The Application Of Partial Differential Equation In Image Processing

This article mainly studies the application of the digital image process based on PDE. Firstly, the article expatiates on the concept and property of scale space, and give the relationship between continuous scale space and the PDE model, for example, the heat exchange equation ascertain the gauss scale space. Following with the simple linear diffusion equation, it introduces the nonlinear isotropic diffusion and the nonlinear anisotropic diffusion. It not only presents corresponding idiographic diffusion equation models, but also compares the different effects of them in image processing.Afterward, the article analyses the inevitable relationship between the minimum energy of grads and anisotropic diffusion equations. It begins with the method of energy analysis, then constructs variational problem, gets the original model at last.Then, the article analyses the inevitable relationship between the nonlinear filters and anisotropic diffusion equations. It starts with the discussion of format of each kinds of diffusion equations, then analyses their filtering theory one by one, then discovers the deficiency of each diffusion equations in frequency domain. To remedy the deficiency, it goes on with the construction of filter, makes the filter come true with the iterative method in time domain.Finally, according to the rule between each items of PDE and image processing, it improves the original model for the goal of noise-removing, edge enhancement, remaining the original image's information. The difficulty of image processing---edge's noise-removing and blur-removing, will be answered preferably by this article. As the result indicate, the image processed by this method is quite notable in the aspect of SNR enhancement. This article analyses the function of each PDE's items in image processing from the mathematical view, by which we constructs the diffusion model which not only generates the new arithmetic in the article, but also paves the way for people's further research in this field.This dissertation is funded by the opening foundation of the state key laboratory of plastic forming simulation and die and mould technology. The arithmetic of the paper is carried out by programming in matlab, and is verified very effective.