How can I find the number of specific submatrices inside a matrix?

Hi, If i ran this code,

A = randi([0, 1], [10,10]) 

I would get something like

A =

     1     0     0     1     1     1     1     0     1     0
     1     1     0     0     1     0     0     0     0     1
     1     0     1     0     1     1     0     1     1     1
     1     0     1     0     0     1     0     1     1     0
     1     0     1     0     1     0     0     1     0     1
     0     0     0     1     1     1     1     0     0     0
     0     1     0     1     0     1     1     0     1     1
     0     0     0     1     0     1     0     0     0     0
     1     1     0     1     0     1     0     1     1     0
     1     1     0     1     1     0     1     1     1     0

In this matrix i want to find how many instances the submatrix B occurs.

     B = [1 1 ; 1 1]

Does anyone know of an easy way I can achieve this?

[Torsten]

if-statement in for loop over the number of rows and columns of A ?

Answer 1

[Matt J]

    Sa=conv2(A.^2,ones(2),'valid');
    Sb=sum(B(:).^2);

    n= nnz( conv2(A, rot90(B,2),'valid').^2==Sa.*Sb );

[Torsten]

A solution for advanced learners :-)

[Matt J]

:-)

[Image Analyst]

While this is correct for the given matrix of all 1's, it won't work in general for other patterns. It works by comparing the number of 1's in a sliding window over A to the number of 1's in B. It doesn't actually match the pattern. So if there are 2 or 3 in B, it would say there is a match even though the pattern is different. You want to use bwhitmiss(), which is a hit or miss transform specifically meant for this. See my answer below for the general answer that works for other patterns.

[Matt J]

Convolution will work, but needed adjustment to deal with arbitrary patterns of integers;

Answer 2

[Image Analyst]

You want to use the "hit or miss transform" done by bwhitmiss(). Using conv2 will not work for arbitrary patterns. See illustrations below:

A =[...
    1     0     0     1     1     1     1     0     1     0
    1     1     0     0     1     0     0     0     0     1
    1     0     1     0     1     1     0     1     1     1
    1     0     1     0     0     1     0     1     1     0
    1     0     1     0     1     0     0     1     0     1
    0     0     0     1     1     1     1     0     0     0
    0     1     0     1     0     1     1     0     1     1
    0     0     0     1     0     1     0     0     0     0
    1     1     0     1     0     1     0     1     1     0
    1     1     0     1     1     0     1     1     1     0];
B = logical([0, 1; 1, 1]);
numMatchesMJ = nnz( conv2(A,B,'valid')==nnz(B) ) % 10 is incorrect

numMatchesMJ = 10

BW = bwhitmiss(A,B,~B);
BW = BW(1:end-1, 1:end-1) % 1 if upper left corner matches.

BW = 9×9 logical array
   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   0   0   0
   0   0   0   1   0   0   0   0   0
   0   0   0   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0
   0   0   0   0   0   0   0   0   0
   0   0   0   0   0   0   1   0   0

numMatches = nnz(BW) % 3 is correct.

numMatches = 3

% Another example
B = logical([1, 0; 1, 1]);
numMatchesMJ = nnz( conv2(A,B,'valid')==nnz(B) ) % 7 is incorrect

numMatchesMJ = 7

BW = bwhitmiss(A,B,~B);
BW = BW(1:end-1, 1:end-1) % 1 if upper left corner matches.

BW = 9×9 logical array
   1   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   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   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

numMatches = nnz(BW) % 4 is correct.

numMatches = 4