Generic orthogonal moments: Jacobi–Fourier moments for invariant image description

Ping, Ziliang; Ren, Haiping; Zou, Jian; Sheng, Yunlong; Bo, Wurigen

doi:10.1016/j.patcog.2006.07.016

Cited by 103 publications

(65 citation statements)

References 14 publications

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“…(8.1) are replaced by summations and the image is normalized inside the unit disk, this approach is known as zeroth-order approximation or direct method. Ping et al [12] rst used the shifted orthonormal Jacobi polynomials as kernel for circular moments, which are de ned as follows…”

Section: Generic Jacobi Fourier Momentsmentioning

confidence: 99%

“…Bhatia and Wolf [3] pointed out that there is an in nite number of complete sets of radial orthogonal polynomials which can be obtained from the Jacobi polynomials. The variation of parameters α and β of the Jacobi polynomials can produce di erent sets of known orthogonal moments [7,12], such as orthogonal Fourier Mellin moments [14] (α = β = 2), Chebyshev Fourier moments [13] (α = 2, β = 3/2), Pseudo-Jacobi Fourier moments [2] (α = 4, β = 3), Legendre Fourier Moments (α = β = 1), Zernike [17] J s m + 1, m + 1, r 2 and Pseudo-Zernike Moments [18] (J s (2m + 2, m + 2, r) , n = m + s).…”

Section: Introductionmentioning

confidence: 99%

“…Ping et al [12] appoints the Jacobi-Fourier moments as Generic orthogonal moments and suggested that the common formulation of the orthogonal moments through the Jacobi polynomials will be an advantage for performance analysis of the orthogonal moments; and for searching a prime orthogonal moment. This last idea has been ignored due to its high computational costs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generic Orthogonal Moments and Applications

Camacho-Bello¹,

Toxqui-Quitl²,

Padilla-Vivanco³

2014

Moments and Moment Invariants - Theory and Applications

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We present a detailed analysis of the Jacobi-Fourier moments and their applications in digital image processing. In order to reach numerical stability during the computation of the Jacobi radial polynomials a recursive approach is described. Also, some discussions are done about the best values of the parameters α and β in terms of its performance. Moreover, the digital image applications studied here are divided in low or high orders n of the polynomials. Typically, the pattern recognition applications are based in low order polynomials whilst image reconstruction can be achieved by using high order polynomials. On the other hand, the polar pixel approach is taken into account, in order to increase the numerical accuracy in the calculation of the

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Section: Generic Jacobi Fourier Momentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generic Orthogonal Moments and Applications

Camacho-Bello¹,

Toxqui-Quitl²,

Padilla-Vivanco³

2014

Moments and Moment Invariants - Theory and Applications

View full text Add to dashboard Cite

show abstract

“…Exponential moments have translation invariance, scaling invariability and rotation invariance, therefore, when the license-plate tilt, far/near changes, discoloration due to pollution，weather changes, lack of light and so on , they still have a good recognition effect. (Ping and Ren et al, 2007) This paper is organized as follows: In section 2, introduce the exponential moments. In section 3, multidistortion invariance proof of exponential moments.…”

Section: Introductionmentioning

confidence: 99%

Vehicle License-plate Recognition Based on Exponential Moments

2017

Revista Tecnica De La Facultad De Ingenieria Universidad Del Zu

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This paper proposed a new vehicle license-plate recognition algorithm based on exponential moments. In this paper, exponential moments' translation invariance, scaling invariance and rotation invariance were applied to the vehicle license-plate recognition. It has good recognition effect under the circumstance of license-plate inclined, and good at against weather changes and illumination insufficiency. This method can recognize the vehicle license-plate without tilt correction and proportional adjustment, which not only shorten the positioning time, but also proved the accuracy of the recognition.This research has good practical significance for future smart city contruction.

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“…Some orthogonal moments are derived from the basis set of pseudo-Zernike, 16 ChebyshevFourier, 17 orthogonal Fourier-Mellin, 18 radial harmonic Fourier, 19 and Bessel-Fourier 20 polynomials. Additionally, new orthogonal basis sets of circular moments have been proposed from the generic formula of the Jacobi radial polynomials, [21][22][23] where each set can be generated by combinations of two real parameters, which are commonly denoted as α and β. Also, Jacobi-Fourier moments (JFMs) have been successfully proven in pattern recognition, 24 image analysis, 25 and machine vision applications.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of color biomedical images by means of quaternion generic Jacobi-Fourier moments in the framework of polar pixels

et al. 2016

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Abstract. A detailed analysis of the quaternion generic Jacobi-Fourier moments (QGJFMs) for color image description is presented. In order to reach numerical stability, a recursive approach is used during the computation of the generic Jacobi radial polynomials. Moreover, a search criterion is performed to establish the best values for the parameters α and β of the radial Jacobi polynomial families. Additionally, a polar pixel approach is taken into account to increase the numerical accuracy in the calculation of the QGJFMs. To prove the mathematical theory, some color images from optical microscopy and human retina are used. Experiments and results about color image reconstruction are presented.

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Generic orthogonal moments: Jacobi–Fourier moments for invariant image description

Cited by 103 publications

References 14 publications

Generic Orthogonal Moments and Applications

Generic Orthogonal Moments and Applications

Vehicle License-plate Recognition Based on Exponential Moments

Reconstruction of color biomedical images by means of quaternion generic Jacobi-Fourier moments in the framework of polar pixels

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