Fast and accurate computation of Racah moment invariants for image classification

Benouini, Rachid; Batioua, Imad; Zenkouar, Khalid; Zahi, Azeddine; Fadili, Hakim El; Qjidaa, Hassan

doi:10.1016/j.patcog.2019.02.014

Cited by 33 publications

(16 citation statements)

References 24 publications

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“…It is important to point out that some recent methods for computing the invariant moments [ 3 , 17 , 20 , 37 , 39 ] are numerically unstable for large-size images (>1024 × 1024).For this reason, no comparison with these works is carried out. In addition, accelerating and stabilizing the computation of the previously mentioned methods might be a potentially interesting direction for further research.…”

Section: Resultsmentioning

confidence: 99%

“…Generally, the derivation process of the orthogonal moment invariants relies on the algebraic relation between the orthogonal moments and the geometric ones, to express the orthogonal moment invariants as a linear combination of geometric moment invariants. [ 3 , 14 , 18 , 20 , 30 ]. However, this process is limited by two major drawbacks: (i) the numerical instability due to gamma and factorial functions involved in the computation of the orthogonal moment invariants, and (ii) the high computational cost [ 3 ].…”

Section: Introductionmentioning

confidence: 99%

“…[ 3 , 14 , 18 , 20 , 30 ]. However, this process is limited by two major drawbacks: (i) the numerical instability due to gamma and factorial functions involved in the computation of the orthogonal moment invariants, and (ii) the high computational cost [ 3 ]. To overcome these problems when computing Racah moment invariants (RMIs), a fast and accurate computation method is proposed in [ 3 ].…”

Section: Introductionmentioning

confidence: 99%

“…This method is based on the use of recursive formulas of certain factors involved in RMIs computation. However, this method and others presented in [ 3 , 17 , 20 , 39 ] are not suitable for computing the invariant moments of large-size images (≥1024 × 1024), since these methods involve the use of certain terms depending on gamma and factorial functions when computing the image moment invariants. Motivated by overcoming these problems, a fast and numerically stable computation of large-size image moment invariants is proposed in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, HMIs execution time is considerably reduced by using matrix multiplications and recursive formulas. It is important to note that the fast computation of moment invariants is relevant for real-time applications [ 3 ].…”

Section: Introductionmentioning

confidence: 99%

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

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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.

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