scholarly journals Construction of Target Controllable Image Segmentation Model Based on Homotopy Perturbation Technology

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Shu-Li Mei
Keyword(s):  
Image Segmentation ◽  
Numerical Method ◽  
Variational Approach ◽  
Homotopy Perturbation Method ◽  
Nonlinear Pdes ◽  
Variational Model ◽  
The Novel ◽  
Lower Efficiency ◽  
Homotopy Perturbation ◽  
Novel Model

Based on the basic idea of the homotopy perturbation method which was proposed by Jihuan He, a target controllable image segmentation model and the corresponding multiscale wavelet numerical method are constructed. Using the novel model, we can get the only right object from the multiobject images, which is helpful to avoid the oversegmentation and insufficient segmentation. The solution of the variational model is the nonlinear PDEs deduced by the variational approach. So, the bottleneck of the variational model on image segmentation is the lower efficiency of the algorithm. Combining the multiscale wavelet interpolation operator and HPM, a semianalytical numerical method can be obtained, which can improve the computational efficiency and accuracy greatly. The numerical results on some images segmentation show that the novel model and the numerical method are effective and practical.

scholarly journals Shannon Wavelet Precision Integration Method for Pathologic Onion Image Segmentation Based on Homotopy Perturbation Technology

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Haihua Wang ◽  
Shu-Li Mei
Keyword(s):  
Image Segmentation ◽  
Burkholderia Cepacia ◽  
Integration Method ◽  
Interpolation Property ◽  
Variational Model ◽  
Nonlinear Odes ◽  
Precise Integration ◽  
Homotopy Perturbation ◽  
Analytical Scheme ◽  
Shannon Wavelet

Image segmentation variational method is good at processing the images with blurry and complicated contours, which is useful in quality identification of pathologic picture of onion. An adaptive Shannon wavelet precise integration method (WPIM) on digital image segmentation was proposed based on the image processing variational model to improve the processing speed and eliminate the artifacts of the images. First, taking full advantage of the interpolation property of the Shannon wavelet function, a multiscale Shannon wavelet interpolation scheme was constructed based on the homotopy perturbation method (HPM). The image pixels of the Burkholderia cepacia (ex-Burkholder) infected onions were taken as the collocation points of the WPIM. Then, with this scheme, the image segmentation model (C-V model) can be discretized into a system of nonlinear ODEs and solved by the half-analytical scheme combining the HPM and the precision integration method. At last, the numerical precision and efficiency of WPIM were discussed and compared with other common segmentation methods such as OSTU method and Sobel operator. The results show that the contour curve of the segmentation object obtained by the new method has many excellent properties such as closed and clear topological structure and the artifacts can be eliminated.

scholarly journals Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control

2019 ◽  
Vol 38 (2) ◽  
pp. 706-727 ◽  
Author(s):  
Reza Novin ◽  
Mohammad Ali Fariborzi Araghi
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
The Novel ◽  
Validity And Reliability ◽  
Hypersingular Integral ◽  
Homotopy Perturbation ◽  
Hypersingular Integral Equations ◽  
Ideal Tool ◽  
Novel Method

This paper attempts to propose and investigate a modification of the homotopy perturbation method to study hypersingular integral equations of the first kind. Along with considering this matter, of course, the novel method has been compared with the standard homotopy perturbation method. This method can be conveniently fast to get the exact solutions. The validity and reliability of the proposed scheme are discussed. Different examples are included to prove so. According to the results, we further state that new simple homotopy perturbation method is so efficient and promises the exact solution. The modification of the homotopy perturbation method has been discovered to be the significant ideal tool in dealing with the complicated function-theoretic analytical structures within an analytical method.

Homotopy perturbation method for MHD non-Newtonian Williamson fluid over exponentially stretching sheet with viscous dissipation and convective boundary condition

2019 ◽  
Vol 30 (11) ◽  
pp. 1950088 ◽  
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Perturbation Method ◽  
Numerical Method ◽  
Homotopy Perturbation Method ◽  
Stretching Sheet ◽  
Fluid Temperature ◽  
Williamson Fluid ◽  
Homotopy Perturbation ◽  
Exponential Stretching ◽  
Special Cases

This research is aimed at presenting the two-dimensional steady fluid flow, represented by Williamson constitutive model past a nonlinear exponential stretching sheet theoretically. The system of ODEs describing the physical problem is successfully solved numerically with the help of the homotopy perturbation method (HPM). Special attention is given to study the convergence analysis of the proposed method. The influences of the physical governing parameters acting on the fluid velocity and the fluid temperature are explained with the help of the figures and tables. Further, the presented numerical method is employed to calculate both the rate of heat transfer and the drag force for the Williamson fluid flow. In particular, it is observed that both the Eckert number and the dimensionless convective parameter have the effect of enhancing the temperature of the stretching surface, while the inverse was noted for the dimensionless mixed convection parameter. Finally, the comparison with previous numerical investigations of other authors at some special cases which is reported here proves that the results obtained via homotopy perturbation method are accurate and the numerical method is reliable.

scholarly journals Numerical method for fractional Zakharov-Kuznetsov equations with He’s fractional derivative

2019 ◽  
Vol 23 (4) ◽  
pp. 2163-2170 ◽  
Author(s):  
Kang-Le Wang ◽  
Shao-Wen Yao
Keyword(s):  
Fractional Derivative ◽  
Perturbation Method ◽  
Numerical Method ◽  
Homotopy Perturbation Method ◽  
Solution Process ◽  
Fractional Complex Transform ◽  
Homotopy Perturbation

In this paper, a fractional Zakharov-Kuznetsov equation with He's fractional derivative is studied by the fractional complex transform and He's homotopy perturbation method. The solution process is elucidated step by step to show its simplicity and effectiveness of the proposed method.

scholarly journals Research on the Novel Method of Edge Detection Based on the Isotropic Diffusion Model and Total Variation Model

2016 ◽  
Vol 16 (5) ◽  
pp. 97-108
Author(s):  
Xiaoming Wan
Keyword(s):  
Image Segmentation ◽  
The Novel ◽  
Morphological Reconstruction ◽  
Weighted Function ◽  
Isotropic Diffusion ◽  
Morphological Gradient ◽  
Total Variation Model ◽  
Novel Method ◽  
Watershed Method ◽  
Novel Model

Abstract A novel model of image segmentation based on watershed method is proposed in this work. To prevent the over segmentation of traditional watershed, our proposed algorithm has five stages. Firstly, the morphological reconstruction is applied to smooth the flat area and preserve the edge of the image. Secondly, multiscale morphological gradient is used to avoid the thickening and merging of the edges. Thirdly, for contrast enhancement the top/bottom hat transformation is used. Fourthly, the morphological gradient of an image is modified by imposing regional minima at the location of both the internal and the external markers. Finally, a weighted function is used to combine the top/bottom hat transformation algorithm and the markers algorithm to get the algorithm. The experimental results show the superiority of the new algorithm in terms of suppression over segmentation.

scholarly journals A Novel Effective Approach for Solving Fractional Nonlinear PDEs

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Hossein Aminikhah ◽  
Nasrin Malekzadeh ◽  
Hadi Rezazadeh
Keyword(s):  
Partial Differential Equations ◽  
Perturbation Method ◽  
Population Model ◽  
Homotopy Perturbation Method ◽  
Analytical Procedure ◽  
Nonlinear Pdes ◽  
Fractional Partial Differential Equations ◽  
Homotopy Perturbation ◽  
Analytical Approximations ◽  
Biological Population

The present work introduces an effective modification of homotopy perturbation method for the solution of nonlinear time-fractional biological population model and a system of three nonlinear time-fractional partial differential equations. In this approach, the solution is considered a series expansion that converges to the nonlinear problem. The new approximate analytical procedure depends only on two iteratives. The analytical approximations to the solution are reliable and confirm the ability of the new homotopy perturbation method as an easy device for computing the solution of nonlinear equations.

scholarly journals A Novel Homotopy Perturbation Method with Applications to Nonlinear Fractional Order KdV and Burger Equation with Exponential-Decay Kernel

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shabir Ahmad ◽  
Aman Ullah ◽  
Ali Akgül ◽  
Manuel De la Sen
Keyword(s):  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Order Partial Differential Equation ◽  
The Novel ◽  
Homotopy Perturbation ◽  
Novel Approach ◽  
In Series ◽  
Novel Method

In this paper, we introduce the Yang transform homotopy perturbation method (YTHPM), which is a novel method. We provide formulae for the Yang transform of Caputo-Fabrizio fractional order derivatives. We derive an algorithm for the solution of Caputo-Fabrizio (CF) fractional order partial differential equation in series form and show its convergence to the exact solution. To demonstrate the novel approach, we include some examples with detailed solutions. We use tables and graphs to compare the exact and approximate solutions.

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