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 :
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
.
  1 Comment
devi sowjanya
devi sowjanya on 6 Mar 2021
Can you please provide the framing function code

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Accepted Answer

Kirby Fears
Kirby Fears on 21 Sep 2015
Edited: Kirby Fears on 21 Sep 2015
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.
  1 Comment
Manolis Michailidis
Manolis Michailidis on 29 Sep 2015
Thank you i finally solved it, for M0=n1-1 shifts i had to replace in the loops N with n1 and it works. I get the results i want , from the start i wanted the correlation to be biased it the region [-1 1] and that's what i get. So thanks a lot for your effort.

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More Answers (2)

Kirby Fears
Kirby Fears on 18 Sep 2015
Edited: Kirby Fears on 18 Sep 2015
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.
  2 Comments
Kirby Fears
Kirby Fears on 21 Sep 2015
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.

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Image Analyst
Image Analyst on 29 Sep 2015
Do you have the Image Processing Toolbox? If so, why not just use the built-in function normxcorr2()?
  1 Comment
Manolis Michailidis
Manolis Michailidis on 29 Sep 2015
Yes i have it, i was just curious and wanted to confirm the result with the matlabs, anyway thank you i will take a look at the function you mentioned. It's always nice to learn something new.

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