Inpainting by an Inverse Problem Resolution

The in painting is a fundamental process in the image processing, which has several applications, such as image restoration, reconstructing damaged parts, the removal of unwanted objects in the image etc. The goal is to produce a revised image where treated parts are perfectly fused in it. In this paper we propose an approach which involves the direct solution of a system of Navier-Stokes equations for an incompressible Newtonian fluid. The main idea is to consider the image intensity as a function of the stream flow. The resolution algorithm automatically transports the information correction to the damaged part of the image, a process which can simultaneously reconstruct several damaged regions by solving an inverse problem, without requiring the user to specify a location treatment. The mathematical analysis of the Navier-Stokes (NS) equations is sufficiently developed, see for example R. Temam (1977), so we try to draw analogies between these equations and in painting which may introduce ideas of fluid mechanics and dynamics in problems of image processing.