
- 7.Jahid T, Hmimid A, Karmouni H, Sayyouri M, Qjidaa H, Rezzouk A (2017) Image analysis by Meixner moments and a digital filter. Multimed Tools Appl:1–21Google Scholar
- 8.Jahid T, Karmouni H, Sayyouri M et al (2018) Fast Algorithm of 3D Discrete Image Orthogonal Moments Computation Based on 3D Cuboid. Journal of Mathematical Imaging and Vision:1–21Google Scholar
- 10.Karmouni H, Jahid T, Sayyouri M et al (2017) Fast 3D image reconstruction by cuboids and 3D Charlier’s moments. J Real-Time Image Proc 2019:1–17Google Scholar
- 13.Koekoek R, Lesky PA, Swarttouw RF. (2010). Hypergeometric orthogonal polynomials and their qanalogues. Springer Monographs in Mathematics, Library of Congress Control Number, 2010923797Google Scholar
- 16.Lan X, Ye M, Shao R, Zhong B, Jain DK, Zhou H (2019) Online Non-negative Multi-modality Feature Template Learning for RGB-assisted Infrared Tracking. IEEE AccessGoogle Scholar
- 17.Lan X, Ye M, Shao R, Zhong B, Yuen PC, Zhou H (2019) Learning Modality-Consistency Feature Templates: A Robust RGB-Infrared Tracking System. IEEE Trans Ind ElectronGoogle Scholar
- 18.Lan X, Ye M, Zhang S, Zhou H, Yuen PC (2018) Modality-correlation-aware sparse representation for RGB-infrared object tracking. Pattern Recogn LettGoogle Scholar
- 25.Sayyouri M, Hmimd A, Qjidaa H (2012) A fast computation of Charlier moments for binary and gray-scale images. Information Science and Technology Colloquium (CIST), Fez, pp 101–105Google Scholar
- 26.Sayyouri M, Hmimd A, Qjidaa H (2012) A Fast Computation of Hahn Moments for Binary and Gray-Scale Images. IEEE, International Conference on Complex Systems ICCS’12, Agadir, pp 1–6Google Scholar