Image analysis using new set of separable two-dimensional discrete orthogonal moments based on Racah polynomials

Batioua, Imad; Benouini, Rachid; Zenkouar, Khalid; Fadili, Hakim El

doi:10.1186/s13640-017-0172-7

Cited by 21 publications

(9 citation statements)

References 27 publications

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“…In contrast, the classical strategy is to use the tensor product of two same orthogonal polynomials. This new definition is more flexible and may have better performance in certain situations [155][156][157][158].…”

Section: Definition Extensionmentioning

confidence: 99%

A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

Qi,

Zhang,

Wang

et al. 2021

Preprint

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Image representation is an important topic in computer vision and pattern recognition. It plays a fundamental role in a range of applications towards understanding visual contents. Moment-based image representation has been reported to be effective in satisfying the core conditions of semantic description due to its beneficial mathematical properties, especially geometric invariance and independence. This paper presents a comprehensive survey of the orthogonal moments for image representation, covering recent advances in fast/accurate calculation, robustness/invariance optimization, and definition extension. We also create a software package for a variety of widely-used orthogonal moments and evaluate such methods in a same base. The presented theory analysis, software implementation, and evaluation results can support the community, particularly in developing novel techniques and promoting realworld applications.

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Section: Definition Extensionmentioning

confidence: 99%

A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

Qi,

Zhang,

Wang

et al. 2021

Preprint

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“…Lakhili et al applied neural network on 3D Racah moments computed in Cartesian coordinates in [33]. In [34], Batioua et al combine Racah polynomials with other types.…”

Section: Introductionmentioning

confidence: 99%

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

Mahmmod,

Abdulhussain,

Suk

et al. 2023

IEEE Access

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Discrete Racah polynomials (DRPs) are highly efficient orthogonal polynomials and used in various scientific fields for signal representation. They find applications in disciplines like image processing and computer vision. Racah polynomials were originally introduced by Wilson and later modified by Zhu to be orthogonal on a discrete set of samples. However, when the degree of the polynomial is high, it encounters numerical instability issues. In this paper, we propose a novel algorithm called Improved Stabilization (ImSt) for computing DRP coefficients. The algorithm partitions the DRP plane into asymmetric parts based on the polynomial size and DRP parameters. We have optimized the use of stabilizing conditions in these partitions. To compute the initial values, we employ the logarithmic gamma function along with a new formula. This combination enables us to compute the initial values efficiently for a wide range of DRP parameter values and large polynomial sizes. Additionally, we have derived a symmetry relation for the case when the Racah polynomial parameters are zero (a = 0, α = 0, β = 0). This symmetry makes the Racah polynomials symmetric about the main diagonal, and we present a different algorithm for this specific scenario. We have demonstrated that the ImSt algorithm works for a broader range of parameters and higher degrees compared to existing algorithms. A comprehensive comparison between ImSt and the existing algorithms has been conducted, considering the maximum polynomial degree, computation time, restriction error analysis, and reconstruction error. The results of the comparison indicate that ImSt outperforms the existing algorithms for various values of Racah polynomial parameters.

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“…Image moments and moment functions have been extensively applied in the domains of image analysis [2–8], pattern recognition [9–13, 67–69], image retrieval [14–17], medical image analysis [18–21] and image watermarking [22–25]. This is due to their attractive properties and interpretations, such as the compact representation of the image content, the robustness to noise and the invariance against geometric deformations 1.…”

Section: Introductionmentioning

confidence: 99%

Fractional‐order generalized Laguerre moments and moment invariants for grey‐scale image analysis

Benouini

Batioua

Zenkouar

et al. 2020

IET Image Processing

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Here, a new set of fractional-order moments, named fractional-order generalized Laguerre moments (FGLM), is introduced. These proposed moments are defined on the Cartesian coordinate system and their basis functions are represented by the fractional-order generalized Laguerre polynomials. Contrary to the classical Chebyshev, Legendre and Gegenbauer moments, which provide only global feature, our proposed FGLM have the ability to extract both global and local features. Moreover, a new set of rotation, scale and translation invariants of the FGLM, is derived and introduced for image classification and invariant pattern recognition. Just as important, we have presented a systematic parameter selection method for finding the optimal fractional parameter values with respect to pattern recognition applications. Finally, several recursive methods for reducing the computation time of our proposed invariants are also provided in this study. Therefore, to demonstrate the performance of the introduced fractional-order moments and moment invariants, a number of experimental analysis are performed in terms of global and local features extraction, robustness to noise, invariance to geometric deformations, object recognition and computational speed. The presented theoretical and experimental results clearly show that the proposed fractional-order moments and their corresponding invariants could be extremely useful in the field of image analysis.

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Image analysis using new set of separable two-dimensional discrete orthogonal moments based on Racah polynomials

Cited by 21 publications

References 27 publications

A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

Fractional‐order generalized Laguerre moments and moment invariants for grey‐scale image analysis

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