Image inpainting and denoising by nonlinear partial differential equations

A new approach is presented for recovering shapes from noisy and damaged images as well as the filling in of missing information or the removal of objects from an image. The procedure allows for the denoising and inpainting of images simultaneously. The denoising is performed by the smoothing equation working inside and outside of the inpainting domain but in completely different ways. Inside the inpainting domain the smoothing is carried out by the mean curvature flow, while the smoothing of the outside of the inpainting domain is carried out in a way to encourage smoothing within a region and discourage smoothing across boundaries. Besides smoothing, the approach here presented permits the transportation of available information from the outside towards the inside of the inpainting domain. This combination permits the simultaneous use of filling-in and differentiated smoothing of different regions of an image. The experimental results show the effective performance of the combination of these two procedures in image restoration.