An image filtering model based on Universal Partial Differential Equations

Based on the research and analysis of the evolution process of three different level models, a concept of anisotropic diffusion equation which gathers all the majority of them is introduced. Furthermore, we propose the definition of UPDE (Universal Partial Differential Equations)-a more general equation, which is better in diffusion filtering and also keeps the edge´s information in an image at the same time. In addition, UPDE have most of local geometry structure characteristic of above three models. So we can conveniently control the new function through different smoothing parameter. Finally, some applications are shown through the experiment of image patch and smoothing.