Orthogonal Fourier–Mellin moments for invariant pattern recognition

Sheng, Yunlong; Shen, Lixin

doi:10.1364/josaa.11.001748

Cited by 314 publications

(157 citation statements)

References 10 publications

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“…The N IRE is used for the performance analysis of orthogonal moments [14]. It is de ned as the normalized mean square error between the input image f (i, j) and its reconstruction f (i, j), in discrete form is given by,…”

Section: Image Reconstructionmentioning

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%

See 1 more Smart Citation

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: Image Reconstructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

“…Though Legendre moments have good retrieval properties, they are not invariant to linear operation and rotation. The Fourier-Mellin moment is one of the complex moments and it was proposed by Sheng and Shen [12]; it can be transformed to rotation and translation invariants. It attains good results in shape recognition.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study on Weighted Central Moment and Its Application in 2D Shape Retrieval

et al. 2016

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Moment invariants have been extensively studied and widely used in object recognition. The pioneering investigation of moment invariants in pattern recognition was due to Hu, where a set of moment invariants for similarity transformation were developed using the theory of algebraic invariants. This paper details a comparative analysis on several modifications of the original Hu moment invariants which are used to describe and retrieve two-dimensional (2D) shapes with a single closed contour. The main contribution of this paper is that we propose several different weighting functions to calculate the central moment according to human visual processing. The comparative results are detailed through experimental analysis. The results suggest that the moment invariants improved by weighting functions can get a better retrieval performance than the original one does.

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“…Hu (1962), presented an invariant moment set which they are derived from the 2nd and the 3rd order moments. The invariant moment set is used in many application like character recognition system (Hu, 1962) and 3-D aircraft identification system (Dudani et al, 1977); Somaie and Ipson (1995); Eakins et al (2002) and Sheng and Shen (1994), presented the full face identification system using the 2-D isodensity moments. The geometrical and the template matching techniques could be common systems for the recognition task, while the correlation function was often used to compute the matching ratio (Gonzalez and Woods, 2002).…”

Section: Introductionmentioning

confidence: 99%

Features Extraction Based on Linear Regression Technique

Magld¹

2012

Journal of Computer Science

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Problem statement:The matching problem of complex objects is one of the most difficult task in the pattern recognition field. These problems are made difficult by seemingly infinite varieties of shapes and classes which are used. The difficulties are related to absolute shape measurement, given the impossibility of directly mapping shapes, as such, into a feature space. Approach: In this study, an object was modeled using boundaries pixel distance. The invariant has been resulted from the distance of each boundaries pixel to their central point. By performing linear regression on each set of sorted distances, a unique set of numerical features from the coefficients of this linear function has been produced. This unique set of numerical values is then proposed as an object's features. Results: The experiments show that the coefficient of linear function from boundaries' distance plot of each object has produced better recognition than polynomial function of degree more than one. Conclusion/Recommendations: More than 200 hundreds trademark's images have been tested and almost 90% of successful rate of accuracy has been achieved.

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Orthogonal Fourier–Mellin moments for invariant pattern recognition

Cited by 314 publications

References 10 publications

Generic Orthogonal Moments and Applications

Generic Orthogonal Moments and Applications

A Comparative Study on Weighted Central Moment and Its Application in 2D Shape Retrieval

Features Extraction Based on Linear Regression Technique

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