New set of generalized legendre moment invariants for pattern recognition

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

doi:10.1016/j.patrec.2019.03.001

Cited by 21 publications

(7 citation statements)

References 20 publications

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Mentioning

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“…where q c1c2...cn are non-negative integers. Similar to (16), the properties of determinants allow us to consider only…”

Section: Relative Invariant Primitive To Ramentioning

confidence: 99%

“…The order of the RAGHM I is the highest order of Gaussian-Hermite moments it depends upon, namely max j,i { m α=1 p j i,α }. Obviously, it is the same as the order of the differntial operator D defined by (16), and is equal to the maximum number of times that X i (∇ i ) appears in D.…”

Section: The Construction Of Raghmismentioning

confidence: 99%

“…The interpolation not only leads to the loss of precision but also increases the computation time. Hence, the latter one, moments orthogonal on a square, are preferred by many researchers, such as Legendre moments [15], [16], Chebyshev moments [17], [18], Krawtchouk moments [19], [20], Gegenbauer moments [21] and Gaussian-Hermite moments [22]. However, the construction of rotation invariants from these moments is very difficult.…”

Section: Introductionmentioning

confidence: 99%

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Gaussian-Hermite Moment Invariants of General Multi-Channel Functions

Mo¹,

Li²,

Zhao³

2022

Preprint

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With the development of data acquisition technology, multi-channel data is collected and widely used in many fields. Most of them can be expressed as various types of vector functions. Feature extraction of vector functions for identifying certain patterns of interest is a critical but challenging task. In this paper, we focus on constructing moment invariants of general vector functions. Specifically, we define rotation-affine transform to describe real deformations of general vector functions, and then design a structural frame to systematically generate Gaussian-Hermite moment invariants to this transform model. This is the first time that a uniform frame has been proposed in the literature to construct orthogonal moment invariants of general vector functions. Given a certain type of multi-channel data, we demonstrate how to utilize the new method to derive all possible invariants and to eliminate various dependences among them. For RGB images, 2D and 3D flow fields, we obtain the complete and independent sets of the invariants with low orders and low degrees. Based on synthetic and popular datasets of vector-valued data, the experiments are carried out to evaluate the stability and discriminability of these invariants, and also their robustness to noise. The results clearly show that the moment invariants proposed in our paper have better performance than other previously used moment invariants of vector functions in RGB image classification, vortex detection in 2D vector fields and template matching for 3D flow fields.

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“…where q c1c2...cn are non-negative integers. Similar to (16), the properties of determinants allow us to consider only…”

Section: Relative Invariant Primitive To Ramentioning

confidence: 99%

Section: The Construction Of Raghmismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Gaussian-Hermite Moment Invariants of General Multi-Channel Functions

Mo¹,

Li²,

Zhao³

2022

Preprint

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show abstract

“…Benouini et al [15] presented the orthogonal fractionalorder Chebyshev moments (FrOCMs). Benouini et al [16] derived the Legendre polynomials of fractional order and defined what is called generalized Legendre moment invariants. These fractional-order moments are devoted to gray-scale images.…”

Section: They Pointed Out That Qrhfms Show Better Characteristicsmentioning

confidence: 99%

Novel Multi-Channel Fractional-Order Radial Harmonic Fourier Moments for Color Image Analysis

2020

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The classical radial harmonic Fourier moments (RHFMs) and the quaternion radial harmonic Fourier moments (QRHFMs) are gray-scale and color image descriptors. The radial harmonic functions with integer orders are not able to extract fine features from the input images. In this paper, the authors derived novel fractional-order radial harmonic functions in polar coordinates. The obtained functions are used to defined novel multi-channel fractional-order radial harmonic moments (FrMRHFMs) for color image description and analysis. The invariants to geometric transformations for these new moments are derived. A theoretical comparison between FrMRHFMs and QRHFMs is performed from the aspects of kernel function and the spectrum analysis. Numerical simulation is carried out to test these new moments in terms of image reconstruction capabilities, invariance to the similarity transformations, color image recognition and the CPU computational times. The obtained theoretical and numerical results clearly show that the proposed FrMRHFMs is superior to the QRHFMs and the existing fractional-order orthogonal moments. INDEX TERMS Color image analysis, fractional-order orthogonal moments, radial harmonic Fourier moments, rotation invariance.

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“…Moment descriptors are widely used for the analysis, storage and transmission of signals and images. They are successfully used in different applications such as pattern recognition [ 3 , 13 ], classification [ 16 , 28 ], reconstruction [ 7 , 21 ], compression [ 14 , 34 ] and watermarking [ 12 ]. The moments are defined as the coefficients of projection of signals or images on often orthogonal basis.…”

Section: Introductionmentioning

confidence: 99%

Optimal reconstruction and compression of signals and images by Hahn moments and artificial bee Colony (ABC) algorithm

Bencherqui

Daoui

Karmouni

et al. 2022

Multimed Tools Appl

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In this paper, we present an efficient and optimal method for optimization of Hahn parameters a and b using the Artificial Bee Colony algorithm (ABC) in order to improve the quality of reconstruction and the compression of bio-signals and 2D / 3D color images of large sizes. The proposed methods are essentially based on two concepts: the development of a recursive calculation of the initial terms of Hahn polynomials in order to avoid the problems of instability of polynomial values and the use of ABC algorithm to optimize the values of the parameters a and b of the discrete orthogonal Hahn polynomials ( HPs ) during the reconstruction and the compression of bio-signals and 2D / 3D color images. The simulation results performed on bio-signals and on large size 2D / 3D color images clearly show the efficiency and superiority of the proposed methods over conventional methods in terms of reconstruction of signals and images.

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New set of generalized legendre moment invariants for pattern recognition

Cited by 21 publications

References 20 publications

Gaussian-Hermite Moment Invariants of General Multi-Channel Functions

Gaussian-Hermite Moment Invariants of General Multi-Channel Functions

Novel Multi-Channel Fractional-Order Radial Harmonic Fourier Moments for Color Image Analysis

Optimal reconstruction and compression of signals and images by Hahn moments and artificial bee Colony (ABC) algorithm

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