huc.m

图像对齐（inage registration）工具箱

function f=hu(a)
%Computing Hu moment invariants with central  moments, normalized for contrast
% a(n,n) - image matrix
 
 n=size(a,1);
 m00 =sum(sum(a));
 v=ones(1,n);
 w=1:1:n;
 ii=w'*v;
 jj=ii';
 
 tx=sum(sum(a.*jj))/m00; 
 ty=sum(sum(a.*ii))/m00;
 
 jj=jj-tx ;
 ii=ii-ty;
 
 q=2;

 m11=sum(sum(a.*jj.*ii));
 m02=sum(sum(a.*ii.*ii)); 
 m20=sum(sum(a.*jj.*jj)); 


 m11=(m11/(m00^q));
 m02=(m02/(m00^q));
 m20=(m20/(m00^q));

 q=2.5;
 
 m12=sum(sum(a.*ii.*jj.*ii));
 m21=sum(sum(a.*jj.*jj.*ii));
 m30=sum(sum(a.*jj.*jj.*jj));
 m03=sum(sum(a.*ii.*ii.*ii));
 
 
 m12=(m12/(m00^q));
 m03=(m03/(m00^q));
 m30=(m30/(m00^q));
 m21=(m21/(m00^q));


 f(1)=m20+m02;

 
 
 f(2)=(m20-m02)^2 +4*m11^2;

 
 f(3)=(m30-3*m12)^2 + (m03-3*m21)^2;

 f(4)=(m30+m12)^2 + (m03+m21)^2;

 f(5)=(m30-3*m12)*(m30+m12)*((m30+m12)^2-3*(m03+m21)^2);
 f(5)=f(5)+(3*m21-m03)*(m03+m21)*(3*(m30+m12)^2-(m03+m21)^2);

 
 f(6)=(m20-m02)*((m30+m12)^2-(m03+m21)^2);
 f(6)=f(6)+4*m11*(m30+m12)*(m03+m21);

 
 f(7)=(3*m21-m03)*(m30+m12)*((m30+m12)^2-3*(m03+m21)^2);
 f(7)=f(7)+(3*m12-m30)*(m03+m21)*(3*(m30+m12)^2-(m03+m21)^2);