Normalized cross-correlation function
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Hello, i am trying to write a normilized cross-correlation method function , but i can't complete it. Here are the details of the formula :
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/149206/image.png)
My code is
x=rand(1,1000);
N=length(x); %// length of signal
n1=128; %// length of window
xf=framing(x,n1,n1/2,rectwin(n1)); %this function frames the signal i will get xf(128,14)
win_num=size(xf,2);
for col=1:win_num
for m=1:n1+1
for n=1:n1-m
ccor(m,col)=sum(xf(n+m,col)*(xf(n,col)))/ sqrt(sum(xf(n)^2)*sum(xf(n+m)^2) );
end
end
end
Note that i want to see the correlation values betwen -1 and 1 like in the figure but instead i get
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/149208/image.png)
.
채택된 답변
Kirby Fears
2015년 9월 21일
편집: Kirby Fears
2015년 9월 21일
Hi Manolis,
To directly replicate what the equations say (shifting indices with +1), the calculation would look more like this:
x=rand(1,1000);
N=length(x); %// length of signal
n1=128; %// length of window
xf=framing(x,n1,n1/2,rectwin(n1)); %this function frames the signal i will get xf(128,14)
win_num=size(xf,2);
% M0=???
ccor=NaN(M0+1,win_num);
for col=1:win_num
for m=1:M0+1,
[term1,term2,term3]=deal(0);
for n=1:N-m,
term1=term1+xf(n,col)*xf(n+m,col);
term2=term2+xf(n,col)^2;
term3=term3+xf(n+m,col)^2;
end
ccor(m,col)=term1/sqrt(term2*term3);
end
end
You would just need to explicitly specify M0. This calculation can be simplified as follows:
x=rand(1,1000);
N=length(x); %// length of signal
n1=128; %// length of window
xf=framing(x,n1,n1/2,rectwin(n1)); %this function frames the signal i will get xf(128,14)
win_num=size(xf,2);
% M0=???
ccor=NaN(M0+1,win_num);
for col=1:win_num
for m=1:M0+1,
term1=sum(xf(1:N-m,col).*xf(1+m:N,col));
term2=sum(xf(1:N-m,col).^2);
term3=sum(xf(1+m:N,col).^2);
ccor(m,col)=term1/sqrt(term2*term3);
end
end
I don't have the toolbox required to run this code, so it may have bugs. Hope this helps.
추가 답변 (2개)
Kirby Fears
2015년 9월 18일
편집: Kirby Fears
2015년 9월 18일
Hi Manolis,
You are looping n and m by starting at 1, but in the formula you posted the sum starts at 0. You will need to correct your calculations to include the 0 terms in the summation. You should also consider pre-allocating "ccor" to save yourself some computational time.
You may have access to the xcorr function which calculates cross correlations. It has several options to control normalization.
Hope this helps.
댓글 수: 2
Kirby Fears
2015년 9월 21일
Indeed the loop variables are only used as indices, so you are correct. My mistake. I assumed the loop variables were also used as numeric values in the summand. I'm writing another answer below.
Image Analyst
2015년 9월 29일
Do you have the Image Processing Toolbox? If so, why not just use the built-in function normxcorr2()?
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