%基于小波變換模極大的多尺度圖像邊緣檢測matlab源代碼 該算法采用的是樣條小波，
% 為了更好的檢測邊緣，用a tuous 算法代替了mallat算法。 
% 該算法和mallat快速算法主要區別： 
% 1 a tuous 算法不需要抽取偶數樣本，所以奇異檢測定位更準確，相應的重構是不需要插零。
% 2 a tuous 算法需要對濾波器進行伸縮。 

clear all;
load woman;
I = ind2gray(X,map);
imshow(I);
I1 = imadjust(I,stretchlim(I),[0,1]);
figure;imshow(I1);
[N,M] = size(I);

h = [0.125,0.375,0.375,0.125];
g = [0.5,-0.5];
delta = [1,0,0];

J = 2;

a(1:N,1:M,1,1:J+1) = 0;
dx(1:N,1:M,1,1:J+1) = 0;
dy(1:N,1:M,1,1:J+1) = 0;
d(1:N,1:M,1,1:J+1) = 0;

a(:,:,1,1) = conv2(h,h,I,'same');
dx(:,:,1,1) = conv2(delta,g,I,'same');
dy(:,:,1,1) = conv2(g,delta,I,'same');

x = dx(:,:,1,1);
y = dy(:,:,1,1);
d(:,:,1,1) = sqrt(x.^2+y.^2);
I1 = imadjust(d(:,:,1,1),stretchlim(d(:,:,1,1)),[0 1]);
figure;
imshow(I1);

lh = length(h);
lg = length(g);

for j = 1:J+1
    lhj = 2^j*(lh-1)+1;
    lgj = 2^j*(lg-1)+1;
    hj(1:lhj)=0;
    gj(1:lgj)=0;
    for n = 1:lh
        hj(2^j*(n-1)+1)=h(n);
    end
    for n = 1:lg
        gj(2^j*(n-1)+1)=g(n);
    end
    a(:,:,1,j+1) = conv2(hj,hj,a(:,:,1,j),'same');
    dx(:,:,1,j+1) = conv2(delta,gj,a(:,:,1,j),'same');
    dy(:,:,1,j+1) = conv2(gj,delta,a(:,:,1,j),'same');
    x = dx(:,:,1,j+1);
    y = dy(:,:,1,j+1);
    dj(:,:,1,j+1) = sqrt(x.^2+y.^2);
    I1 = imadjust(dj(:,:,1,j+1),stretchlim(dj(:,:,1,j+1)),[0 1]);
    figure;imshow(I1);
end