Mixed Finite Element Method for Nonlinear Diffusion Equation in Image Processing

Hjouji, Amal; El-Mekkaoui, Jaouad; Jourhmane, Mostafa

doi:10.1134/s1054661819020020

Cited by 9 publications

(7 citation statements)

References 22 publications

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“…We describe the main steps used to implement the discrete variational problem (9) in FEniCS [2,[10][11][12]. This description contains the definitions of the finite element mesh and the discrete function spaces V h and Vh , the generation of two finite element functions u re f and u 0 that represent the true image and the noisy image respectively, and the definitions of the bilinear form (10) and the linear form (11).…”

Section: Finite Element For Image Denoisingmentioning

confidence: 99%

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Automated Finite Element Solution of Diffusion Models for Image Denoising

BOUFALA

Kalmoun

2023

Tatra Mountains Mathematical Publications

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We present in this paper a numerical solution of a generalized diffusion-based image denoising model, using the finite element computing platform FEniCS. The generalized model contains as special cases three classical denoising techniques: linear isotropic diffusion, total variation, and Perona-Malik method. The numerical simulation using four classical grayscale images demonstrates the superior performance of the finite element method over the finite difference method in terms of both the denoising quality and the computational work.

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Section: Finite Element For Image Denoisingmentioning

confidence: 99%

“…These iterations are equivalent to iterated regularization in which a series of Tikhonov functionals are iteratively minimized [15]. Recently, there has been considerable effort to apply the finite element method (FEM) in solving the two particular cases p = 0 and p = 1 of (2)-(3), see for instance [7,9] for p = 0 and [1,3,4,8] for p = 1.…”

Section: Introductionmentioning

confidence: 99%

Automated Finite Element Solution of Diffusion Models for Image Denoising

BOUFALA

Kalmoun

2023

Tatra Mountains Mathematical Publications

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“…At the same time, with images of the scene lens must be continuous on time; you can use the limited time approach to the shot clustering, and literature [14] puts forward within the fixed time window T lens clustering method based on similarity shots, but because in the image, based on the plot and story rhythm slow degree is different, the length of the image lens also varies greatly, so it is more reasonable to use a fixed lens window than a fixed time window. Literature [15] proposed an algorithm for image scene detection based on a sliding window with fixed lens window length. Literature [16] analyzes the background pictures in the same scene shot to complete scene boundary detection of film and television images.…”

Section: Related Workmentioning

confidence: 99%

Application of Image Recognition Method Based on Diffusion Equation in Film and Television Production

Guo

2021

Advances in Mathematical Physics

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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.

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“…Generally, the imaging problems are inverse and ill posed. To deal with such problems the energybased regularization is considered as an efficient and most successful approach [2,3,6,9,17,22,23].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Numerical Regularization for Variational Denoising Model with Complementary Approach

Amur,

Amur

et al. 2023

VFAST trans. math.

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Denoising is a process to suppress the noise and preserve the important information in the image. In this paper, a complementary approach is proposed for variational denoising problem. A FEM (Finite Element Method) based post optimization method (mesh refinement strategy) is designed which is based on a priori estimate called mean square error. The post optimization algorithm is adaptive and intelligent in nature which allows the adaptive choice of the regularization parameters. The manual choice of the smoothing parameters is taken uniformly on spatial domain and testing of the automatic selection of these parameters in adaptive way. This is an interesting idea of computation. The intelligent and automatic choice of the values for the smoothing function is smaller in the less regular regions of the image, to refine the grid and keep constant in the other complementary regions is one of the main interests, which produces the better and enhanced version of the noisy image. The obtained results have been compared to some other methods.

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Mixed Finite Element Method for Nonlinear Diffusion Equation in Image Processing

Cited by 9 publications

References 22 publications

Automated Finite Element Solution of Diffusion Models for Image Denoising

Automated Finite Element Solution of Diffusion Models for Image Denoising

Application of Image Recognition Method Based on Diffusion Equation in Film and Television Production

Adaptive Numerical Regularization for Variational Denoising Model with Complementary Approach

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