Find matrix inside larger matrix with tolerance

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Richard Batelaan
Richard Batelaan 2021-6-21
回答： DGM 2021-6-21
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)
  1 个评论
DGM
DGM 2021-6-21
编辑：DGM 2021-6-21
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.

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采纳的回答

DGM
DGM 2021-6-21
Ran in:
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

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