Highly Efficient Local Non-Texture Image Inpainting Based on Partial Differential Equation

2014 ◽  
Author(s):  
Chuang Zhu ◽  
Huizhu Jia ◽  
Meng Li ◽  
Xiaofeng Huang ◽  
Xiaodong Xie
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Inpainting ◽  
Texture Image ◽  
Partial Differential ◽  
Highly Efficient

scholarly journals Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Yi-Fei Pu ◽  
Ji-Liu Zhou ◽  
Patrick Siarry ◽  
Ni Zhang ◽  
Yi-Guang Liu
Keyword(s):  
Differential Equation ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Fractional Order ◽  
Differential Calculus ◽  
Order Partial Differential Equation ◽  
Texture Image ◽  
Fractional Partial Differential Equation ◽  
Partial Differential ◽  
Integer Order

The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.

Fractional partial differential equation denoising models for texture image

2014 ◽  
Vol 57 (7) ◽  
pp. 1-19 ◽  
Author(s):  
YiFei Pu ◽  
Patrick Siarry ◽  
JiLiu Zhou ◽  
YiGuang Liu ◽  
Ni Zhang ◽  
...  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Texture Image ◽  
Fractional Partial Differential Equation ◽  
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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