Nonlinear Higher Order Partial Differential Equations In Image Inpaiting And Zooming Of Applications

In the passing away of the past decade, the partial differential equations in image processing applications has become applied mathematics, computer vision recognition technology and digital image processing and analysis of the important areas of research focus; in image enhancement, image denoising, image restoration, image zooming, image segmentation, and so has a very wide range of applications; and caused more and more the attention of mathematicians. Study the reasons, the first partial differential equation can directly image gradient, tangent, and other illumination, curvature and other geometric information; they can effectively simulate isotropic diffusion, anisotropic diffusion of information transmission mechanism. Mathematical theory, then, the image processing module for solving partial differential equations have a very mature as a strong variety of numerical methods for their support. Again, partial differential equations in image processing methods beyond the traditional approach has the visual effect.This article explores the targeted partial differential equations in image restoration, image amplification and other aspects of application and research, the main work of research and innovations are as follows:1. From the curvature-driven diffusion model theory of image restoration model of behavior analysis, we obtained the model led to a very slow rate of fixed causes, and correction factors led to the slow removal of singular factor, which lost the edge of the protection mechanism, with the shock filter be amended, resulting in a third-order nonlinear partial differential equations based on the image restoration new model (SF_CDD model), and numerical experiments have achieved good visual effect.2. By the curvature-driven diffusion model inspired design ideas; the curvature tensor diffusion-driven mechanism into the partial differential equation model for image restoration. Numerical experiments show that the algorithm also achieved better visual results.3. A linear affine invariant geometric heat diffusion equation for image zooming, but also the known pixel by raising the temperature to accelerate the heat transfer process, the visual result is better than traditional interpolation amplification.4. Based on the image zooming and repair the mathematical nature of (fill interpolation) the similarity of the images will lead SF_CDD amplification model, due to the diffusion coefficient which contains the geometric information of isophotes, so the mechanism with smooth edges, and because the introduction of image enhancement method - the impact of filter. Hence its protection and even inhibit the phenomenon of sharpening serrated edge effect.