Image Inpainting Application Based On Partial Differential Equation

Digital image inpainting is a technique of repairing a partially damaged or missing image. It fills the missing part of an image, to make it look natural after repairing by employing information of the undamaged part according to some rules. Digital image inpainting derives from restoration of artworks, and has been applied to repair ancient paintings. With the wide spread of multimedia, this technique becomes an important task in a variety of applications, such as object removal, super resolution, image compression and video error concealment.At present the image inpainting can be divided into two kinds: the image inpainting based on partial differential equations (PDEs) and the image inpainting based on texture synthesis.The main ideal of PDE-based image inpainting model is to change the image inpainting process into a series of PDE s or energy function models, so we can deal with the image with numerical iterations and intelligent optimization methods. This algorithm propagates the useful information which is around the inpainting domain in the direction of the isophotes automatically. It is also smoothing the noise while preserving the edges. In this paper, we mainly study several types of PDE-based image inpainting models: BSCB model, Curvature Driven Diffusion (CDD) model, TV inpainting, elastic inpainting and Mumford-Shah inpainting. We also present simulations on some models and make some simple analysis.PDE-based inpainting model works well to small damaged blocks, but doesn't have good effect for big damaged blocks inpainting. So we must use the inpainting method based on texture synthesis to solve the problem. In this paper, we also introduce three kinds of models in a simple way.Finally, we propose a method based on TV-Stokes equation to do digital image inpainting. It takes two steps. In the first step, we try to propagate the isophote directions into the inpainting domain. An energy minimization model combined with the zero divergence condition is used to get a nonlinear Stokes equation. Both steps reduce to the solving of some nonlinear partial differential equations. The discretization and the experimentation of the method are illuminated in details. We also present compare and analysis of the effects between the traditional TV model arid our improved method.