anisotropic diffusion equation
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2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yanghong Liu ◽  
Jintao Liu

In this paper, a three-dimensional anisotropic diffusion equation is used to conduct an in-depth study and analysis of students’ concentration in video recognition in English teaching classrooms. A multifeature fusion face live detection method based on diffusion model extracts Diffusion Kernel (DK) features and depth features from diffusion-processed face images, respectively. DK features provide a nonlinear description of the correlation between successive face images and express face image sequences in the temporal dimension; depth features are extracted by a pretrained depth neural network model that can express the complex nonlinear mapping relationships of images and reflect the more abstract implicit information inside face images. To improve the effectiveness of the face image features, the extracted DK features and depth features are fused using a multicore learning method to obtain the best combination and the corresponding weights. The two features complement each other, and the fused features are more discriminative, which provides a strong basis for the live determination of face images. Experiments show that the method has excellent performance and can effectively discriminate the live nature of faces in images and resist forged face attacks. Based on the above face detection and expression recognition algorithms, the classroom concentration analysis system based on expression recognition is designed to achieve real-time acquisition and processing of classroom images, complete student classroom attendance records using face detection and face recognition methods, and analyze students’ concentration from the face integrity and facial expression of students facing the blackboard by combining face detection and expression recognition to visualize and display students’ classroom data for teachers, students, and parents with more data support and help.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yong Chen ◽  
Taoshun He

The purpose of this paper is to develop an effective edge indicator and propose an image scale-space filter based on anisotropic diffusion equation for image denoising. We first develop an effective edge indicator named directional local variance (DLV) for detecting image features, which is anisotropic and robust and able to indicate the orientations of image features. We then combine two edge indicators (i.e., DLV and local spatial gradient) to formulate the desired image scale-space filter and incorporate the modulus of noise magnitude into the filter to trigger time-varying selective filtering. Moreover, we theoretically show that the proposed filter is robust to the outliers inherently. A series of experiments are conducted to demonstrate that the DLV metric is effective for detecting image features and the proposed filter yields promising results with higher quantitative indexes and better visual performance, which surpass those of some benchmark models.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Liyuan Guo

On the basis of studying the basic theory of anisotropic diffusion equation, this paper focuses on the application of anisotropic diffusion equation in image recognition film production. In order to further improve the application performance of P-M (Perona-Malik) anisotropic diffusion model, an improved P-M anisotropic diffusion model is proposed in this paper, and its application in image ultrasonic image noise reduction is discussed. The experimental results show that the model can effectively suppress the speckle noise and preserve the edge features of the image. Based on the image recognition technology, an image frame testing system is designed and implemented. The method of image recognition diffusion equation is used to extract and recognize the multilayer feature points of the test object according to the design of artificial neural network. To a certain extent, it improves the accuracy of image recognition and the audience rating of film and television. Use visual features of the film and television play in similarity calculation for simple movement scene segmentation problem, at the same time, the camera to obtain information, use the lens frame vision measuring the change of motion of the camera, and use weighted diffusion equation and the visual similarity of lens similarity calculation and motion information, by considering the camera motion of image recognition, effectively solve the sports scene of oversegmentation problem such as fighting and chasing.


2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xiaoqin Li

This paper uses partial differential equation image processing techniques to establish image texture analysis models based on nonlinear anisotropic diffusion equations for image denoising, image segmentation, and image decomposition. This paper proposes a class of denoising models based on the hybrid anisotropic diffusion equation from the characteristics of different noise types. The model exhibits anisotropic diffusion near the image boundary, which can protect the boundary well, and isotropic diffusion inside the image; so, it can remove the noise effectively. We use the immovable point theory to prove the uniqueness of the model solution and further discuss other properties such as asymptotics of the solution. We propose a class of image texture analysis algorithms based on anisotropic diffusion equations and discrete gray level sets. First, a class of nonconvex generalized functions is proposed to remove the noise from the original image to obtain a smooth image while sharpening the edges. Then, an energy generalization function based on the gray level set is proposed, and the existence of the global minimum of this energy generalization function is discussed. Finally, an equivalent form of this energy generalization is given in the discrete case, and an image texture analysis algorithm is designed based on the equivalent form. The algorithm is improved by initial position optimization, dynamic adjustment of parameters, and adaptive selection of thresholds so that the ants can search along the real edges. Experiments show that the improved algorithm for image edge detection can obtain more complete edges and better detection results. The energy generalization function is calculated directly on the discrete gray level set instead of solving the corresponding partial differential equation, which can avoid the selection of the initial level set and the reinitialization of the level set, thus greatly improving the segmentation efficiency. The new algorithm has a high improvement in segmentation efficiency and can efficiently handle large size complex images.


SPE Journal ◽  
2021 ◽  
pp. 1-19
Author(s):  
Wenjuan Zhang ◽  
Mohammed Al Kobaisi

Summary A class of monotone cell-centered nonlinear finite-volume methods has been proposed in the past decade to solve the anisotropic diffusion equation. The nonlinear two-point flux approximation (TPFA) (NTPFA) method preserves the nonnegativity of the solution values but can violate the discrete maximum/minimum principle (DMP). To enforce DMP, the nonlinear multipoint flux approximation (NMPFA) method ought to be used. In this work, we propose a novel NTPFA method that can reduce the severity of DMP violations significantly compared with the standard NTPFA method. The new formulation uses conormal decomposition for the construction of the one-sided fluxes. To define the unique flux through a connection between two cells, we choose a convex combination of the two one-sided fluxes such that the absolute differences of the magnitudes of the two transmissibility terms associated with the two neighboring cells are minimized, thus bringing the discrete coefficient matrix closer to having the zero row-sum property. Numerical experiments are conducted to test the performance of the new NTPFA method. The results demonstrate that the new scheme has comparable convergence order for both the solution and the flux compared with the standard NTPFA method or the classical multi-point flux approximation (MPFA-O) method. Moreover, the new NTPFA formulation shows marked improvements over the standard NTPFA in terms of reducing DMP violations. However, depending on the specific problem configuration, our new NTPFA formulation can lead to a system of nonlinear equations that is more difficult to solve.


Author(s):  
Santosh Kumar ◽  
Nitendra Kumar ◽  
Khursheed Alam

Background: In the image processing area, deblurring and denoising are the most challenging hurdles. The deblurring image by a spatially invariant kernel is a frequent problem in the field of image processing. Methods: For deblurring and denoising, the total variation (TV norm) and nonlinear anisotropic diffusion models are powerful tools. In this paper, nonlinear anisotropic diffusion models for image denoising and deblurring are proposed. The models are developed in the following manner: first multiplying the magnitude of the gradient in the anisotropic diffusion model, and then apply priori smoothness on the solution image by Gaussian smoothing kernel. Results: The finite difference method is used to discretize anisotropic diffusion models with forward-backward diffusivities. Conclusion: The results of the proposed model are given in terms of the improvement.


2021 ◽  
Vol 18 (5) ◽  
pp. 6581-6607
Author(s):  
Jimin Yu ◽  
◽  
Jiajun Yin ◽  
Shangbo Zhou ◽  
Saiao Huang ◽  
...  

<abstract><p>The image denoising model based on anisotropic diffusion equation often appears the staircase effect while image denoising, and the traditional super-resolution reconstruction algorithm can not effectively suppress the noise in the image in the case of blur and serious noise. To tackle this problem, a novel model is proposed in this paper. Based on the original diffusion equation, we propose a new method for calculating the adaptive fidelity term and its coefficients, which is based on the relationship between the image gradient and the diffusion function. It is realized that the diffusion speed can be slowed down by adaptively changing the coefficient of the fidelity term, and it is proved mathematically that the proposed fractional adaptive fidelity term will not change the existence and uniqueness of the solution of the original model. At the same time, washout filter is introduced as the control item of the model, and a new model of image super-resolution reconstruction and image denoising is constructed. In the proposed model, the order of fractional differential will be determined adaptively by the local variance of the image. And we give the numerical calculation method of the new model in the frequency domain by the method of Fourier transform. The experimental results show that the proposed algorithm can better prevent the staircase effect and achieve better visual effect. And by introducing washout filter to act as the control of the model, the stability of the system can be improved and the system can converge to a stable state quickly.</p></abstract>


2020 ◽  
Vol 10 (18) ◽  
pp. 6437
Author(s):  
Xiaobin Gong ◽  
Min Tao ◽  
Gang Su ◽  
Baohua Li ◽  
Jian Guan ◽  
...  

In iterative pseudo-inverse ghost imaging (IPGI), how much the noise interference item of the current iteration approximates the real noise greatly depends on the clarity of initial image. In order to improve IPGI, we propose a method that introduces anisotropic diffusion to construct a more accurate noise interference term, where anisotropic diffusion adapts to both the image and the noise, so that it balances the tradeoff between noise removal and preservation of image details. In our algorithm, the anisotropic diffusion equation is used to denoise the result of each iteration, then the denoised image is used to construct the noise interference term for the next iteration. Compared to IPGI, our method has better performance in visual effects and imaging quality, as the image edges and details are better preserved according to the experimental results.


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