scholarly journals Image representation based on fractional order Legendre and Laguerre orthogonal moments

2021 ◽  
Vol 8 (2) ◽  
pp. 54-59
Author(s):  
R. M. Farouk ◽  
◽  
Qamar A. A. Awad ◽  
Keyword(s):  
Fractional Order ◽  
Image Representation ◽  
Computational Time ◽  
Gray Level ◽  
Global Features ◽  
Orthogonal Functions ◽  
Orthogonal Moments ◽  
Fractional Moments ◽  
Gray Level Image ◽  
Detection Filter

In this paper, we have introduced new sets of fractional order orthogonal basis moments based on Fractional order Legendre orthogonal Functions (FLeFs) and Fractional order Laguerre orthogonal Functions (FLaFs) for image representation. We have generated a novel set of Fractional order Legendre orthogonal Moments (FLeMs) from fractional order Legendre orthogonal functions and a new set of Fractional order Laguerre orthogonal Moments (FLaMs) from the fractional order Laguerre orthogonal functions. The new presented sets of (FLeMs) and (FLaMs) are tested with the recently introduced Fractional order Chebyshev orthogonal Moments (FCMs). This edge detection filter can be used successfully in the gray level image and color images. The new sets of fractional moments are used to reconstruct the gray level image. The numerical results show FLeMs and FLaMs are promised techniques for image representation. The computational time of the proposed techniques is compared with the computational time of Chebyshev orthogonal Moments techniques and gives better results. Also, the fractional parameters give the flexibility of studying global features of the image at different positions of moments.

Scene Classification by Fuzzy Local Moments

1998 ◽  
Vol 12 (07) ◽  
pp. 921-938 ◽  
Author(s):  
H. D. Cheng ◽  
Rutvik Desai
Keyword(s):  
Parallel Implementation ◽  
Entropy Measure ◽  
Translation Invariance ◽  
Gray Level ◽  
Global Features ◽  
Local Moments ◽  
English Alphabet ◽  
Gray Level Image ◽  
Global Moment ◽  
Moment Features

The identification of images irrespective of their location, size and orientation is one of the important tasks in pattern analysis. The use of global moment features has been one of the most popular techniques for this purpose. We present a simple and effective method for gray-level image representation and identification which utilizes fuzzy radial moments of image segments (local moments) as features as opposed to global features. A multilayer perceptron neural network is employed for classification. Fuzzy entropy measure is applied to optimize the parameters of the membership function. The technique does not require translation, scaling or rotation of the image. Furthermore, it is suitable for parallel implementation which is an advantage for real-time applications. The classification capability and robustness of the technique are demonstrated by experiments on scaled, rotated and noisy gray-level images of uppercase and lowercase characters and digits of English alphabet, as well as the images of a set of tools. The proposed approach can handle rotation, scale and translation invariance, noise and fuzziness simultaneously.

scholarly journals Quaternion fractional-order color orthogonal moment-based image representation and recognition

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bing He ◽  
Jun Liu ◽  
Tengfei Yang ◽  
Bin Xiao ◽  
Yanguo Peng
Keyword(s):  
Fractional Order ◽  
Color Image ◽  
Laguerre Polynomials ◽  
Color Images ◽  
Polar Coordinates ◽  
Coordinate Space ◽  
Geometric Invariant ◽  
Global Features ◽  
Orthogonal Moments ◽  
Image Descriptors

AbstractInspired by quaternion algebra and the idea of fractional-order transformation, we propose a new set of quaternion fractional-order generalized Laguerre orthogonal moments (QFr-GLMs) based on fractional-order generalized Laguerre polynomials. Firstly, the proposed QFr-GLMs are directly constructed in Cartesian coordinate space, avoiding the need for conversion between Cartesian and polar coordinates; therefore, they are better image descriptors than circularly orthogonal moments constructed in polar coordinates. Moreover, unlike the latest Zernike moments based on quaternion and fractional-order transformations, which extract only the global features from color images, our proposed QFr-GLMs can extract both the global and local color features. This paper also derives a new set of invariant color-image descriptors by QFr-GLMs, enabling geometric-invariant pattern recognition in color images. Finally, the performances of our proposed QFr-GLMs and moment invariants were evaluated in simulation experiments of correlated color images. Both theoretical analysis and experimental results demonstrate the value of the proposed QFr-GLMs and their geometric invariants in the representation and recognition of color images.

scholarly journals Novel Color Orthogonal Moments-Based Image Representation and Recognition

2020 ◽  
Author(s):  
Bing He ◽  
Jun Liu ◽  
Tengfei Yang ◽  
Bin Xiao ◽  
Yanguo Peng
Keyword(s):  
Fractional Order ◽  
Color Image ◽  
Laguerre Polynomials ◽  
Color Images ◽  
Polar Coordinates ◽  
Coordinate Space ◽  
Geometric Invariant ◽  
Global Features ◽  
Orthogonal Moments ◽  
Image Descriptors

Abstract Inspired by quaternion algebra and the idea of fractional-order transformation, we propose a new set of quaternion fractional-order generalized Laguerre orthogonal moments (QFr-GLMs) based on fractional-order generalized Laguerre polynomials. Firstly, the proposed QFr-GLMs are directly constructed in Cartesian coordinate space, avoiding the need for conversion between Cartesian and polar coordinates; therefore, they are better image descriptors than circularly orthogonal moments constructed in polar coordinates. Moreover, unlike the latest Zernike moments based on quaternion and fractional-order transformations, which extract only the global features from color images, our proposed QFr-GLMs can extract both the global and local color features. This paper also derives a new set of invariant color-image descriptors by QFr-GLMs, enabling geometric-invariant pattern recognition in color images. Finally, the performances of our proposed QFr-GLMs and moment invariants were evaluated in simulation experiments of correlated color images. Both theoretical analysis and experimental results demonstrate the value of the proposed QFr-GLMs and their geometric invariants in the representation and recognition of color images.

scholarly journals Image Reconstruction Based on Novel Sets of Generalized Orthogonal Moments

2020 ◽  
Vol 6 (6) ◽  
pp. 54
Author(s):  
R. M. Farouk
Keyword(s):  
Fractional Order ◽  
General Framework ◽  
Recurrence Relations ◽  
Global Features ◽  
Orthogonal Moments ◽  
Recurrence Formulas ◽  
Intensity Images ◽  
Generalized Orthogonal ◽  
The Given ◽  
Comprehensive Study

In this work, we have presented a general framework for reconstruction of intensity images based on new sets of Generalized Fractional order of Chebyshev orthogonal Moments (GFCMs), a novel set of Fractional order orthogonal Laguerre Moments (FLMs) and Generalized Fractional order orthogonal Laguerre Moments (GFLMs). The fractional and generalized recurrence relations of fractional order Chebyshev functions are defined. The fractional and generalized fractional order Laguerre recurrence formulas are given. The new presented generalized fractional order moments are tested with the existing orthogonal moments classical Chebyshev moments, Laguerre moments, and Fractional order Chebyshev Moments (FCMs). The numerical results show that the importance of our general framework which gives a very comprehensive study on intensity image representation based GFCMs, FLMs, and GFLMs. In addition, the fractional parameters give a flexibility of studying global features of images at different positions and scales of the given moments.

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

scholarly journals Optimal Fractional PID Controller for Buck Converter Using Cohort Intelligent Algorithm

2021 ◽  
Vol 4 (3) ◽  
pp. 50
Author(s):  
Preeti Warrier ◽  
Pritesh Shah
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Power Converters ◽  
Buck Converter ◽  
Optimization Techniques ◽  
Superior Performance ◽  
Computational Time ◽  
Optimization Approach ◽  
Response Characteristics ◽  
Fractional Order Controller

The control of power converters is difficult due to their non-linear nature and, hence, the quest for smart and efficient controllers is continuous and ongoing. Fractional-order controllers have demonstrated superior performance in power electronic systems in recent years. However, it is a challenge to attain optimal parameters of the fractional-order controller for such types of systems. This article describes the optimal design of a fractional order PID (FOPID) controller for a buck converter using the cohort intelligence (CI) optimization approach. The CI is an artificial intelligence-based socio-inspired meta-heuristic algorithm, which has been inspired by the behavior of a group of candidates called a cohort. The FOPID controller parameters are designed for the minimization of various performance indices, with more emphasis on the integral squared error (ISE) performance index. The FOPID controller shows faster transient and dynamic response characteristics in comparison to the conventional PID controller. Comparison of the proposed method with different optimization techniques like the GA, PSO, ABC, and SA shows good results in lesser computational time. Hence the CI method can be effectively used for the optimal tuning of FOPID controllers, as it gives comparable results to other optimization algorithms at a much faster rate. Such controllers can be optimized for multiple objectives and used in the control of various power converters giving rise to more efficient systems catering to the Industry 4.0 standards.

scholarly journals Using Fractional Bernoulli Wavelets for Solving Fractional Diffusion Wave Equations with Initial and Boundary Conditions

2021 ◽  
Vol 5 (4) ◽  
pp. 212
Author(s):  
Monireh Nosrati Sahlan ◽  
Hojjat Afshari ◽  
Jehad Alzabut ◽  
Ghada Alobaidi
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Wave Equations ◽  
Bernoulli Polynomials ◽  
Fractional Diffusion ◽  
Computational Time ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Diffusion Wave ◽  
Klein Gordon

In this paper, fractional-order Bernoulli wavelets based on the Bernoulli polynomials are constructed and applied to evaluate the numerical solution of the general form of Caputo fractional order diffusion wave equations. The operational matrices of ordinary and fractional derivatives for Bernoulli wavelets are set via fractional Riemann–Liouville integral operator. Then, these wavelets and their operational matrices are utilized to reduce the nonlinear fractional problem to a set of algebraic equations. For solving the obtained system of equations, Galerkin and collocation spectral methods are employed. To demonstrate the validity and applicability of the presented method, we offer five significant examples, including generalized Cattaneo diffusion wave and Klein–Gordon equations. The implementation of algorithms exposes high accuracy of the presented numerical method. The advantage of having compact support and orthogonality of these family of wavelets trigger having sparse operational matrices, which reduces the computational time and CPU requirements.

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