Mixed Finite Element Method for Nonlinear Diffusion Equation in Image Processing


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In this paper we present a robust approach for dealing with numerical solutions of partial differential equations (PDEs) arising in image processing and computer vision. In this context, we introduce the nonlinear Perona-Malik diffusion equation and its improvement by Catté et al. After a semi-implicit approximation in scale we introduce a new variable and we show that the weak formulation of the problem obtained has a unique solution in a well-chosen space. We use the discretization by mixed finite element method (MFEM) based on Galerkin technique and Taylor-hode elements P2P1 and Q2Q1. To validate our approach some numerical results are given.

Sobre autores

Amal Hjouji

Faculty of Sciences and Technology

Autor responsável pela correspondência
Email: hjouji.amal@gmail.com
Marrocos, Beni Mellal

Jaouad El-Mekkaoui

Polydisciplinary Faculty

Autor responsável pela correspondência
Email: jawad.mekkaou@gmail.com
Marrocos, Beni Mellal

Mostafa Jourhmane

Faculty of Sciences and Technology

Email: jawad.mekkaou@gmail.com
Marrocos, Beni Mellal

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