Crop matrix based on entries

I am working with matrix that contains only zeros and ones. I am trying to find a way to crop the matrix to include only the parts of the image where there are ones.

[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;

0,0,1,0,0,0,0,0,0,0;

0,1,1,1,0,0,0,0,0,0;

0,0,0,1,0,0,0,1,0,0;

0,0,1,1,0,0,1,1,0,0;

0,0,0,1,0,0,1,1,0,0;

0,0,1,0,0,0,0,0,0,0;

0,0,0,0,0,0,0,0,0,0]

This is just an example of the matrix but I am really working with a 10000x10000 array. The ones are largely near the center of that image so I am trying to basically filter out all of the extraneous zeros. Any ideas on how I would accomplish this?

Answer 1

[Matt J]

A=[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;
 0,0,1,0,0,0,0,0,0,0;
 0,1,1,1,0,0,0,0,0,0;
 0,0,0,1,0,0,0,1,0,0;
 0,0,1,1,0,0,1,1,0,0;
 0,0,0,1,0,0,1,1,0,0;
 0,0,1,0,0,0,0,0,0,0;
 0,0,0,0,0,0,0,0,0,0];

I=find(any(A,2));
J=find(any(A,1));

A=A(min(I):max(I)  , min(J):max(J))

A = 7×7

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

[Alec Bledsoe]

Got it. It took me a second to figure out what was going on there. Thanks for the help.

[Image Analyst]

You could also skip the any() calls:

[r, c] = find(A); % Find all non-zero rows and columns.
ACropped = A(min(r):max(r), min(c):max(c));

Not sure which way is faster - you'd have to try both with tic() and toc() to see.

[Matt J]

Using any() is going to be much faster (EDIT: when there is a thin boundary of zeros) because it requires finding only the first 1 in the columns and rows of A.

A=randi([0,1],6000);
A([1:10,end-10:end],:)=0;
A(:,[1:10,end-10:end])=0;

timeTest(A)

Elapsed time is 0.004106 seconds.
Elapsed time is 0.694781 seconds.
 

When the boundary is thick (as seems to be the case for the OP), using any() is slower, but only because we are not given the matrix in sparse form.

A=randi([0,1],6000);
A([1:2500,end-2500:end],:)=0;
A(:,[1:2500,end-2500:end])=0;

timeTest(A)

Elapsed time is 0.526749 seconds.
Elapsed time is 0.063143 seconds.
 

timeTest(sparse(A))

Elapsed time is 0.001937 seconds.
Elapsed time is 0.006975 seconds.
 

function timeTest(A)

    tic;
    I=find(any(A,2));
    J=find(any(A,1));
    
    [a,b,c,d]=deal(min(I), max(I), min(J), max(J));
    toc;
    
    tic;
    [r, c] = find(A); % Find all non-zero rows and columns.
    [a,b,c,d]=deal(min(r), max(r), min(c), max(c));
    toc

    disp ' ' 
end