scholarly journals Accurate Computation of Fractional-Order Exponential Moments

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Shujiang Xu ◽  
Qixian Hao ◽  
Bin Ma ◽  
Chunpeng Wang ◽  
Jian Li
Keyword(s):  
Numerical Integration ◽  
Fractional Order ◽  
Numerical Instability ◽  
Calculation Methods ◽  
Image Description ◽  
Accurate Calculation ◽  
Orthogonal Moments ◽  
Instability Problem ◽  
Exponential Moments ◽  
Numerical Integration Error

Exponential moments (EMs) are important radial orthogonal moments, which have good image description ability and have less information redundancy compared with other orthogonal moments. Therefore, it has been used in various fields of image processing in recent years. However, EMs can only take integer order, which limits their reconstruction and antinoising attack performances. The promotion of fractional-order exponential moments (FrEMs) effectively alleviates the numerical instability problem of EMs; however, the numerical integration errors generated by the traditional calculation methods of FrEMs still affect the accuracy of FrEMs. Therefore, the Gaussian numerical integration (GNI) is used in this paper to propose an accurate calculation method of FrEMs, which effectively alleviates the numerical integration error. Extensive experiments are carried out in this paper to prove that the GNI method can significantly improve the performance of FrEMs in many aspects.

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.

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

2007 ◽  
Vol 40 (4) ◽  
pp. 1245-1254 ◽  
Author(s):  
Ziliang Ping ◽  
Haiping Ren ◽  
Jian Zou ◽  
Yunlong Sheng ◽  
Wurigen Bo
Keyword(s):  
Image Description ◽  
Orthogonal Moments

Robustness of Boundary Control of Fractional Wave Equations With Delayed Boundary Measurement Using Fractional Order Controller and the Smith Predictor

2005 ◽  
Author(s):  
Jinsong Liang ◽  
Weiwei Zhang ◽  
YangQuan Chen ◽  
Igor Podlubny
Keyword(s):  
Fractional Order ◽  
Wave Equations ◽  
Small Difference ◽  
Smith Predictor ◽  
Fractional Wave Equation ◽  
Instability Problem ◽  
Boundary Measurement ◽  
Fractional Wave Equations ◽  
Fractional Order Controller ◽  
Better Than

In this paper, we analyze the robustness of the fractional wave equation with a fractional order boundary controller subject to delayed boundary measurement. Conditions are given to guarantee stability when the delay is small. For large delays, the Smith predictor is applied to solve the instability problem and the scheme is proved to be robust against a small difference between the assumed delay and the actual delay. The analysis shows that fractional order controllers are better than integer order controllers in the robustness against delays in the boundary measurement.

scholarly journals Improved Calibration of Numerical Integration Error in Sigma-Point Filters

2020 ◽  
pp. 1-1
Author(s):  
Jakub Pruher ◽  
Toni Karvonen ◽  
Christopher James Oates ◽  
Ondrej Straka ◽  
Simo Sarkka
Keyword(s):  
Numerical Integration ◽  
Sigma Point ◽  
Integration Error ◽  
Numerical Integration Error

scholarly journals Product Cost Calculation Methods in Construction

2018 ◽  
Vol 7 (3.2) ◽  
pp. 6
Author(s):  
Alla Dmitrenko ◽  
Galyna Lebedyk ◽  
Mykola Nesterenko
Keyword(s):  
Production Cost ◽  
Cost Price ◽  
Cost Calculation ◽  
Operational Control ◽  
Calculation Methods ◽  
Accurate Calculation ◽  
Product Cost ◽  
Practical Activity ◽  
Construction Products ◽  
The Cost

The order of accounting and features of the methodology of cost expenditures at the concrete enterprises of the field was studied and it has been found out the fact that in the practical activity of the enterprise, they tend to apply the normative method of cost expenditures accounting. It has been conducted a detailed research of enterprises which use the normative method of cost expenditure accounting, and the calculation of the planned cost price. In addition, given advantages of the normative method of cost expenditure accounting have two functions: it provides the operational control over the production cost expenditures by accounting for cost expenditures under current norms and their changes and provides accurate calculation of the cost price of construction products. 

scholarly journals Behavior of the Numerical Integration Error

2014 ◽  
Vol 05 (10) ◽  
pp. 1412-1426
Author(s):  
Tchavdar Marinov ◽  
Joe Omojola ◽  
Quintel Washington ◽  
LaQunia Banks
Keyword(s):  
Numerical Integration ◽  
Integration Error ◽  
Numerical Integration Error
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