Partial Differential Equation Methods for Image Inpainting

2015 ◽  
Author(s):  
Carola-Bibiane Schonlieb
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Inpainting ◽  
Partial Differential

A new partial differential equation for image inpainting

2021 ◽  
Vol 39 (3) ◽  
pp. 137-155
Author(s):  
Mounder Benseghir ◽  
Fatma Zohra Nouri ◽  
Pierre Clovis Tauber
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Image Inpainting ◽  
Complex Geometries ◽  
Partial Differential ◽  
Nonlinear Structure ◽  
Grey Scale ◽  
Nonlinear High Order

A considerable interest in the inpainting problem have attracted many researchers in applied mathematics community. In fact in the last decade, nonlinear high order partial dierential equations have payed a central role in high quality inpainting developments. In this paper, we propose a technique for inpainting that combines an anisotropic diusion process with an edge-corner enhancing shock ltering. This technique makes use of a partial differential equation that is based on a nonlinear structure tensor which increases the accuracy and robustness of the coupled diusion and shock ltering. A methodology of partition and adjustment is used to estimate the contrast parameters that control the strength of the diffusivity functions. We focus on restoring large missing regions in grey scale images containing complex geometries parts. Our model is extended to a three dimensional case, where numerical experimentations were carried out on lling brain multiple sclerosis lesions in medical images. The efficiency and the competitiveness of the proposed algorithm is numerically compared to other approaches on both synthetic and real images.

A Partial Differential Equation Algorithm for Image Denoising

2013 ◽  
Vol 816-817 ◽  
pp. 554-556
Author(s):  
Min Ma ◽  
Liang Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Image Restoration ◽  
Image Denoising ◽  
Anisotropic Diffusion ◽  
Image Inpainting ◽  
Partial Differential ◽  
Simulation Results ◽  
Different Levels

Image restoration is necessary in many applications as the captured images are inevitably noise-contaminated. Typically, the partical differential equations based methods, which is a primary class of image inpainting techniques, is well accepted. In this paper,anisotropic diffusion (P-M) model was introduced to image denoisng. Simulation results were implemented of the proposed method by using Matlab, in which different levels of noise were compared to show the advantages and the disadvantages.

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