A model and numerical scheme for processing of color images
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| Názov: | A model and numerical scheme for processing of color images |
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| Autori: | Krivá, Zuzana, Mikula, Karol |
| Informácie o vydavateľovi: | Slovak University of Technology, Bratislava |
| Predmety: | Nonlinear parabolic equations, Systems of parabolic equations, boundary value problems, finite volume method, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Image processing (compression, reconstruction, etc.) in information and communication theory, adaptively, grid coarsening, RGB image |
| Popis: | 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 \[ d=g\left(\sum^3_{i=1} |\nabla G_\sigma * u_i|\right), \] together with zero Neumann and initial conditions in each channel \[ \begin{aligned} \partial_\nu u_i=0, \;& i=1,2,3,\quad \text{on }I\times \partial\Omega,\\ u_i(0,\cdot)=u_i^0,\;& i=1,2,3,\quad \text{in }\Omega.\end{aligned} \] 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. |
| Druh dokumentu: | Article |
| Popis súboru: | application/xml |
| Prístupová URL adresa: | https://zbmath.org/1607253 |
| Prístupové číslo: | edsair.c2b0b933574d..b25c5b54773f0ac854b4d0d0d4eefbfe |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | 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 \[ d=g\left(\sum^3_{i=1} |\nabla G_\sigma * u_i|\right), \] together with zero Neumann and initial conditions in each channel \[ \begin{aligned} \partial_\nu u_i=0, \;& i=1,2,3,\quad \text{on }I\times \partial\Omega,\\ u_i(0,\cdot)=u_i^0,\;& i=1,2,3,\quad \text{in }\Omega.\end{aligned} \] 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. |
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