How can I cluster data points according to their adjacency in a matrix?

Hi guys, is there a way which I could separate out the different clusters of 1 (based on adjacency) in a 2D matrix into separate matrices? The input and desired output are as below. Thank you!

input = [0 0 0 0 0 0 0 0;
0 0 0 0 1 1 1 0;
0 0 0 0 1 1 0 0;
0 0 0 0 0 1 0 0;
0 0 1 1 0 0 0 0;
0 1 1 1 1 0 0 0;
0 0 0 0 0 1 0 0] ;


output(:, : , 1) = [0 0 0 0 0 0 0 0;
0 0 0 0 1 1 1 0;
0 0 0 0 1 1 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] ;

output(:, : , 2) = [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 1 0 0 0 0;
0 1 1 1 1 0 0 0;
0 0 0 0 0 1 0 0] ;

Answer 1

[Image Analyst]

Don't use "input" as the name of your variable - it's the name of a built-in function.

To answer your question, use bwlabel() if you have the Image Processing Toolbox:

>> yourMatrix = [0 0 0 0 0 0 0 0;
0 0 0 0 1 1 1 0;
0 0 0 0 1 1 0 0;
0 0 0 0 0 1 0 0;
0 0 1 1 0 0 0 0;
0 1 1 1 1 0 0 0;
0 0 0 0 0 1 0 0] ;
>> labeledMatrix = bwlabel(yourMatrix)
labeledMatrix =
     0     0     0     0     0     0     0     0
     0     0     0     0     2     2     2     0
     0     0     0     0     2     2     0     0
     0     0     0     0     0     2     0     0
     0     0     1     1     0     0     0     0
     0     1     1     1     1     0     0     0
     0     0     0     0     0     1     0     0
     

Now pick out region 2, if that's what you want, using ismember().

>> region2 = ismember(labeledMatrix, 2)
region2 =
  7×8 logical array
   0   0   0   0   0   0   0   0
   0   0   0   0   1   1   1   0
   0   0   0   0   1   1   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
   

If you want them in your 3-D output array, you could do this (untested):

   [labeledMatrix, numRegions] = bwlabel(yourMatrix);
   [rows, columns] = size(yourMatrix);
   output = zeros(rows, columns, numRegions)
   for k = 1 : numregions
       output(:, :, k) = ismember(labeledMatrix, k)
   end