Normalized cross-correlation function

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

.

[devi sowjanya]

Can you please provide the framing function code

Answer 1

[Kirby Fears]

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.

[Manolis Michailidis]

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.

Answer 2

[Kirby Fears]

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.

[Manolis Michailidis]

Hello, indeed the index starts from 0 but matlab's indexing is from 1 so i considered that in mind. The pre-allocating is not my primary concern , on the other hand i know the xcoor(...,'coeff') can do it , but i wanted to write my own function , so do you have any ideas where is the error? thank you.

[Kirby Fears]

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.

Answer 3

[Image Analyst]

Do you have the Image Processing Toolbox? If so, why not just use the built-in function normxcorr2()?

[Manolis Michailidis]

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.