Image Processing And Appliacation Based On Navier-Stokes Equation

With the continuous development of the society, the digital image has become an indispensable part of people’s lives, so it is particularly important to the image processing. During the production of the images, since the system or other random factors, the resulting images often contain different levels of noise. In order to using these images, we have to filtering these images with noise. There are many commonly image denoising ways, like mean filtering, median filtering, wavelet transform, and so on. In recent years, image denoising based on partial differential equations(PDE) has been rapid developed. Which, the Navier-Stokes(N-S) equation is a basic PDE in fluid mechanics, and it has a certain role in promoting the image processing.Firstly, this paper introduces the N-S equations and Lattice Boltzmann Method(LBM); studies several deterministic image models for understanding the mathematical model of the image in nature; learns several methods of image processing and their connection and lay a foundation for finding a better image processing method. Then, through researching the N-S equation, this paper propose a image denoising model based on the N-S equation. We use the finite difference and the finite element method to solve the proposed model and carry out numerical experiments for different interference on the Matlab and the finite element simulation platform PEPG. Comparison of the results with the regularization of the P-M model shows that the proposed denoising model can not only remove the noise, but also protect the edge features of the image, and the processing effect is better than the regularization of the P-M model on a certain level. At last, this paper focus on the research of LBM, which is a simple and efficient method for the calculation of the traditional numerical calculation method. Using the LBM to deduce the proposed model at the same time determining the the difficulty of LBM. We carry out numerical experiments for the common image and interference on the Matlab by using the LBM of the proposed model. Ultimately concluded the LBM of the proposed model has a better denoising ability and operation efficiency than the P-M model, and further verify the denoising ability of the proposed model.