What is the best approach to find a smaller matrix within a larger matrix (may not be identical, but need region if highest match)??

I am looking to find where (and if) in a larger matrix does a smaller matrix lie? I am trying xcorr2, but it seems like sometimes it might return a lower correlation coefficient value in the correlation matrix for positions where there is an exact match, as opposed to some other locations. Eg, Larger matrix [0.1 0.2 0.3 0.4; 0.5 0.6 0.7 0.8; 0.9 1.0 1.1 1.2; 1.3 1.4 1.5 1.6] and smaller matrix [1.0 1.1; 1.4 1.5] returns 4,4 for the element with max value in the correlation matrix (consistent with its definition of the sum of the element-wise product), but I want the return to be 4,3 (location of exact match).

Answer 1

[Image Analyst]

You can't use corss correlation reliably to find a math. It's just a myth. See attached demo for proof. However, you can use normxcorr2() like DGM said, and I'm attaching another demo for that that works on a color image.

Alternatively you can scan the matrix getting a submatrix and using isequal() to compare the submatrix to the template matrix for perfect equality. That would probably be fine for microscopic-sized matrices like the examples you gave.

Answer 2

[DGM]

This isn't really a good answer, since I can't offer an explanation of why it works differently, but it works if I do it like this:

a = [0.1 0.2 0.3 0.4; 0.5 0.6 0.7 0.8; 0.9 1.0 1.1 1.2; 1.3 1.4 1.5 1.6];
b = [1.0 1.1; 1.4 1.5];
c=normxcorr2(b,a)

c = 5×5

0.7001 0.9507 0.9802 0.9849 0.4201 0.6471 1.0000 1.0000 1.0000 0.0731 0.4819 1.0000 1.0000 1.0000 -0.0467 0.4057 1.0000 1.0000 1.0000 -0.1019 -0.4201 -0.9598 -0.9606 -0.9613 -0.7001

[mx,idx] = max(c(:));
[idxr idxc] = ind2sub([5 5],idx)

idxr = 4

idxc = 3

Someone who has more experience with the task can probably offer more help.

[SNIreaPER]

@DGM It looks like a better approach is to find the sum of the squares of the differences, element-by-element (instead of taking the sum of the squares of the products, as in xcorr) and finding the indices corresponding to where this minimum occurs. I gave it some thought, and looks like here is a solution:

clc
clear all
sum=0, sum_min=inf;
A = [0.1 0.2 0.3 0.4; 0.5 0.6 0.7 0.8; 0.9 1.0 1.1 1.2; 1.3 1.4 1.5 1.6];
B = [1.0 1.1; 1.4 1.5];
for i=1:3
    for j=1:3
        temp=A(i:i+1,j:j+1);
        for a=1:2
            for b=1:2
                sum=sum+(temp(a,b)-B(a,b))^2;
            end
        end
        if sum<sum_min
            sum_min=sum;
            imin=i;
            jmin=j;
        end
        sum=0;
    end
end

A(imin:imin+1,jmin:jmin+1)

What I am wondering is, why do people use correlation instead of this. Let's see if anyone has any alternate answers.