M. CHOUDER Rafaa

MCA

Directory of teachers

Department

Mathematics Department

Research Interests

Mathematics and applications images processing numerical analysis Artificial Intelligence

Contact Info

University of M'Sila, Algeria

Email : rafaa.chouder@univ-msila.dz

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Recent Publications

2024-12-18

Additive Operator Splitting Scheme for a General Mean Curvature Flow and Application in Edges Enhancement

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

M. CHOUDER Rafaa, (2024-12-18), "Additive Operator Splitting Scheme for a General Mean Curvature Flow and Application in Edges Enhancement", [national] Journal of numerical analysis and approximation theory , Editura Academiei Romane

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2024-11-27

Fast difference scheme for a general mean curvature flow

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

M. CHOUDER Rafaa, (2024-11-27), "Fast difference scheme for a general mean curvature flow", [national] Second National Conference on Mathematics and Applications , University of M'sila

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2024-08-20

Self-similar solutions for a new free-boundary problem and image contour enhancement

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

M. CHOUDER Rafaa, (2024-08-20), "Self-similar solutions for a new free-boundary problem and image contour enhancement", [national] Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms , Watam Press

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2023-03-12

Modèles Mathématiques pour le Traitement d'Images

Abstract
Citation

M. CHOUDER Rafaa, (2023-03-12), "Modèles Mathématiques pour le Traitement d'Images", [national] الاسبوع الجامعي للرياضيات , University of M'sila

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2022-10-26

EDGES ENHANCEMENT VIA GENERALIZED MEAN CURVATURE FLOW

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

M. CHOUDER Rafaa, (2022-10-26), "EDGES ENHANCEMENT VIA GENERALIZED MEAN CURVATURE FLOW", [national] Rencontre d'Analyse Mathématique et ses Applications , University of M'sila

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2019-10-01

New exact solutions to nonlinear diffusion equation that occurs in image processing

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

M. CHOUDER Rafaa, (2019-10-01), "New exact solutions to nonlinear diffusion equation that occurs in image processing", [national] International Journal of Computing Science and Mathematics , Inderscience Publishers (IEL)

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2018-02-11

Auto-simularité et contour d'image

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

M. CHOUDER Rafaa, (2018-02-11), "Auto-simularité et contour d'image", [national] University of M"sila

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2018-02-01

Travelling Profile Solutions For Nonlinear Degenerate Parabolic Equation And Contour Enhancement In Image Processing

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

M. CHOUDER Rafaa, (2018-02-01), "Travelling Profile Solutions For Nonlinear Degenerate Parabolic Equation And Contour Enhancement In Image Processing", [national] Applied Mathematics E-Notes , Applied Mathematics E-Notes

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2017-12-07

Les contours d'image par EDPs de diffusion

Abstract
Citation

M. CHOUDER Rafaa, (2017-12-07), "Les contours d'image par EDPs de diffusion", [national] Journées doctorales du laboratoire de mathématiques pures et appliquées- JD 2017 , University of M'sila

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2016-12-01

New exact solutions to nonlinear diffusion equations that occur in image processing

Abstract
Citation

M. CHOUDER Rafaa, (2016-12-01), "New exact solutions to nonlinear diffusion equations that occur in image processing", [national] Journées doctorales du laboratoire de mathématiques pures et appliquées- JD 2016 , University of M'sila

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2014-05-11

Self-similar asymptotics for nonlinear degenerate parabolic equations

Abstract
Citation

M. CHOUDER Rafaa, (2014-05-11), "Self-similar asymptotics for nonlinear degenerate parabolic equations", [national] CONGRÈS DES MATHÉMATICIENS ALGÉRIENS CMA’2014 , Tlemcen, Algeria

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