Digital image inpainting using finite volume approach and the Navier-Stokes equations

Authors:
B. A. Youssef;E. H. Atta
Affiliations:
Computer Based Engineering Application Department, Informatics Institute, Moubark City for Scientific Research and Technological Applications, Alexandria, Egypt;Computer Graphics Department, Informatics Institute, Moubark City for Scientific Research and Technological Applications, Alexandria, Egypt
Venue:
MACMESE'07 Proceedings of the 9th WSEAS international conference on Mathematical and computational methods in science and engineering
Year:
2007

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Abstract

This paper presents a new numerical method for image inpainting based on the vorticity stream function formulation of the Navier-Stokes Equations. The method employs a finite volume discretization and a Runge-Kutta time stepping scheme with dissipative terms. A stability analysis of the proposed numerical method has been performed to determine the maximum allowable time step for which the computation will be stable. It is shown that the expression for the maximum time step contains terms that are functions of the image isophote gradient and curvature. The method has been implemented for a number of grey level and colored images and the results indicate that the method is effective in terms of solution quality and computational efficiency.