Research On Image Inpainting And Enlargement Algorithms Based On Partial Differential Equation

The methods for digital image processing are various, among which those based on partial differential equation(PDE) have formed an important branch. The basic idea of them is to inflect an image using a PDE whose solution is the processed image, and then solve it. Although PDEs have been almost applied to the whole field of image processing, this paper is mainly focused on the algorithms of image enlargement and image inpainting.Image enlargement aimed at image resolution enhancement has been studied for many years. It can be done in various ways including those based on PDEs. In this paper, the development of image enlargement in recent years are summarized and analyzed firstly. Then, two algorithms named adjacent interpolation smoothing algorithm and image enlargement algorithm based on diffusivity function are proposed respectively. The former, which combines th adjacent diffusion method and an amended PDE , has low complexity and high quality. The latter can zoom an image in a fractional factor directly, and performs better at both integer and fractional zooming ratios by introducing the diffusivity function of the anisotropy diffusion model into image interpolation. Moreover, combined with the star-shaped interpolation method, the second algorithm is further applied to image inpainting, and called as adaptive interpolation algorithm for image inpainting.Image inpainting refers to reconstructing the corrupt regions where the data are all destroyed. A primary class of the technique is to build up a partial differential equation, consider it as a boundary problem, and solve it by some iterative method. The most respresentative and creative one of the inpainting algorithms is BSCB model. After summarizes the development of image inpainting technique, this paper points the research at the improvement on BSCB model, and proposes three algorithms to solve the two drawbacks of this model. The first is selective adaptive interpolation which develops the traditional adaptive interpolation algorithm by introducing a priority value. Besides much faster than BSCB model, it can improve the inpainting effects. The second takes selective adaptive interpolation as a preprocessing step, reduces the operation time and improves the inpainting quality further. The last one called neighborhood difference diffusion model is a new PDE proposed by this paper. To avoid the produce of blurry edge, it redefines the diffusion direction and information during the process of image inpainting, and solves the problem to some extent.