Image Inpainting Based On Partial Differential Equation

Image inpainting is a technology with wide application prospects.As a branch of digital image processing,it has become an important research direction in computer vision and other disciplines.During the process of collecting,transmitting and storing the image,some of the information may be lost or contaminated.Image inpainting is the technique of restoring the damaged pixels through the pixel information of the unbroken area,so that the inpainting result is suitable for human vision.According to the type of image,the restoring method can be divided into texture image inpainting and non-texture image inpainting.This paper mainly considers the process of non-texture image inpainting through the partial differential equation models.TV model and CDD model are traditional variational differential equation models.These low-order equations can repair small-scale damaged images,but for the images that loss large-scale information,the results are not satisfactory.In this paper,the CahnHilliard(C-H)equation model is used for image inpainting.In this paper,the C-H equation model is used to deal with binary image inpainting first.As for the numerical method,we use the tailored finite point method to construct numerical discrete scheme.Compared with the convex splitting method,TFPM reduces the parameters in the model and the computational efficiency can be improved.For binary images,the tailored finite point method of C-H model has a better inpainting effect.In particular,this model shows good result when dealing with large-scale information loss.By adjusting the potential well function W(u)and introducing the imaginary part,we get the complex version of the C-H equation and use this model to achieve restoration of grayscale images as well as binary images.In this paper,the fourth-order equation is transformed into two coupled second-order equations,and the equation with nonlinear term is solved by TFPM,the other one is solved by traditional method.The numerical results show that this model has a good inpainting effect on the grayscale image with scratches and watermarks.More theoretical analysis,such as convergence analysis,remains to be further studied.