An anisotropic PDE model for image inpainting

Halim, Abdul Hakim; Kumar, B. V. Rathish

doi:10.1016/j.camwa.2019.12.002

Cited by 21 publications

(11 citation statements)

References 13 publications

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“…Now, we will discuss the consistency, stability and convergence of the time discretized model (18) that is for the fractional model with α = 2.…”

Section: Appendix Bmentioning

confidence: 99%

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A Fractional Image Inpainting Model Using a Variant of Mumford-Shah Model

Halim¹,

Rohim²,

Kumar³

et al. 2022

Preprint

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In this paper, we propose a fourth order PDE model for image inpainting based on a variant of the famous Mumford-Shah (MS) image segmentation model. Convexity splitting is used to discrtised the time and we replace the Laplacian by its fractional counterpart in the time discretised scheme. Fourier spectral method is used for space discretization. Consistency, stability and convergence of the time discretised model has been carried out. The model is tested on some standard test images and compared them with the result of some models existed in the literature.

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“…Now, we will discuss the consistency, stability and convergence of the time discretized model (18) that is for the fractional model with α = 2.…”

Section: Appendix Bmentioning

confidence: 99%

“…The mCH model has few drawbacks, like it is applicable for binary images only. Then several authors have come up with inapinting models [14,15,16,17,18] by modifying the Cahn-Hilliard model to overcome the drawbacks of mCH model.…”

Section: Introductionmentioning

confidence: 99%

A Fractional Image Inpainting Model Using a Variant of Mumford-Shah Model

Halim¹,

Rohim²,

Kumar³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The ill-posedness of image inpainting can be distilled into the following: how to seek the most proper hypothesis for the corrupted region conditioned on the valid surroundings. In the past decade, researchers have devoted substantial efforts to this field, which can be mainly divided into three categories: diffusion-based methods [ 17 , 18 , 19 , 20 ], patch-based methods [ 21 , 22 , 23 , 24 , 25 , 26 ], and CNN (Convolutional Neural Network)-based methods [ 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 ].…”

Section: Introductionmentioning

confidence: 99%

“…Based on the priori knowledge that image pixels are piece-wise smooth, the diffusion-based methods [ 17 , 18 , 19 , 20 ] establish a variety of anisotropic PDEs (Partial Differential Equations) for modeling the process of information diffusion. Although these methods attempt to mimic the paradigm of manual inpainting, they are suitable only for the corrupted region with slender shape and homogeneous texture.…”

Section: Introductionmentioning

confidence: 99%

Progressively Inpainting Images Based on a Forked-Then-Fused Decoder Network

Yang

Han

2021

Sensors

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Image inpainting aims to fill in corrupted regions with visually realistic and semantically plausible contents. In this paper, we propose a progressive image inpainting method, which is based on a forked-then-fused decoder network. A unit called PC-RN, which is the combination of partial convolution and region normalization, serves as the basic component to construct inpainting network. The PC-RN unit can extract useful features from the valid surroundings and can suppress incompleteness-caused interference at the same time. The forked-then-fused decoder network consists of a local reception branch, a long-range attention branch, and a squeeze-and-excitation-based fusing module. Two multi-scale contextual attention modules are deployed into the long-range attention branch for adaptively borrowing features from distant spatial positions. Progressive inpainting strategy allows the attention modules to use the previously filled region to reduce the risk of allocating wrong attention. We conduct extensive experiments on three benchmark databases: Places2, Paris StreetView, and CelebA. Qualitative and quantitative results show that the proposed inpainting model is superior to state-of-the-art works. Moreover, we perform ablation studies to reveal the functionality of each module for the image inpainting task.

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“…Then image inpainting techniques are divided into two broad categories: non-textured and textured structure methods. 1The nontextured structure method utilizes higher order partial differential equation (PDE) [4], or extreme value of function of prior model and data model to generate the mending patches, which is effective in small-sized breakage. Bertalmio et al…”

Section: Introductionmentioning

confidence: 99%

Consecutive Context Perceive Generative Adversarial Networks for Serial Sections Inpainting

et al. 2020

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Image inpainting is a hot topic in computer vision research and has been successfully applied to both traditional and digital mediums, such as oil paintings or old photos mending, image or video denoising and super-resolution. With the introduction of artificial intelligence (AI), a series of algorithms, represented by semantic inpainting, have been developed and better results were achieved. Medical image inpainting, as one of the most demanding applications, needs to meet both the visual effects and strict content correctness. 3D reconstruction of microstructures, based on serial sections, could provide more spatial information and help us understand the physiology or pathophysiology mechanism in histology study, in which extremely high-quality continuous images without any defects are required. In this paper, we proposed a novel Consecutive Context Perceive Generative Adversarial Networks (CCPGAN) for serial sections inpainting. Our method can learn semantic information from its neighboring image, and restore the damaged parts of serial sectioning images to maximum extent. Validated with 2 sets of serial sectioning images of mouse kidney, qualitative and quantitative results suggested that our method could robustly restore breakage of any size and location while achieving near realtime performance.

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An anisotropic PDE model for image inpainting

Cited by 21 publications

References 13 publications

A Fractional Image Inpainting Model Using a Variant of Mumford-Shah Model

A Fractional Image Inpainting Model Using a Variant of Mumford-Shah Model

Progressively Inpainting Images Based on a Forked-Then-Fused Decoder Network

Consecutive Context Perceive Generative Adversarial Networks for Serial Sections Inpainting

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