Mixed Finite Element Method for Nonlinear Diffusion Equation in Image Processing

Abstract

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 P₂–P₁ and Q₂–Q₁. To validate our approach some numerical results are given.