The most critical part of a neutron computed tomography(NCT) system is the image processing algorithm,which directly affects the quality and speed of the reconstructed images.Various types of noise in the system can d...The most critical part of a neutron computed tomography(NCT) system is the image processing algorithm,which directly affects the quality and speed of the reconstructed images.Various types of noise in the system can degrade the quality of the reconstructed images.Therefore,to improve the quality of the reconstructed images of NCT systems,efficient image processing algorithms must be used.The anisotropic diffusion filtering(ADF) algorithm can not only effectively suppress the noise in the projection data,but also preserve the image edge structure information by reducing the diffusion at the image edges.Therefore,we propose the application of the ADF algorithm for NCT image reconstruction.To compare the performance of different algorithms in NCT systems,we reconstructed images using the ordered subset simultaneous algebraic reconstruction technique(OS-SART) algorithm with different regular terms as image processing algorithms.In the iterative reconstruction,we selected two image processing algorithms,the Total Variation and split Bregman solved total variation algorithms,for comparison with the performance of the ADF algorithm.Additionally,the filtered back-projection algorithm was used for comparison with an iterative algorithm.By reconstructing the projection data of the numerical and clock models,we compared and analyzed the effects of each algorithm applied in the NCT system.Based on the reconstruction results,OS-SART-ADF outperformed the other algorithms in terms of denoising,preserving the edge structure,and suppressing artifacts.For example,when the 3D Shepp–Logan was reconstructed at 25 views,the root mean square error of OS-SART-ADF was the smallest among the four iterative algorithms,at only 0.0292.The universal quality index,mean structural similarity,and correlation coefficient of the reconstructed image were the largest among all algorithms,with values of 0.9877,0.9878,and 0.9887,respectively.展开更多
The synthesis of visual information from multiple medical imaging inputs to a single fused image without any loss of detail and distortion is known as multimodal medical image fusion.It improves the quality of biomedi...The synthesis of visual information from multiple medical imaging inputs to a single fused image without any loss of detail and distortion is known as multimodal medical image fusion.It improves the quality of biomedical images by preserving detailed features to advance the clinical utility of medical imaging meant for the analysis and treatment of medical disor-ders.This study develops a novel approach to fuse multimodal medical images utilizing anisotropic diffusion(AD)and non-subsampled contourlet transform(NSCT).First,the method employs anisotropic diffusion for decomposing input images to their base and detail layers to coarsely split two features of input images such as structural and textural information.The detail and base layers are further combined utilizing a sum-based fusion rule which maximizes noise filtering contrast level by effectively preserving most of the structural and textural details.NSCT is utilized to further decompose these images into their low and high-frequency coefficients.These coefficients are then combined utilizing the principal component analysis/Karhunen-Loeve(PCA/KL)based fusion rule independently by substantiating eigenfeature reinforcement in the fusion results.An NSCT-based multiresolution analysis is performed on the combined salient feature information and the contrast-enhanced fusion coefficients.Finally,an inverse NSCT is applied to each coef-ficient to produce the final fusion result.Experimental results demonstrate an advantage of the proposed technique using a publicly accessible dataset and conducted comparative studies on three pairs of medical images from different modalities and health.Our approach offers better visual and robust performance with better objective measurements for research development since it excellently preserves significant salient features and precision without producing abnormal information in the case of qualitative and quantitative analysis.展开更多
The volatile pollutants that spill into natural waters cause water pollution. Air pollution arises from the water pollution because of volatilization. Mass exchange caused by turbulent fluctuation is stronger in the d...The volatile pollutants that spill into natural waters cause water pollution. Air pollution arises from the water pollution because of volatilization. Mass exchange caused by turbulent fluctuation is stronger in the direction normal to the air-water interface than in other directions due to the large density difference between water and air. In order to explore the characteristics of anisotropic diffusion of the volatile pollutants at the air-water interface, the relationship between velocity gradient and mass transfer rate was established to calculate the turbulent mass diffusivity. A second-order accurate smooth transition differencing scheme (STDS) was proposed to guarantee the boundedness for the flow and mass transfer at the air-water interface. Simulations and experiments were performed to study the trichloroethylene (C2HC13) release. By comparing the anisotropic coupling diffusion model, isotropic coupling diffusion model, and non-coupling diffusion model, the features of the transport of volatile pollutants at the air-water interface were determined. The results show that the anisotropic coupling diffusion model is more accurate than the isotropic coupling diffusion model and non-coupling diffusion model. Mass transfer significantly increases with the increase of the air-water relative velocity at a low relative velocity. However, at a higher relative velocity, an increase in the relative velocity has no effect on mass transfer.展开更多
We numerically study the phase behaviors of colloids with anisotropic diffusion in two dimensions. It is found that the diffusion anisotropy of colloidal particles plays an important role in the phase transitions. A s...We numerically study the phase behaviors of colloids with anisotropic diffusion in two dimensions. It is found that the diffusion anisotropy of colloidal particles plays an important role in the phase transitions. A strong diffusion anisotropy induces the large vibration of particles, subsequently, the system goes into a disordered state. In the presence of the strong-coupling, particles with weak diffusion anisotropy can freeze into hexagonal crystals. Thus, there exists a solid-liquid transition. With the degree of diffusion anisotropy increasing, the transition points are shifted to the strongercoupled region. A competition between the degree of diffusion anisotropy and coupling strength widens the transition region where the heterogeneous structures coexist, which results in a broad-peak probability distribution curve for the local order parameter. Our study may be helpful for the experiments related to the phase behavior in statistical physics, materials science and biophysical systems.展开更多
We consider a fluid stirred by the locomotions of squirmers through it and generalize the stochastic hydrodynamic model proposed by Thiffeault and Childress,Phys.Lett.A(2010)and Lin et al.,J.Fluid Mech.(2011)to the ca...We consider a fluid stirred by the locomotions of squirmers through it and generalize the stochastic hydrodynamic model proposed by Thiffeault and Childress,Phys.Lett.A(2010)and Lin et al.,J.Fluid Mech.(2011)to the case in which the swimmers move in anisotropically random directions.A non-diagonal effective diffusivity tensor is derived with which the diffusive preference of a passive particle along any given direction can be computed to provide more details of the phenomena beyond scalar statistics.We further identify a fraction from the orthogonal decomposition of the drift-induced particle displacement to distinguish the underlying nonlinear mixing mechanism for different types of swimmers.Numerical simulations verify the analytical results with explicit examples of prescribed,anisotropic stirring motions.We also connect our formulation to several measures used in clinical medical research such as diffusion tensor imaging where anisotropic diffusion has a significant consequence.展开更多
Nowadays in the medicalfield,imaging techniques such as Optical Coherence Tomography(OCT)are mainly used to identify retinal diseases.In this paper,the Central Serous Chorio Retinopathy(CSCR)image is analyzed for vari...Nowadays in the medicalfield,imaging techniques such as Optical Coherence Tomography(OCT)are mainly used to identify retinal diseases.In this paper,the Central Serous Chorio Retinopathy(CSCR)image is analyzed for various stages and then compares the difference between CSCR before as well as after treatment using different application methods.Thefirst approach,which was focused on image quality,improves medical image accuracy.An enhancement algorithm was implemented to improve the OCT image contrast and denoise purpose called Boosted Anisotropic Diffusion with an Unsharp Masking Filter(BADWUMF).The classifier used here is tofigure out whether the OCT image is a CSCR case or not.150 images are checked for this research work(75 abnormal from Optical Coherence Tomography Image Retinal Database,in-house clinical database,and 75 normal images).This article explicitly decides that the approaches suggested aid the ophthalmologist with the precise retinal analysis and hence the risk factors to be minimized.The total precision is 90 percent obtained from the Two Class Support Vector Machine(TCSVM)classifier and 93.3 percent is obtained from Shallow Neural Network with the Powell-Beale(SNNWPB)classifier using the MATLAB 2019a program.展开更多
We analyze in this work anisotropic heat conduction induced by a harmonically oscillating laser source incident on rotating conductors, exploiting an analogy with an effect discovered long ago, called the Zel’dovich ...We analyze in this work anisotropic heat conduction induced by a harmonically oscillating laser source incident on rotating conductors, exploiting an analogy with an effect discovered long ago, called the Zel’dovich effect. We re-covered the main results of a recently published paper that predicts the translational Doppler frequency shift of a thermal wave induced on a sample moving with uniform rectilinear motion. We extend then this framework to take into account the frequency shift of a thermal field propagating on a rotating platform. We show that it coincides with the rotational frequency shift which has been recently observed on surface acoustic waves and hydrodynamic surface waves, called rotational superradiance. Finally, we use an analogy with the Tolman effect to deduce a simple estimate of the average temperature gradient induced by rotation, showing the existence of a new cooling effect associated with heat torque transfer.展开更多
When DR (Digital Radiography) images are filtered, it is necessary to preserve the edges and key details. But the existing methods may inevitably take fine details mistaken for noise to remove. In order to solve the...When DR (Digital Radiography) images are filtered, it is necessary to preserve the edges and key details. But the existing methods may inevitably take fine details mistaken for noise to remove. In order to solve the problem an improved anisotropic diffu- sion filtering model is proposed. Firstly, a novel diffusion function is introduced based on Perona and Malik model, which well overcomes the high rate of convergence. Secondly, the gradient threshold is modified to an adaptive estimation function, so it is bet- ter at adaptive threshold regulations according to the pixels and iteration times. Finally, the edges are extracted from the restored im- ages and the results are evaluated quantificationally. It is shown from the experiments that the proposed method is effective not only in noise reduction but also in details preserved.展开更多
In this paper, we present a new scheme to segment a given image. This scheme utilizes neuro-fuzzy system to derive a proper set of contour pixels based on multi-scale images. We use these fuzzy derivatives to develop ...In this paper, we present a new scheme to segment a given image. This scheme utilizes neuro-fuzzy system to derive a proper set of contour pixels based on multi-scale images. We use these fuzzy derivatives to develop a new curve evolution model. The model automatically detect smooth boundaries, scaling the energy term, and change of topology according to the extracted con- tour pixels set. We present the numerical implementation and the experimental results based on the semi-implicit method. Experi- mental results show that one can obtains a high clualitv edge contour.展开更多
We present a new method for calculation of quasi-potential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the fini...We present a new method for calculation of quasi-potential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the finite difference upwind scheme,the first-order line integral is used as its update rule.With sufficient accuracy,the new simplified method can greatly speed up the computational time.Once the quasi-potential has been computed,the minimum action path(MAP)can also be obtained.Since the MAP is of concern in most stochastic situations,the effectiveness of this new method is checked by analyzing the accuracy of the MAP.Two cases of isotropic diffusion and anisotropic diffusion are considered.It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time.Meanwhile anisotropy will affect the accuracy of the computed MAP.展开更多
A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle.The condition is weaker than the existi...A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle.The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix.Numerical results are presented to verify the theoretical findings.展开更多
Image super-resolution methods-based existing edge indicating operators—namely Gauss curvature,mean curvature and gradient-cannot effectively identify the edges,ramps and flat regions and suffer from the loss of fine...Image super-resolution methods-based existing edge indicating operators—namely Gauss curvature,mean curvature and gradient-cannot effectively identify the edges,ramps and flat regions and suffer from the loss of fine textures.To address these issues,this paper presents a fractional anisotropic diffusion equation based on a new edge indicator,named fractional-order difference curvature,which can characterize the intensity variations in images.We introduce the frequency-domain definition for fractional-order derivative by the Fourier transform,which is easy to implement numerically.The new edge indicator is better than the existing edge indicating operators in distinguishing between ramps and edges and can better handle the fine textures.Comparative results for natural images validate that the proposed method can yield a visually pleasing result and better values of MSSIM and PSNR.展开更多
A weak Galerkin discretization of the boundary value problem of a general anisotropic diffusion problem is studied for preservation of the maximum principle.It is shown that the direct application of the M-matrix theo...A weak Galerkin discretization of the boundary value problem of a general anisotropic diffusion problem is studied for preservation of the maximum principle.It is shown that the direct application of the M-matrix theory to the stiffness matrix of the weak Galerkin discretization leads to a strong mesh condition requiring all of the mesh dihedral angles to be strictly acute(a constant-order away from 90 degrees).To avoid this difficulty,a reduced system is considered and shown to satisfy the discrete maximum principle under weaker mesh conditions.The discrete maximum principle is then established for the full weak Galerkin approximation using the relations between the degrees of freedom located on elements and edges.Sufficient mesh conditions for both piecewise constant and general anisotropic diffusion matrices are obtained.These conditions provide a guideline for practical mesh generation for preservation of the maximum principle.Numerical examples are presented.展开更多
Noise reduction is one of the most important concerns in electronic speckle pattern interferometry(ESPI). According to partial differential equation(PDE) filtering theory, we present an anisotropic PDE noisereduction ...Noise reduction is one of the most important concerns in electronic speckle pattern interferometry(ESPI). According to partial differential equation(PDE) filtering theory, we present an anisotropic PDE noisereduction model based on fringe structure information for interferometric fringe patterns. This model is based on coherence diffusion and Perona-Malik(P-M) diffusion. The former can protect the structure information of fringe pattern, while the latter can effectively filter off the noise inside the fringes. The proposed model generated by the two diffusion methods helps to obtain good effects of denoising and fidelity. ESPI fringes and the phase pattern are tested. Experimental results validate the performance of the proposed filtering model.展开更多
We analyze the well-posedness of an anisotropic,nonlocal diffusion equation.Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector c...We analyze the well-posedness of an anisotropic,nonlocal diffusion equation.Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus,we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation.Furthermore,we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s∈[0.5,1).We also present an application of the advection-diffusion equation to anomalous transport of solutes.展开更多
We present an efficient implementation of volumetric anisotropic image diffusion filters on modern programmable graphics processing units(GPUs),where the mathematics behind volumetric diffusion is effectively reduced ...We present an efficient implementation of volumetric anisotropic image diffusion filters on modern programmable graphics processing units(GPUs),where the mathematics behind volumetric diffusion is effectively reduced to the diffusion in 2D images.We hereby avoid the computational bottleneck of a time consuming eigenvalue decomposition in R3.Instead,we use a projection of the Hessian matrix along the surface normal onto the tangent plane of the local isodensity surface and solve for the remaining two tangent space eigenvectors.We derive closed formulas to achieve this and prevent the GPU code from branching.We show that our most complex volumetric anisotropic diffusion filters gain a speed up of more than 600 compared to a CPU solution.展开更多
In this paper,we construct a global repair technique for the finite element scheme of anisotropic diffusion equations to enforce the repaired solutions satisfying the discrete maximum principle.It is an extension of t...In this paper,we construct a global repair technique for the finite element scheme of anisotropic diffusion equations to enforce the repaired solutions satisfying the discrete maximum principle.It is an extension of the existing local repair technique.Both of the repair techniques preserve the total energy and are easy to be implemented.The numerical experiments show that these repair techniques do not destroy the accuracy of the finite element scheme,and the computational cost of the global repair technique is cheaper than the local repair technique when the diffusion tensors are highly anisotropic.展开更多
We present a finite volume based cell-centered method for solving diffusion equations on three-dimensional unstructured grids with general tensor conduction.Our main motivation concerns the numerical simulation of the...We present a finite volume based cell-centered method for solving diffusion equations on three-dimensional unstructured grids with general tensor conduction.Our main motivation concerns the numerical simulation of the coupling between fluid flows and heat transfers.The corresponding numerical scheme is characterized by cell-centered unknowns and a local stencil.Namely,the scheme results in a global sparse diffusion matrix,which couples only the cell-centered unknowns.The space discretization relies on the partition of polyhedral cells into sub-cells and on the partition of cell faces into sub-faces.It is characterized by the introduction of sub-face normal fluxes and sub-face temperatures,which are auxiliary unknowns.A sub-cellbased variational formulation of the constitutive Fourier law allows to construct an explicit approximation of the sub-face normal heat fluxes in terms of the cell-centered temperature and the adjacent sub-face temperatures.The elimination of the sub-face temperatures with respect to the cell-centered temperatures is achieved locally at each node by solving a small and sparse linear system.This system is obtained by enforcing the continuity condition of the normal heat flux across each sub-cell interface impinging at the node under consideration.The parallel implementation of the numerical algorithm and its efficiency are described and analyzed.The accuracy and the robustness of the proposed finite volume method are assessed by means of various numerical test cases.展开更多
A nonlinear finite volume element scheme for anisotropic diffusion problems on general triangular meshes is proposed.Starting with a standard linear conforming finite volume element approximation,a corrective term wit...A nonlinear finite volume element scheme for anisotropic diffusion problems on general triangular meshes is proposed.Starting with a standard linear conforming finite volume element approximation,a corrective term with respect to the flux jumps across element boundaries is added to make the scheme satisfy the discrete maximum principle.The new scheme is free of the anisotropic non-obtuse angle condition which is a severe restriction on the grids for problems with anisotropic diffusion.Moreover,this manipulation can nearly keep the same accuracy as the original scheme.We prove the existence of the numerical solution for this nonlinear scheme theoretically.Numerical results and a grid convergence study are presented for both continuous and discontinuous anisotropic diffusion problems.展开更多
This paper proposes a new model for the image restoration which combines the total variation minimization with the“pure”anisotropic diffusion equation of Alvarez and Morel.According to the introduction of new diffus...This paper proposes a new model for the image restoration which combines the total variation minimization with the“pure”anisotropic diffusion equation of Alvarez and Morel.According to the introduction of new diffusion term,this model can not only remove noise but also enhance edges and keep their locality.And it can also keep textures and large-scale fine features that are not characterized by edges.Due to these favorable characteristics,the processed images turn much clearer and smoother,meanwhile,their significant details are kept,which results in appealing vision.展开更多
基金supported by the National Key Research and Development Program of China (No. 2022YFB1902700)the National Natural Science Foundation of China (No. 11875129)+3 种基金the Fund of the State Key Laboratory of Intense Pulsed Radiation Simulation and Effect (No. SKLIPR1810)Fund of Innovation Center of Radiation Application (No. KFZC2020020402)Fund of the State Key Laboratory of Nuclear Physics and Technology,Peking University (No. NPT2020KFY08)the Joint Innovation Fund of China National Uranium Co.,Ltd.,State Key Laboratory of Nuclear Resources and Environment,East China University of Technology (No. 2022NRE-LH-02)。
文摘The most critical part of a neutron computed tomography(NCT) system is the image processing algorithm,which directly affects the quality and speed of the reconstructed images.Various types of noise in the system can degrade the quality of the reconstructed images.Therefore,to improve the quality of the reconstructed images of NCT systems,efficient image processing algorithms must be used.The anisotropic diffusion filtering(ADF) algorithm can not only effectively suppress the noise in the projection data,but also preserve the image edge structure information by reducing the diffusion at the image edges.Therefore,we propose the application of the ADF algorithm for NCT image reconstruction.To compare the performance of different algorithms in NCT systems,we reconstructed images using the ordered subset simultaneous algebraic reconstruction technique(OS-SART) algorithm with different regular terms as image processing algorithms.In the iterative reconstruction,we selected two image processing algorithms,the Total Variation and split Bregman solved total variation algorithms,for comparison with the performance of the ADF algorithm.Additionally,the filtered back-projection algorithm was used for comparison with an iterative algorithm.By reconstructing the projection data of the numerical and clock models,we compared and analyzed the effects of each algorithm applied in the NCT system.Based on the reconstruction results,OS-SART-ADF outperformed the other algorithms in terms of denoising,preserving the edge structure,and suppressing artifacts.For example,when the 3D Shepp–Logan was reconstructed at 25 views,the root mean square error of OS-SART-ADF was the smallest among the four iterative algorithms,at only 0.0292.The universal quality index,mean structural similarity,and correlation coefficient of the reconstructed image were the largest among all algorithms,with values of 0.9877,0.9878,and 0.9887,respectively.
文摘The synthesis of visual information from multiple medical imaging inputs to a single fused image without any loss of detail and distortion is known as multimodal medical image fusion.It improves the quality of biomedical images by preserving detailed features to advance the clinical utility of medical imaging meant for the analysis and treatment of medical disor-ders.This study develops a novel approach to fuse multimodal medical images utilizing anisotropic diffusion(AD)and non-subsampled contourlet transform(NSCT).First,the method employs anisotropic diffusion for decomposing input images to their base and detail layers to coarsely split two features of input images such as structural and textural information.The detail and base layers are further combined utilizing a sum-based fusion rule which maximizes noise filtering contrast level by effectively preserving most of the structural and textural details.NSCT is utilized to further decompose these images into their low and high-frequency coefficients.These coefficients are then combined utilizing the principal component analysis/Karhunen-Loeve(PCA/KL)based fusion rule independently by substantiating eigenfeature reinforcement in the fusion results.An NSCT-based multiresolution analysis is performed on the combined salient feature information and the contrast-enhanced fusion coefficients.Finally,an inverse NSCT is applied to each coef-ficient to produce the final fusion result.Experimental results demonstrate an advantage of the proposed technique using a publicly accessible dataset and conducted comparative studies on three pairs of medical images from different modalities and health.Our approach offers better visual and robust performance with better objective measurements for research development since it excellently preserves significant salient features and precision without producing abnormal information in the case of qualitative and quantitative analysis.
基金supported by the National Natural Science Foundation of China (Grant No. 51109106)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No.11KJB570001)
文摘The volatile pollutants that spill into natural waters cause water pollution. Air pollution arises from the water pollution because of volatilization. Mass exchange caused by turbulent fluctuation is stronger in the direction normal to the air-water interface than in other directions due to the large density difference between water and air. In order to explore the characteristics of anisotropic diffusion of the volatile pollutants at the air-water interface, the relationship between velocity gradient and mass transfer rate was established to calculate the turbulent mass diffusivity. A second-order accurate smooth transition differencing scheme (STDS) was proposed to guarantee the boundedness for the flow and mass transfer at the air-water interface. Simulations and experiments were performed to study the trichloroethylene (C2HC13) release. By comparing the anisotropic coupling diffusion model, isotropic coupling diffusion model, and non-coupling diffusion model, the features of the transport of volatile pollutants at the air-water interface were determined. The results show that the anisotropic coupling diffusion model is more accurate than the isotropic coupling diffusion model and non-coupling diffusion model. Mass transfer significantly increases with the increase of the air-water relative velocity at a low relative velocity. However, at a higher relative velocity, an increase in the relative velocity has no effect on mass transfer.
基金Project supported in part by the National Natural Science Foundation of China (Grant Nos. 12075090, 11905086 and 12165015)the GDUPS (2016), and the Major Basic Research Project of Guangdong Province, China (Grant No. 2017KZDXM024)+2 种基金the Natural Science Foundation of Jiangxi Province, China (Grant Nos. 2021BAB201015 and GJJ200820)Science and Technology Planning Project of Ganzhou City (Grant No. 202101095077)High-level Scientific Research Foundation for the Introduction of Talents of Jiangxi University of Science and Technology。
文摘We numerically study the phase behaviors of colloids with anisotropic diffusion in two dimensions. It is found that the diffusion anisotropy of colloidal particles plays an important role in the phase transitions. A strong diffusion anisotropy induces the large vibration of particles, subsequently, the system goes into a disordered state. In the presence of the strong-coupling, particles with weak diffusion anisotropy can freeze into hexagonal crystals. Thus, there exists a solid-liquid transition. With the degree of diffusion anisotropy increasing, the transition points are shifted to the strongercoupled region. A competition between the degree of diffusion anisotropy and coupling strength widens the transition region where the heterogeneous structures coexist, which results in a broad-peak probability distribution curve for the local order parameter. Our study may be helpful for the experiments related to the phase behavior in statistical physics, materials science and biophysical systems.
基金supported by the National Natural Science Foundation of China(Grant No.12071429).
文摘We consider a fluid stirred by the locomotions of squirmers through it and generalize the stochastic hydrodynamic model proposed by Thiffeault and Childress,Phys.Lett.A(2010)and Lin et al.,J.Fluid Mech.(2011)to the case in which the swimmers move in anisotropically random directions.A non-diagonal effective diffusivity tensor is derived with which the diffusive preference of a passive particle along any given direction can be computed to provide more details of the phenomena beyond scalar statistics.We further identify a fraction from the orthogonal decomposition of the drift-induced particle displacement to distinguish the underlying nonlinear mixing mechanism for different types of swimmers.Numerical simulations verify the analytical results with explicit examples of prescribed,anisotropic stirring motions.We also connect our formulation to several measures used in clinical medical research such as diffusion tensor imaging where anisotropic diffusion has a significant consequence.
文摘Nowadays in the medicalfield,imaging techniques such as Optical Coherence Tomography(OCT)are mainly used to identify retinal diseases.In this paper,the Central Serous Chorio Retinopathy(CSCR)image is analyzed for various stages and then compares the difference between CSCR before as well as after treatment using different application methods.Thefirst approach,which was focused on image quality,improves medical image accuracy.An enhancement algorithm was implemented to improve the OCT image contrast and denoise purpose called Boosted Anisotropic Diffusion with an Unsharp Masking Filter(BADWUMF).The classifier used here is tofigure out whether the OCT image is a CSCR case or not.150 images are checked for this research work(75 abnormal from Optical Coherence Tomography Image Retinal Database,in-house clinical database,and 75 normal images).This article explicitly decides that the approaches suggested aid the ophthalmologist with the precise retinal analysis and hence the risk factors to be minimized.The total precision is 90 percent obtained from the Two Class Support Vector Machine(TCSVM)classifier and 93.3 percent is obtained from Shallow Neural Network with the Powell-Beale(SNNWPB)classifier using the MATLAB 2019a program.
文摘We analyze in this work anisotropic heat conduction induced by a harmonically oscillating laser source incident on rotating conductors, exploiting an analogy with an effect discovered long ago, called the Zel’dovich effect. We re-covered the main results of a recently published paper that predicts the translational Doppler frequency shift of a thermal wave induced on a sample moving with uniform rectilinear motion. We extend then this framework to take into account the frequency shift of a thermal field propagating on a rotating platform. We show that it coincides with the rotational frequency shift which has been recently observed on surface acoustic waves and hydrodynamic surface waves, called rotational superradiance. Finally, we use an analogy with the Tolman effect to deduce a simple estimate of the average temperature gradient induced by rotation, showing the existence of a new cooling effect associated with heat torque transfer.
基金Supported by Natural Science Foundation of China(61163047)Natural Science Foundation of Jiangxi Province(20114BAB201036)
文摘When DR (Digital Radiography) images are filtered, it is necessary to preserve the edges and key details. But the existing methods may inevitably take fine details mistaken for noise to remove. In order to solve the problem an improved anisotropic diffu- sion filtering model is proposed. Firstly, a novel diffusion function is introduced based on Perona and Malik model, which well overcomes the high rate of convergence. Secondly, the gradient threshold is modified to an adaptive estimation function, so it is bet- ter at adaptive threshold regulations according to the pixels and iteration times. Finally, the edges are extracted from the restored im- ages and the results are evaluated quantificationally. It is shown from the experiments that the proposed method is effective not only in noise reduction but also in details preserved.
基金Supported by National Science Foundation of China(60403036)National Science Foundation of Shandong Province(Y2003G01)
文摘In this paper, we present a new scheme to segment a given image. This scheme utilizes neuro-fuzzy system to derive a proper set of contour pixels based on multi-scale images. We use these fuzzy derivatives to develop a new curve evolution model. The model automatically detect smooth boundaries, scaling the energy term, and change of topology according to the extracted con- tour pixels set. We present the numerical implementation and the experimental results based on the semi-implicit method. Experi- mental results show that one can obtains a high clualitv edge contour.
基金the National Natural Science Foundation of China(Grant Nos.11772149 and 12172167)the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures(Grant No.MCMS-I19G01).
文摘We present a new method for calculation of quasi-potential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the finite difference upwind scheme,the first-order line integral is used as its update rule.With sufficient accuracy,the new simplified method can greatly speed up the computational time.Once the quasi-potential has been computed,the minimum action path(MAP)can also be obtained.Since the MAP is of concern in most stochastic situations,the effectiveness of this new method is checked by analyzing the accuracy of the MAP.Two cases of isotropic diffusion and anisotropic diffusion are considered.It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time.Meanwhile anisotropy will affect the accuracy of the computed MAP.
基金the National Science Foundation(USA)under Grant DMS-0712935.
文摘A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle.The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix.Numerical results are presented to verify the theoretical findings.
基金This work was supported by National Natural Science Foundation of China(No.61701060)Major Project of Fundamental Science and Frontier Technology Research of Chongqing CSTC(Grant Nos.cstc2015jcyjBX0124 and cstc2015jcyjBX0090)+1 种基金Chongqing Research Program of Basic Research and Frontier Technology(No.cstc2017jcyjAX0007)Scientific and Technological Research Program of Chongqing Municipal Education Commission(No.KJ1600410).
文摘Image super-resolution methods-based existing edge indicating operators—namely Gauss curvature,mean curvature and gradient-cannot effectively identify the edges,ramps and flat regions and suffer from the loss of fine textures.To address these issues,this paper presents a fractional anisotropic diffusion equation based on a new edge indicator,named fractional-order difference curvature,which can characterize the intensity variations in images.We introduce the frequency-domain definition for fractional-order derivative by the Fourier transform,which is easy to implement numerically.The new edge indicator is better than the existing edge indicating operators in distinguishing between ramps and edges and can better handle the fine textures.Comparative results for natural images validate that the proposed method can yield a visually pleasing result and better values of MSSIM and PSNR.
基金This work was supported in part by the NSF under Grant DMS-1115118.
文摘A weak Galerkin discretization of the boundary value problem of a general anisotropic diffusion problem is studied for preservation of the maximum principle.It is shown that the direct application of the M-matrix theory to the stiffness matrix of the weak Galerkin discretization leads to a strong mesh condition requiring all of the mesh dihedral angles to be strictly acute(a constant-order away from 90 degrees).To avoid this difficulty,a reduced system is considered and shown to satisfy the discrete maximum principle under weaker mesh conditions.The discrete maximum principle is then established for the full weak Galerkin approximation using the relations between the degrees of freedom located on elements and edges.Sufficient mesh conditions for both piecewise constant and general anisotropic diffusion matrices are obtained.These conditions provide a guideline for practical mesh generation for preservation of the maximum principle.Numerical examples are presented.
基金supported by the National Natural Science Foundation of China under Grant No.61102150
文摘Noise reduction is one of the most important concerns in electronic speckle pattern interferometry(ESPI). According to partial differential equation(PDE) filtering theory, we present an anisotropic PDE noisereduction model based on fringe structure information for interferometric fringe patterns. This model is based on coherence diffusion and Perona-Malik(P-M) diffusion. The former can protect the structure information of fringe pattern, while the latter can effectively filter off the noise inside the fringes. The proposed model generated by the two diffusion methods helps to obtain good effects of denoising and fidelity. ESPI fringes and the phase pattern are tested. Experimental results validate the performance of the proposed filtering model.
文摘We analyze the well-posedness of an anisotropic,nonlocal diffusion equation.Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus,we apply our analysis to a class of fractional-order operators and present rigorous estimates for the solution of the corresponding anisotropic anomalous diffusion equation.Furthermore,we extend our analysis to the anisotropic diffusion-advection equation and prove well-posedness for fractional orders s∈[0.5,1).We also present an application of the advection-diffusion equation to anomalous transport of solutes.
文摘We present an efficient implementation of volumetric anisotropic image diffusion filters on modern programmable graphics processing units(GPUs),where the mathematics behind volumetric diffusion is effectively reduced to the diffusion in 2D images.We hereby avoid the computational bottleneck of a time consuming eigenvalue decomposition in R3.Instead,we use a projection of the Hessian matrix along the surface normal onto the tangent plane of the local isodensity surface and solve for the remaining two tangent space eigenvectors.We derive closed formulas to achieve this and prevent the GPU code from branching.We show that our most complex volumetric anisotropic diffusion filters gain a speed up of more than 600 compared to a CPU solution.
基金supported by General Program of Science and Technology Development Project of Beijing Municipal Education Commission KM201310011006,Program of the Young People of Outstanding Ability for the Construction of the Teachers Procession YETP1445,Major Research Plan of the National Natural Science Foundation of China 91130015,National Natural Science Foundation of China 61201113,11101013,11401015.The second author is supported by the National Nature Science Foundation of China 11171036.
文摘In this paper,we construct a global repair technique for the finite element scheme of anisotropic diffusion equations to enforce the repaired solutions satisfying the discrete maximum principle.It is an extension of the existing local repair technique.Both of the repair techniques preserve the total energy and are easy to be implemented.The numerical experiments show that these repair techniques do not destroy the accuracy of the finite element scheme,and the computational cost of the global repair technique is cheaper than the local repair technique when the diffusion tensors are highly anisotropic.
文摘We present a finite volume based cell-centered method for solving diffusion equations on three-dimensional unstructured grids with general tensor conduction.Our main motivation concerns the numerical simulation of the coupling between fluid flows and heat transfers.The corresponding numerical scheme is characterized by cell-centered unknowns and a local stencil.Namely,the scheme results in a global sparse diffusion matrix,which couples only the cell-centered unknowns.The space discretization relies on the partition of polyhedral cells into sub-cells and on the partition of cell faces into sub-faces.It is characterized by the introduction of sub-face normal fluxes and sub-face temperatures,which are auxiliary unknowns.A sub-cellbased variational formulation of the constitutive Fourier law allows to construct an explicit approximation of the sub-face normal heat fluxes in terms of the cell-centered temperature and the adjacent sub-face temperatures.The elimination of the sub-face temperatures with respect to the cell-centered temperatures is achieved locally at each node by solving a small and sparse linear system.This system is obtained by enforcing the continuity condition of the normal heat flux across each sub-cell interface impinging at the node under consideration.The parallel implementation of the numerical algorithm and its efficiency are described and analyzed.The accuracy and the robustness of the proposed finite volume method are assessed by means of various numerical test cases.
基金supported by the Postdoctoral Science Foundation of China(No.2017M620689)the National Science Foundation of China(Nos.11571048,11401034)the CAEP developing fund of science and technology(No.2014A0202009).
文摘A nonlinear finite volume element scheme for anisotropic diffusion problems on general triangular meshes is proposed.Starting with a standard linear conforming finite volume element approximation,a corrective term with respect to the flux jumps across element boundaries is added to make the scheme satisfy the discrete maximum principle.The new scheme is free of the anisotropic non-obtuse angle condition which is a severe restriction on the grids for problems with anisotropic diffusion.Moreover,this manipulation can nearly keep the same accuracy as the original scheme.We prove the existence of the numerical solution for this nonlinear scheme theoretically.Numerical results and a grid convergence study are presented for both continuous and discontinuous anisotropic diffusion problems.
文摘This paper proposes a new model for the image restoration which combines the total variation minimization with the“pure”anisotropic diffusion equation of Alvarez and Morel.According to the introduction of new diffusion term,this model can not only remove noise but also enhance edges and keep their locality.And it can also keep textures and large-scale fine features that are not characterized by edges.Due to these favorable characteristics,the processed images turn much clearer and smoother,meanwhile,their significant details are kept,which results in appealing vision.