Fast computation of Charlier moments and its inverses using Clenshaw’s recurrence formula for image analysis

Jahid, Tarik; Karmouni, Hicham; Hmimid, Abdeslam; Sayyouri, Mhamed; Qjidaa, Hassan

doi:10.1007/s11042-018-6757-z

Search citation statements

Order By: Relevance

Paper Sections

Select...

) Charlier Polynomials1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2022

Publication Types

Select...

Article5

Book1

Relationship

Self Cite1

Independent5

Authors

Journals

Cited by 9 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where w c (x; p) and ρ c (n; p) are the weight function and squared norm of CHP C p n (x), respectively. The weight function is expressed as follows [136], [139]:…”

Section: ) Charlier Polynomialsmentioning

confidence: 99%

Vision-Based Human Detection Techniques: A Descriptive Review

Sumit

Mirjalili

2021

IEEE Access

View full text Add to dashboard Cite

“…where w c (x; p) and ρ c (n; p) are the weight function and squared norm of CHP C p n (x), respectively. The weight function is expressed as follows [136], [139]:…”

Section: ) Charlier Polynomialsmentioning

confidence: 99%

Vision-Based Human Detection Techniques: A Descriptive Review

Sumit

Mirjalili

2021

IEEE Access

View full text Add to dashboard Cite

“…Applications of DOMs include signal and image reconstruction [8,9,50], image classification [3,16,20,39], face recognition [33], image watermarking [24,41,44], signal zero-watermarking [10], edge detection [35], image encryption [43], signal compression [11,2] and image compression [13,42]. The computation of DOMs involves the computation of kernel discrete orthogonal polynomials (DOPs) such as Tchebichef [27,28], Krawtchouk [45,47], Hahn [46,50], Meixner [12,21], Charlier [8,19,34], dual Hahn [20,48], Racah [49] and Shmaliy [26] polynomials.…”

Section: Introductionmentioning

confidence: 99%

Fast and stable computation of higher-order Hahn polynomials and Hahn moment invariants for signal and image analysis

Daoui

Karmouni

Sayyouri

et al. 2021

Multimed Tools Appl

Self Cite

View full text Add to dashboard Cite

This article presents, on the one hand, new algorithms for the fast and stable computation of discrete orthogonal Hahn polynomials of high order (HPs) based on the elimination of all gamma and factorial functions that cause the numerical fluctuations of HPs, and based on the use of appropriate stability conditions. On the other hand, a new method for the fast and numerically stable computation of Hahn moment invariants (HMIs) is also proposed. This method is mainly based on the use of new recursive relations of HPs and of matrix multiplications when calculating HMIs. To validate the efficiency of the algorithms proposed for the calculation of HPs, several signals and large images (≥4000 × 4000) are reconstructed by Hahn moments (HMs) up to the last order with a reconstruction error tending towards zero ( MSE ≃ 10 −10 ). The efficiency of the proposed method for calculating HMIs is demonstrated on large medical images (2048 × 2048) with a very low relative error ( RE ≃ 10 −10 ). Finally, comparisons with some recent work in the literature are provided.

show abstract