Partial Differential Equation In The Digital Image Inpainting

PDE-based digital image processing is a new research topic. Because of its efficiency in experiement, more and more mathematicians begin to notice it. Now, PDEs have been widely used in many aspects of image processing and computer visual,including image segmentation, tracking moving objects, object edges detection , image interpolation and so on. which have been obtained many expected results.The basic idea of analysising image processing problems through PDEs is putting the image information into the PDE models so that we can get the expected results by solving the equations.In this thesis, we focus on the applied models in dealing the image inpainting problem. Furthermore, we will show their different applications such as scratch removal in digital photos and old films, text erasing, disocclusion. Image inpainting is an inverse problem, which is solved by constructing mathematical models, getting the energy function then solving the problem by using variation calculus methods.What noticed us is that the image inpainting model couldn't deal with the images which have lost their crucial information. We will show its limitation in the examples.