The AOS Algorithms For Image Processing Based On ROF Model And C-V Model

The AOS algorithms for image processing based on ROF model andC-V modelImage processing is the basis of computer vision and important part of iamge understanding. As electron and computer technology developed, especially , computer and information technic boose, digital image go deep into every field of people lift gradually. such as vision communication, robot guide, physic diagnoses. remote sensing and astronomical observation and so on.In the last century 60s-70s, PDE is introduced into the research of image restoration and denoise. In the 90s, PDE is applied for image processing field systematically. Theoretical system of PDE for image processing formed. Today. In chapter three, we mainly discuss ROF model, namelyand construct AOS scheme for ROF model,where, u^k = (u_1,1^k, u_1,2^k, u_1,3^k,…,. u_i,j-1^k, u_i,j^k, u_i,j+1^k,…, u_N,N-1^k, u_N,N^k)^T, A(uⁿ)_xdenote the difference coefficient matrix of x axis, A(nⁿ)_ydenote denote the difference coefficient matrix of y axis, the elements of matrix is:where. It is obvious that a_ij(uⁿ)_xand a_ij(uⁿ)_yis strictly diagonally dominant matrices. We solve these matrices with AOS algorithm.Then, we programme to implement AOS algorithm of ROF model. Comparing numerical result with explicit scheme. we validate the validity of AOS schemes.In the chapter four, We study the image segmentation model. and stress on Chan and Vese's C-V model which based on Mumford-Shah. theory, namelyWe study the structure of Level Set of C-V model and numerical algorithm. And we improve numerical discrete scheme with AOS schemes:At the last, We programme to implement the AOS algorithm of C-V model.Comparing numerical experiment result with the previous discrete scheme, it shows that AOS algorithm calculation speed is faster than the previous scheme.