Image Processing Methods Based On Nonlinear Dynimics

The purpose of image processing is to extract the features from an image in lower quality,which is good to the image analysis and the further research.In order to successfully realize all kinds of operation in image processing,it’s necessary to study the mathematical theory on nonlinear systems.What’s more important,to understand and grasp the knowledge of nonlinear dynamics properties of the model in accurate way is the key to realize the image processing.This paper proposes two kinds of nonlinear models,which are FitzHugh-Nagumo neuron oscillator model and Hopfield neural network model,and finally they are applied to mage processing.The main contents and innovation are as follows:1.The dynamical properties of FitzHugh-Nagumo model are studied and the cases when the parameters enable each equilibriums stable are given. Then the basic principle of image enhancement and the method of getting an image similar to image binarization are presented.Finally,the conclusions are proved to be right by Matlab.When the system has only one equilibrium point,the model can achieve image enhancement.However,when there are three equilibrium points,the model can get an image similar to binarization.2.Futher study of discrete FitzHugh-Nagumo model with diffusion is made and applied to image processing.On one hand,an algorithm of improved threshold " a " which self-organizes its values depending on the gray level of an image by ordinary differential model is proposed.lt is simple and flexible in realizing the image enhancement and edge detection.On the other hand, an algorithm of improved threshold "a" which self-organizes its values depending on the gray gradient of an image by FitzHugh-Nagumo reaction-diffusion model is proposed. Applying it to a gray image,it achieves edge detection. Compared with the previous algorithm in the experiment,to a certain extent,the proposed method improve the integrity of edge detection.3.The principle of image restoration by the Hopfield neural network model is described. The algorithm of Hopfield neural network,in which its state changes continuously,is used to the irregular motion blur image.The results confirm the validity of this method.