[1] S. Lankton和A.Tannenbaum在2008年发表的文章《Localizing Region-Based Active Contours》。该研究提出了一种基于区域的主动轮廓局部化方法，为本文的实现框架提供了重要的参考。
[2] A Yezzi Jr, A Tsai, A Willsky在1999年的文章《A statistical approach to snakes for bimodal and trimodal imagery》。这篇文章介绍了一种基于统计方法的蛇算法，用于处理双模态和三模态图像。本文在实现Mean Separation模型时借鉴了该方法，并进行了本地化的改进。
[3] Chan, T. F., & Vese, L. A.在2001年发表的文章《Active contours without edges》。该研究提出了一种无边缘的主动轮廓方法，能够有效地处理图像中缺乏明显边缘的情况。本文在实现Chan-Vese模型时参考了该方法，并进行了相应的本地化调整。
function seg = local_AC_MS(Img,mask_init,rad,alpha,num_it,epsilon)
% This function aims to implement Shawn Lankton's local active contour. And
% the energy model is the MS model as defined in eq.(15)-(19).
% The local variables are calculated by filtering operation instead of
% iterating inspired by Chunming Li's IEEE TIP 2008 paper
%
% One small change is that I used a square window instead of disk for
% localization
%
% Input:
% 1. Img: image needs to be segmented
% 2. mask_init: intialization represented by binary image
% 3. rad: the side length of the square window
% 4. alpha: the coeficicent to balance the image fidality term and the
% curvature regularization term
% 5. num_it: maximum number of iterations
% 6. epsilon: epsilon used for delta and heaviside function
% Created by Jincheng Pang, Tufts University @11/09/2012
phi0 = mask2phi(mask_init);
phi = phi0;
B0 = ones(2*rad+1,2*rad+1);
% B0 = fspecial('disk',rad);
KI=conv2(Img,B0,'same');
KONE=conv2(ones(size(Img)),B0,'same');
for ii = 1:num_it
mask = Heaviside2(phi,epsilon);
I=Img.*mask;
temp1=conv2(mask,B0,'same');
temp2=conv2(I,B0,'same');
c1=temp2./(temp1); % local mean value inside
c2=(KI-temp2)./(KONE-temp1); % local mean value outside
A1 = temp1;
A2 = conv2(1-mask,B0,'same');
%%%%%
D = (A1.*A2+eps);
term1 = (A2-A1)./D;
term2 = (A2.*c1.^2-A1.*c2.^2)./D;
term3 = (A2.*c1-A1.*c2)./D;
dataForce = conv2(term1.*Dirac2(phi,epsilon),B0,'same').*Img.*Img + conv2(term2.*Dirac2(phi,epsilon),B0,'same')-2.*Img.*conv2(term3.*Dirac2(phi,epsilon),B0,'same'); %%% During the implementation, Img should be separated out of the filtering operation!!!
