RAFAA Chouder

Achour Hossemddine

Etude d'EDPs liées à l'amélioration de contour d'image par auto similarité intermédiaire

Mouafak Azedine

Image Processing Based on Fractional Partial Differential Equations

Amira Guettaf

Osmosis Filtering for Shadow Removal in Images

Ferradi Ali

Finite Difference Schemes For Image Edge Enhancement Models

Sehissah Rawiya

Finite Differences of Fractional Partial Differential Equations

Many models that use non-linear partial differential equations (PDEs) have been extensively applied for different tasks in image processing. Among these PDE-based approaches, the mean curvature flow filtering has impressive results, for which feature directions in the image are important. In this paper, we explore a general model of mean curvature flow, as proposed in [4, 5]. The model can be re-arranged to a reaction-diffusion form, facilitating the creation of an unconditionally stable semi-implicit scheme for image filtering. The method employs the Additive Operator Split (AOS) technique. Experiments demonstrated that the modified general model of mean curvature flow is highly effective for reducing noise and has a superior job of preserving edges.

Citation

RAFAA Chouder , , (2024-12-18), Additive Operator Splitting Scheme for a General Mean Curvature Flow and Application in Edges Enhancement, Journal of numerical analysis and approximation theory, Vol:53, Issue:2, pages:218-232, Editura Academiei Romane

Many models that use non-linear PDEs have been extensively used for different tasks in image processing. Among numerous PDE-based approaches, the mean curvature flow filtering has impressive results, for which feature directions in the image are important. In this paper, we investigate a general model of mean curvature flow proposed in [1 , 2 ]. This model can be re-arranged to a reaction-diffusion form, where enables the development of an unconditionally stable semi-implicit scheme for image filtering. The method is based on the Additive Operator Split (AOS), originally applied by Weickert [7 ] for the nonlinear diffusion flow. Experiments demonstrated that the modified general model of mean curvature flow is effective for reducing noise and has a superior job of preserving edges.

Citation

RAFAA Chouder , ,(2024-11-27), Fast difference scheme for a general mean curvature flow,Second National Conference on Mathematics and Applications,University of M'sila

The nonlinear di usion equation is used to analyze the process of edge enhancement in image processing, based on a new evolution model consider as a generalization of mean curvature motion. A free boundary problem is formulated describing the image intensity evolution in the boundary layers around the edges of image. An asymptotic selfsimilar solutions to this nonlinear di usion equation are obtained in explicit forms. The solutions demonstrated that the edge enhancement and its rates depends on the parameters of equation. The experimental results demonstrate the e ectiveness of the model in edge preservation.

Citation

RAFAA Chouder , , (2024-08-20), Self-similar solutions for a new free-boundary problem and image contour enhancement, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms, Vol:31, Issue:5, pages:321-337, Watam Press

Abstract

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RAFAA Chouder , ,(2023-03-12), Modèles Mathématiques pour le Traitement d'Images,الاسبوع الجامعي للرياضيات,University of M'sila

Many models which use non-linear PDEs have been extensively used for different tasks in image processing. Among numerous PDE-based approaches, the mean curvature flow filtering has tremendous and impressive results, for which feature directions in the image are important. In this paper, we investigate a class of PDEs for image processing which generalize the mean curvature flow and the Beltrami flow. Numerical approximation by semi-implicit finite difference schemes is used. Numerical experiments display the differences between mean curvature flow, Beltrami flow and the general model studied here, where the focus is on the enhanced edge preservation and the behavior with respect to noise.

Citation

RAFAA Chouder , ,(2022-10-26), EDGES ENHANCEMENT VIA GENERALIZED MEAN CURVATURE FLOW,Rencontre d'Analyse Mathématique et ses Applications,University of M'sila

In this paper, we would like to seek the new exact solutions to nonlinear diffusion equation that occurs in image processing. This equation is called degenerate parabolic equation. The solutions which we se ek are called ‘travelling profiles solutions’. For that, we have used the ‘travelling profiles method’ in order to find, explicitly, new exact solutions to this equation under some conditions. An interesting particular case has been discus sed, this case coincides with particular solutions called ‘intermediate asymptotic solutions’ used to study the contour enhancement in image processing.

Citation

RAFAA Chouder , Benhamidouche NourEddine , , (2019-10-01), New exact solutions to nonlinear diffusion equation that occurs in image processing, International Journal of Computing Science and Mathematics, Vol:10, Issue:4, pages:364-374, Inderscience Publishers (IEL)

La théorie des équations de diffusion non linéaires est utiliser pour analyser le processus d’amélioration de contour en traitement de l'image, le but de la pressente recherche et de chercher de nouvelles solutions exacte d’équations de diffusion non linéaires qui apparaître dans le traitement de l'image appelée équation parabolique dégénérée. pour ça , nous avons utiliser les solutions auto-similaires générales et la méthode de profiles mobiles pour trouvée explicitement de nouvelles solutions exactes de cette équations sous quelques conditions. ces solutions explicites sont liées avec les phénomènes d'améliorations de contour. un cas particulier intéressant a été discuté , ce cas coïncide avec les solutions particulières appelées "solutions asymptotiques intermédiaires" utilisées pour étudier l'amélioration de contour

Citation

RAFAAChouder , ,(2018-02-11); Auto-simularité et contour d'image,University of M"sila,

We propose in this work to find explicit exact solutions called travelling profile solutions to a nonlinear diffusion equation that occurs in image processing. Some of these explicit solutions are related with the phenomenon of contour enhancement in image processing. We present a generalization of the results obtained by Barenblatt to study the contour enhancement in image processing for exponent range of parameter enhancement.

Citation

RAFAA Chouder , Benhamidouche NourEddine , , (2018-02-01), Travelling Profile Solutions For Nonlinear Degenerate Parabolic Equation And Contour Enhancement In Image Processing, Applied Mathematics E-Notes, Vol:18, Issue:1, pages:1-12, Applied Mathematics E-Notes

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RAFAA Chouder , ,(2017-12-07), Les contours d'image par EDPs de diffusion,Journées doctorales du laboratoire de mathématiques pures et appliquées- JD 2017,University of M'sila

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RAFAA Chouder , ,(2016-12-01), New exact solutions to nonlinear diffusion equations that occur in image processing,Journées doctorales du laboratoire de mathématiques pures et appliquées- JD 2016,University of M'sila

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RAFAA Chouder , ,(2014-05-11), Self-similar asymptotics for nonlinear degenerate parabolic equations,CONGRÈS DES MATHÉMATICIENS ALGÉRIENS CMA’2014,Tlemcen, Algeria