Hu矩

close all;
clear all;
I1=imread('lena.bmp');
angle=;
T=[cos(angle),sin(angle),;-sin(angle),cos(angle),;,,];
t1 = maketform('affine',T);
I2 = imtransform(I1,t1,'bilinear','fill',);%旋转
I2=imresize(I2,0.5);%缩放
figure;
imshow(I1);
figure;
imshow(I2);
H1=Humoment(I1)
H2=Humoment(I2)

function Hu = Humoment(I)
I=double(I);
m00=sum(sum(I));
m10=;m01=;
[row,col]=size(I);
for i=:row
    for j=:col
        m10=m10+i*I(i,j);
        m01=m01+j*I(i,j);
    end
end
xb=m10/m00;%重心坐标
yb=m01/m00;

%中心距
u02 = ;u03 = ;u11 = ;u12 = ;u20 = ;u21 = ;u30 = ;
for i=:row
    for j=:col
        u02=u02+(j-yb)^*I(i,j);
        u03=u03+(j-yb)^*I(i,j);
        u11=u11+(i-xb)*(j-yb)*I(i,j);
        u12=u12+(i-xb)*(j-yb)^*I(i,j);
        u20=u20+(i-xb)^*I(i,j);
        u21=u21+(i-xb)^*(j-yb)*I(i,j);
        u30=u30+(i-xb)^*I(i,j);
    end
end

%归一化中心距
n02=u02/m00^;
n03=u03/m00^2.5;
n11=u11/m00^;
n12=u12/m00^2.5;
n20=u20/m00^;
n21=u21/m00^2.5;
n30=u30/m00^2.5;        

%Hu矩
h1 = n20 + n02;
h2 = (n20-n02)^ + *(n11)^;
h3 = (n30-*n12)^ + (*n21-n03)^;
h4 = (n30+n12)^ + (n21+n03)^;
h5 = (n30-*n12)*(n30+n12)*((n30+n12)^-*(n21+n03)^)+(*n21-n03)*(n21+n03)*(*(n30+n12)^-(n21+n03)^);
h6 = (n20-n02)*((n30+n12)^-(n21+n03)^)+*n11*(n30+n12)*(n21+n03);
h7 = (*n21-n03)*(n30+n12)*((n30+n12)^-*(n21+n03)^)-(*n12-n30)*(n21+n03)*(*(n30+n12)^-(n21+n03)^);
Hu = [h1 h2 h3 h4 h5 h6 h7];   

结果：

对于两图像做测试，其中第二幅是第一幅旋转30度并缩小到1/4大小：

上述两幅图计算出的Hu矩都为：

0.0012    0.0000    0.0000    0.0000   -0.0000   -0.0000    0.0000