Find matrix inside larger matrix with tolerance

How can I write a script to find a smaller matrix B inside a larger matrix A with a specified tolerance and return the index/indices where B starts in A? For example, with a tolerance of 0.1:

A =

8 1 4 8 8 5

8 3 10 2 3 10

4 1 1 5 7 4

7 1 5 5 7 6

2 9 4 7 2 3

8 7 8 8 2 8

B =

0.9 1.1 5

1.1 5 4.9

9 3.9 7.1

index = (2,3)

[DGM]

You'll need to define your testing criteria before a tolerance metric has meaning. A tolerance of 0.1 might mean any number of things depending on what the goal was. Consider the matrix B and the corresponding region in A at any given point during evaluation (Ax)

• Match occurs if all(abs(Ax-B)<0.1) (probably what you want?)
• Match occurs if all(rms(Ax-B)<0.1)
• Match occurs if mean2(Ax-B)<0.1
• Match occurs if sum(Ax-B)<0.1

Depending on how loose your requirements are, you may simply be able to use normxcorr2() if you just want to find the closest, if inexact match.

A logical filter as described above could otherwise be implemented using nlfilter() and a user-defined function to make the comparison. That said, if it's something you need to use often, you might find nlfilter() to be inconveniently slow. Replacing it with a simple sliding window routine is often faster.

Answer 1

[DGM]

As I mentioned, you can do this with nlfilter()

A = [8  1  4  8  8  5;
    8  3  10  2  3  10;
    4  1  1  5  7  4;
    7  1  5  5  7  6;
    2  9  4  7  2  3;
    8  7  8  8  2  8];
B = [0.9  1.1  5;
    1.1  5  4.9;
    9  3.9  7.1];
tol = 0.1;

% use nlfilter() 
F = @(x) all(abs(x-B)<=(tol+eps),'all');
map = nlfilter(A,size(B),F) % logical map of matches
[row col] = find(map) % if you really want subscripts instead
% can't run nlfilter() in the browser, so there are no example outputs here

Or you could just do the same process without nlfilter()

filtsize = size(B);
s0 = size(A);
padsize = floor(filtsize/2);
% nlfilter() uses zero-padding, but you could replicate, etc
A = padarray(A,padsize,0,'both');
s = size(A);

matches = false(s0);
osm = filtsize(1)-1;
osn = filtsize(2)-1;

for n = 1:(s(2)-2*padsize(2))
    for m = 1:(s(1)-2*padsize(1))
        sample = A(m:(m+osm),n:(n+osn));
        matches(m,n) = all(abs(sample-B)<=(tol+eps),'all');
    end
end
matches % logical map of matches

matches = 6×6 logical array
   0   0   0   0   0   0
   0   0   0   0   0   0
   0   0   0   0   0   0
   0   0   1   0   0   0
   0   0   0   0   0   0
   0   0   0   0   0   0

[row col] = find(matches) % if you really want subscripts instead

row = 4

col = 3