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Abstract

Partial differential equations can model many physical phenomena and be used to simulate under computer. Osmosis, which is in the form of convection-diffusion equa- tion, has found itself many application areas in image processing. However, slow convergence of this model, which depends on incompatibility of the drift vector field used in the model, under current methods does not allow us to have a fast, and possibly real-time application area. Therefore, we get a deeper look into what incompatibility means and how it effects steady states of the osmosis process in this thesis. In addition, we evaluate several promising methods which offers substantial computational advantage over classical iterative methods.