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.

A Wavelet Collocation Precise Integration Method for Laminated Rectangular Plates with Four Sides Clamped

2013 ◽  
Vol 671-674 ◽  
pp. 1543-1551
Author(s):  
Hong Wei Zhang ◽  
Yan Li Wang ◽  
Guang Hui Qing
Keyword(s):  
Boundary Conditions ◽  
Integration Method ◽  
Current Approach ◽  
Canonical Equation ◽  
Rectangular Plates ◽  
Laminated Plate ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Hamilton Canonical Equation ◽  
Shannon Wavelet

By using Quasi-Shannon wavelet, we develop a wavelet collocation method for the Hamilton canonical equation of elastic bodies, and get the Hamilton canonical equation which is discrete in the plane of the rectangular laminated plate and continuum along its thickness. The approximate solution expressed by Quasi-Shannon wavelet satisfies the clamped boundary conditions of the plate easily. Hence, it is convenient to establish the wavelet collocation precise integration method for the static problem of the rectangular laminated plate with four sides clamped. Numerical results show that the current approach offers excellent predictive capability for rectangular composite laminated plate with clamped boundary conditions.

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-Cosine Wavelet Precise Integration Method for Locust Slice Image Mixed Denoising

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Haihua Wang ◽  
Xinxin Zhang ◽  
Shuli Mei
Keyword(s):  
Wavelet Transform ◽  
Differential Equations ◽  
Sparse Representation ◽  
Integration Method ◽  
Nonlinear Differential Equations ◽  
Variational Model ◽  
Precise Integration ◽  
Edge Preserving ◽  
Precise Integration Method ◽  
Salt And Pepper

A novel denoising method for removing mixed noise from locust slice images is proposed by means of Shannon-cosine wavelet and the nonlinear variational model for the image processing. This method includes two parts that are the sparse representation of the slice images and the novel numerical algorithm for solving the variation model on image denoising based on the sparse representation. In the first part, a parametric Shannon-cosine wavelet function is introduced to construct the multiscale wavelet transform matrix, which is applied to represent the slice images sparsely by adjusting the parameters adaptively based on the texture of the locust slice images. By multiplying the matrix with the signal, the multiscale wavelet transform coefficients of the signal can be obtained at one time, which can be used to identify the salt-and-pepper noises in the slice images. This ensures that the salt-and-pepper noise points are kept away from the sparse representation of the slice images. In the second part, a semianalytical method on solving the system of the nonlinear differential equations is constructed based on the sparse representation of the slice images, which is named the sparse wavelet precise integration method (SWPIM). Substituting the sparse representation of the slice images into the Perona–Malik model which is the famous edge-preserving smoothing model for removing the Gaussian noises of the biomedical images, a system of nonlinear differential equations is obtained, whose scale is far smaller than the one obtained by the difference method. The numerical experiments show that both the values of SSIM and PSNR of the denoised locust slice images are better than the classical methods besides the algorithm efficiency.

scholarly journals Reconstruction of Multi-Temporal Satellite Imagery by Coupling Variational Segmentation and Radiometric Analysis

2021 ◽  
Vol 10 (1) ◽  
pp. 17
Author(s):  
Nicola Case ◽  
Alfonso Vitti
Keyword(s):  
Image Segmentation ◽  
Variational Model ◽  
Great Level ◽  
Radiometric Analysis ◽  
Variational Segmentation ◽  
Landsat 7 ◽  
Multi Temporal ◽  
Original Procedure ◽  
Variational Image ◽  
Homogeneous Regions

Digital images, and in particular satellite images acquired by different sensors, may present defects due to many causes. Since 2013, the Landsat 7 mission has been affected by a well-known issue related to the malfunctioning of the Scan Line Corrector producing very characteristic strips of missing data in the imagery bands. Within the vast and interdisciplinary image reconstruction application field, many works have been presented in the last few decades to tackle the specific Landsat 7 gap-filling problem. This work proposes another contribution in this field presenting an original procedure based on a variational image segmentation model coupled with radiometric analysis to reconstruct damaged images acquired in a multi-temporal scenario, typical in satellite remote sensing. The key idea is to exploit some specific features of the Mumford–Shah variational model for image segmentation in order to ease the detection of homogeneous regions which will then be used to form a set of coherent data necessary for the radiometric reconstruction of damaged regions. Two reconstruction approaches are presented and applied to SLC-off Landsat 7 data. One approach is based on the well-known histogram matching transformation, the other approach is based on eigendecomposition of the bands covariance matrix and on the sampling from Gaussian distributions. The performance of the procedure is assessed by application to artificially damaged images for self-validation testing. Both of the proposed reconstruction approaches had led to remarkable results. An application to very high resolution WorldView-3 data shows how the procedure based on variational segmentation allows an effective reconstruction of images presenting a great level of geometric complexity.

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

Globally convex variational model for multiphsae image segmentation

2015 ◽  
Author(s):  
Huaxiang Liu ◽  
Jiangxiong Fang ◽  
Liting Zhang ◽  
Huaxiang Liu ◽  
Jing Xiao ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Variational Model

scholarly journals A Numerical Method Based on the Parametric Variational Principle for Simulating the Dynamic Behavior of the Pantograph-Catenary System

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Dongdong He ◽  
Qiang Gao ◽  
Wanxie Zhong
Keyword(s):  
Variational Principle ◽  
Dynamic Behavior ◽  
Integration Method ◽  
Time Integration ◽  
Dynamic Responses ◽  
Precise Integration ◽  
Contact Wire ◽  
Parametric Variational Principle ◽  
The Matrix ◽  
Catenary System

Based on the finite element method (FEM), the parametric variational principle (PVP) is combined with a numerical time-domain integral method to simulate the dynamic behavior of the pantograph-catenary system. Based on PVP, formulations for the nonlinear droppers in the catenary and for the contact between the pantograph and the contact wire are proposed. The formulations can accurately determine the tension state or compression state of the nonlinear droppers and the contact state between the pantograph and the contact wire. Based on the periodicity of the catenary and the precise integration method (PIM), a numerical time-integration method is developed for the dynamic responses of the catenary. For this method, the matrix exponential of only one unit cell of the catenary is computed, which greatly improves the computational efficiency. Moreover, the validation shows that the formulations can compute the contact force accurately and represent the nonlinearity of the droppers, which demonstrates the accuracy and reliability of the proposed method. Finally, the dynamic behaviors of the pantograph-catenary system with different types of catenaries are simulated.

Local Kernel-Induced Fitting Variational Model for MRI Image Segmentation

2016 ◽  
Vol 6 (4) ◽  
pp. 1013-1019
Author(s):  
Huaxiang Liu ◽  
Jiangxiong Fang ◽  
Liting Zhang ◽  
Jun Liu ◽  
Zhengjun Zeng
Keyword(s):  
Image Segmentation ◽  
Variational Model ◽  
Mri Image

Medical Imaging Importance in the Real World

2020 ◽  
pp. 136-162
Author(s):  
Ramgopal Kashyap
Keyword(s):  
Image Segmentation ◽  
Edge Detection ◽  
Level Set ◽  
Real World ◽  
Medical Image ◽  
Automatic Segmentation ◽  
Medical Image Segmentation ◽  
Image Resolution ◽  
Variational Model ◽  
Medical Applications

In the medical image resolution, automatic segmentation is a challenging task, and it's still an unsolved problem for most medical applications due to the wide variety connected with image modalities, encoding parameters, and organic variability. In this chapter, a review and critique of medical image segmentation using clustering, compression, histogram, edge detection, parametric, variational model. and level set-based methods is presented. Modes of segmentation like manual, semi-automatic, interactive, and automatic are also discussed. To present current challenges, aim and motivation for doing fast, interactive and correct segmentation, the medical image modalities X-ray, CT, MRI, and PET are discussed in this chapter.

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