%??用GAC水平集演化方法檢測圖像輪廓
close?all;
clear?all;
a=imread（‘1.png‘）;
%?figure;imshow（a）;
a=rgb2gray（a）;?
im=imresize（a[100?100]）;
%?figure;imshow（im）;
imsize=size（im）;
im_1=double（im）;
%?對圖像進(jìn)行高斯濾波
sigma=2;
gauss_filter=fspecial（‘gaussian‘3sigma）;??%默認(rèn)值3*3SIGMA=0.5
b=imfilter（im_1?gauss_filter‘conv‘）;

%?計(jì)算圖像梯度[IxIy]和梯度模值deltI
[Ix?Iy]=gradient（b）;
deltI=abs（sqrt（Ix.^2+Iy.^2））;
k=2;
g=exp（-deltI./k）;
[gxgy]=gradient（g）;

%?初始化圓，定義中心和半徑
center=[floor（size（im）/2）];
radius?=?min（center）-8;
u?=?init_u（?imsize?center?radius）;

%?調(diào)用迭代函數(shù)
filename?=?‘1.png‘;
m_name?=?filename（?1?:?strfind（?filename?‘.‘?）?-?1?）;
num=400;
u_new=die_dai（imugnumm_name）;

%下面是子程序
function??u=die_dai（imugnumm_name
[mn]=size（u）;
[gxgy]=gradient（g）;
u1=u;
newpic=im;?
??????????for?i=2:m-1???????????????
?????????????for?j=2:n-1
?????????????????if?（u（ij）*u（i+1j）<0）|（u（ij）*u（ij+1）<0）==1??
?????????????????????newpic（ij）=0;
?????????????????end
?????????????end
??????????end
figure;imshow（newpic）;???

[gxgy]=gradient（g）;
det=0.05;c=3;dx=1;dy=1;display_it=10;
for?k=1:num
?????if?mod（k5）==0
????????u=re_init_u（?u?）;
?????end

%x和y方向的前向差分和后向差分
diff_x_backward=（?u?-?circshift（?u?[?0?1?]?）?）;
diff_x_forward=（?circshift（?u?[?0?-1?]?）?-?u?）;
diff_y_backward=（?u?-?circshift（?u?[?1?0?]?）?）;
diff_y_forward=（?circshift（?u?[?-1?0?]?）?-?u?）;

du_1=g.*c.*?（?（max（?diff_x_forward0?））.^2?+?（min（?diff_x_backward0?））.^2?+（max（?diff_y_forward0?））.^2?+?（min（?diff_y_backward0?））.^2）;
%計(jì)算更新u的第二部分
du_2=max（gx0）?.*?diff_x_backward?+?min（gx0）?.*?diff_x_forward?+?max（gy0）?.*?diff_y_backward??+?min（gy0）?.*?diff_y_forward??;
%--------

%計(jì)算更新u的第三部分
%中心差分
diff_y_central=（?circshift（?u?[?0?-1?]?）?-?circshift（?u?[?0?1?]?）?）?/?2;
diff_x_central=（?circs