Partial Differential Equations-based Image Repair

This paper first extends the image processing theory to image inpainting field, and discusses the processes of establishing inpainting models. We explain several inpainting models using Coarea formula and get a uniform format of a kind of inpainting models. We propose a new image processing method based on PDE with the reference of curve and level-set function involution theories. Then we establish two inpainting equations using this method. These equations reconstruct missing image information by connecting the broken level lines reaching the damaged regions. The curvature driven inpainting model has simpler algorithm and faster convergence speed compared to the other algorithms that can get the same results. The revised model forces the constructed image to have smooth level lines and sharp edges, so it can improve the inpainting effects deeply. Finally, this paper analyzes the digital TV filter, proposes an adaptive operator λa controlling the difference of the restored image and the original image, and gets a revised digital TV filter.