Numerical Simulation Of Bz Reaction-Diffusion System And Its Application In Image Processing

Reaction-diffusion system can originally be looked backward into Lotka-Volterra model describing chemical oscillation, early in the 20th century. But the concept for reaction-diffusion system was brought forward formally by Alan Turing in his paper published in 1952 analyzing the chemical basis of morphogenes phenomena in biology. Afterwards, Belousov-Zhabotinsky reaction and CIMA (Chlorite Iodide Malonic Acid) reaction show people continuously evolving chemical waves and stationary Turing patterns respectively and exhibit the magic patterns in reaction-diffusion system. In the past decades, due to deeper researches on reaction diffusion system, it has involved problems in many fields such as physics, chemistry, biology etc and enlarged the area of its applications. So it is important to study reaction-diffusion systems for realizing and mastering many elementary laws of nature.In this thesis, a typical reaction-diffusion system named Belousov-Zhabotinsky reaction-diffusion system is studied. The main work done in this paper focus on as follows:First, the dynamics of reaction-diffusion system are analyzed from two different points of view: reaction-diffusion equations and characteristics of excitable media. Then, chemical waves in such a system are simulated by numerical methods.The applications of reaction-diffusion system in image processing are studied. A series of results are obtained such as grayscale transformation, edge enhancement, extraction for different gray-level tissues respectively, restoration for broken contours, and so on.A kind of nonlinear parallel tool which evolves in discrete time, discrete space and discrete states--cellular automata is used here for computing. According to reaction-diffusion equations and excitable media respectively, two different cellular automata are constructed to improve the computing efficiency.The main innovations in this paper is as follows:A combination of reaction-diffusion method and traditional methods is applied to CT image processing: different gray-level tissues can be extracted effectively by half-toning a CT image at a threshold when a special tissue turns to be foreground. In comparison with traditional methods, our method needs less medical knowledge.For the simulation based on characteristics of excitable media, an improvement on the cellular automata brought forward by Gerhardt is presented here by combining the ideas of Weimar. Then, the cellular automata for image processing are constructed considering the specific situation.