A model and numerical scheme for processing of color images (Q2714737)

A model is proposed for processing RGB (red, green, blue) images based on regularized (in the sense of Catte, Lions, Morel and Coll) Perona-Malik nonlinear image selective smoothing equation. The model is represented by a system of nonlinear differential equations with a common diffusion coefficient given by a synchronization of the information coming from all three channels namely the values of the red, green, and blue files measured at each pixel. The nonlinear partial differential equations governing the enhancement procedures are as follows: \(\partial_t u_i-\nabla\cdot (d\nabla u_i)=0\), \(i=1,2,3\) in \(Q_T\equiv I\times \Omega\), where NEWLINE\[NEWLINEd=g\left(\sum^3_{i=1} |\nabla G_\sigma * u_i|\right),NEWLINE\]NEWLINE together with zero Neumann and initial conditions in each channel NEWLINE\[NEWLINE\begin{aligned} \partial_\nu u_i=0, \;& i=1,2,3,\quad \text{on }I\times \partial\Omega,\\ u_i(0,\cdot)=u_i^0,\;& i=1,2,3,\quad \text{in }\Omega.\end{aligned}NEWLINE\]NEWLINE For the numerical solution the authors adjust a finite volume computational method given by Mikula and Ramarosy and propose a coarsening strategy to reduce the number of unknowns in the linear system to be solved at each discrete scale step of the method. The paper concludes with three examples showing how these methods improve and enhance the images.