A Nonlinear Parabolic Model in Processing of Medical Image

Aboulaïch, Rajae; Boujena, S.; Guarmah, E. El

doi:10.1051/mmnp:2008084

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…Note that the diffusion function (5) used in this work is different from that proposed by Perona Malik. The parameter α has a theoretical interest [1], [3].…”

Section: Inpainting and Nonlinear Diffusionmentioning

confidence: 99%

An improved nonlinear model for image inpainting

Boujena¹,

Bellaj²,

Gouasnouane³

et al. 2015

ams

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An important task in image processing is the process of filling in missing parts of damaged images based on the information obtained from the surrounding areas. It is called inpainting. The goals of inpainting are numerous such as removing scratches in old photographic image, removing text and logos, restoration of damaged paintings. In this paper we present a nonlinear diffusion model for image inpainting based on a nonlinear partial differential equation as first proposed by Perona and Malik in [8]. In our previous work [3] the existence, uniqueness and regularity of the solution for the proposed mathematical model are established in an Hilbert space. The discretization of the partial differential equation of the proposed model is performed using finite elements method and finite differences method. For finite differences method our model is very simple to implement, fast, and produces nearly identical results to more complex, and usually slower, known methods. However for finite elements method we observe that it requires large computational cost, especially for high-resolution images. To avoid this slowing problem, domain decomposition algorithm has been proposed, aiming to split one large problem into many smaller problems. To illustrate the effective performance of our method, we present some experimental results on several images.

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“…Note that the diffusion function (5) used in this work is different from that proposed by Perona Malik. The parameter α has a theoretical interest [1], [3].…”

Section: Inpainting and Nonlinear Diffusionmentioning

confidence: 99%

An improved nonlinear model for image inpainting

Boujena¹,

Bellaj²,

Gouasnouane³

et al. 2015

ams

Self Cite

View full text Add to dashboard Cite

show abstract

“…This model is obtained from the one initially proposed by Perona and Malik [4] on which some modifications have been done on conditions 1, 2 and 3.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Let us consider the following model [4], [5]: (1) In this model, 2 R  denotes the domain image, n the unit outer normal of the boundary  , and the…”

Section: Mathematical Modelmentioning

confidence: 99%

One Approach for Image Denoising Based on Finite Element Method and Domain Decomposition Technique

Bellaj¹,

Boujena²,

Guarmah³

et al. 2017

IJAPM

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Abstract:The generation process of medical images is inevitably accompanied by a certain noise which degrades the quality of the image and assigns the final clinical diagnosis. Therefore, the denoising step plays an important role in the treatment of medical images in order to prepare the steps of diagnosis and therapy. In this paper, we propose a nonlinear diffusion model for denoising of large size images. The numerical approach to this problem is based on an algorithm combining the methods of finite element and of domain decomposition. Numerical simulations show that the proposed algorithm is a useful alternative for the treatment of degraded images large size.

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A Nash-game approach to joint image restoration and segmentation

Kallel

Aboulaïch

Habbal

et al. 2014

Applied Mathematical Modelling

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International audienceWe propose a game theory approach to simultaneously restore and segment noisy images. We define two players: one is restoration, with the image intensity as strategy, and the other is segmentation with contours as strategy. Cost functions are the classical relevant ones for restoration and segmentation, respectively. The two players play a static game with complete information, and we consider as solution to the game the so-called Nash Equilibrium. For the computation of this equilibrium we present an iterative method with relaxation. The results of numerical experiments performed on some real images show the relevance and efficiency of the proposed algorithm

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A Nonlinear Parabolic Model in Processing of Medical Image

Cited by 5 publications

References 13 publications

An improved nonlinear model for image inpainting

An improved nonlinear model for image inpainting

One Approach for Image Denoising Based on Finite Element Method and Domain Decomposition Technique

A Nash-game approach to joint image restoration and segmentation

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