P-M Equation Of Two Layers Of Grid Image Filtering Algorithm

In recent years, the partial differential equation and mean curvature motion model in the process of image processing attract people’s attention, especially the characterization of partial differential equations to obtain and characterize the evolution of graphics and other aspects of the extraordinary effect, partial differential equations method in image processing has the anisotropic characteristics and the adaptive ability strongly, it can preserve edge texture and details in the process of denoising. So this model has a huge development both in the field of image denoising and enhancement and segmentation.This dissertation mainly introduces the numerical solution of image denosing in the environment of the partial differential equation framework, especially the numerical solution of regularization of P-M. Firstly, we introduce the background and significance and describe the researching situation and the achievements of the image denosing at home and abroad. Then we discuss two types of diffuse filtering model, represente by thermal model of isotropic diffuse model and represented by P-M model of the anisotropic diffuse model. We analyse P-M model, and then pointe out its advantage and disadvantage. Because regularization can eliminate the "morbid" of P-M equation. Therefore, the partial derivative of time can be represented by forward difference and backward difference when studying regularization P-M equation, get the explicit equation and implicit equation. The explicit equation solution does have a better result, and the implicit scheme can not solve the problem efficienly.In order to overcome these shortcomings, we introduce a two step for the format of the numerical solution. It is a two step process which includes explicit algorithm and implicit algorithm. We using explicit scheme in the odd time horizon and using implicit scheme in the even time horizon discrete P-M equation. In the odd time horizon, all the pixels are involve in computing, In the even time horizon, part of the pixels are involve in computing. So the results compute by implicit is different from the size of the original image, we need to have a interpolation operation to get a image which has a same size with the original image. In this two-step process has complete, we compute the average of the two results after the two steps were completed. A large number of comparative experiment demonstrate that our method is more computational and effectively.