Study Of Image Denoising, Inpainting And Zooming On Partial Differential Equation

Recently, image process technology based on the partial differential equation ( PDE) plays an very important role in the fields of image process and computer vision. It gained the people's wide attention. Using the religious and effective partial differential method as the mathematics tool, all of the math modeling, numerical schemes and application on nonlinear diffusion denoising, mean curvature motion, image segmentation, image inpainting and image zooming were researched in this paper. The paper includes the following five aspects:1. The isophote curvature was introduced in the nonlinear diffusion equation as a new control factor in order to build a novel diffusion model which combined the Curvature-driven with Edge-stopping (abbreviated as C&E model). Experiments show that, using the C&E model in the image denoising, images can be smoothed better.2. As the relaxation algorithm and additive operator splitting (AOS) algorithm were introduced into numerical schemes of level set method, the evolution precision and efficiency of curves was improved.3. The Geodesic Active Contour (GAC) model, the promotion GAC model and the improved GAC model were systematically studied in this paper. Image segmentation was realized by the level set method.4. The C&E model was used to repair the destroyed non-texture gray and color image. The C&E model Compared with BSCB (M.Bertalmio, G.Sapiro, V.Caselles and C.Ballester) and CDD (Curreture-Driven Diffusion) methods, experiment results show that the C&E model exhibits better performance in inpainting of non-texture grey and color image. 5. Nonlinear partial differential method which is combined nonlinear diffusion equation (P-M equation) with the median filtering was proposed and can be applied to image zooming. Experiments show that the zooming effect is better than the the isotropic linear PDE method.Based on the C&E model, the paper formed a PDE system of image denoising, image inpainting and image zooming. It provided key technologys of numerical schemes of level set method. The paper widen the research of method and range of apply in image process.