Image Patches In The Pde Model

The image inpainting is becoming one of the most positive regarded problems in international during recent years. This technology is using the information around the destroyed area to renew or fill in the missing data. At present, the most used tools are partial differential equations, which had taken a great result after a lot of improvement. But still these partial differential equations have some flaws somewhat. At first, this paper presents the image inpainting theory, the theory of establishing inpainting models and the request and principia of low level image inpainting. And then explains several important geometric information in the inpainting model such as the gradient vector and its module, the Laplace operator and the curvature. We are presenting two classes of inpainting models. One of them is the model based on variation, we give emphasis to the total variation model and the Euler's elastica model, then briefly presents the Mumford-Shah model and the Mumford-Shah-Euler model. Another one is the model based on PDE, including the BSCB model and the CDD model. The BSCB did inpaint besides a complex anisotropic diffusion equation so it's hard to do numerical implement, in addition, the CDD did use the amount curvature and this could not describe the curvature in a good way, so we improve these model in this paper. The primary works we do are1. The BSCB model is inpainting by two separated processes, which are transference and diffusion. This paper chose an anisotropic diffusion item to add to the inpainting model, and then the model can do transferring and diffusing at one time. At last, we explain the numerical implementation and the result.2. The CDD model adds the curvature of image to TV model to solve the connection problem, and get a better result. Usually we use the plane curvature equation. We extend the problem from a plane to a surface. We compute with the mean curvature of the main curvatures and get the better result.3. Based on the Euler' elastic model, we get a new model by coupling the BSCB model and the CDD model, which combines the normal and tangent directions inpainting to get a good result.4. Given a uniform format of all these models presented before.