keeping non-zero matrix elements adjacent to each other and ignoring lone elements

Here is an example matrix (but the result shouldn't be constrained to only working on this):

a=zeros(7,7);
a(5,3:6)=1;
a(2,2)=1;
a(2,4)=1;
a(7,1:2)=1

a=
0 0 0 0 0 0 0
0 1 0 1 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 1 1 1 1 0
0 0 0 0 0 0 0
1 1 0 0 0 0 0

I want to get rid of all the 1's that are alone (the noise), such that I only have the line of 1's on the fifth row.

rules: -the 1's are in 'connected lines' if there are adjacent 1's (including diagonally) e.g.:

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

(The connected lines are what I want to keep. I want to get rid of all the 1's that are not in connected lines, the connected lines can intersect each other)

the 'connected lines need to be at least 3 elements long. So in the 7x7 example, there would only be one line that matches this criteria. If a(7,3) was set to 1, then there would be a connected line at the bottom left also I am currently looking at this through a column by column approach, and here is the first draft of my code so far:

   for nnn=2:6
          rowPoss=find(a(:,nnn)==1);
          rowPoss2=find(a(:,nnn+1)==1);

          for nn=1:length(rowPoss)
              if myResult(rowPoss(nn)-1:rowPoss(nn)+1,n-1)==0 %
                  %then?
              end
          end
      end

My difficulty is, during this column by column process, I'd have to enable a way to recognise the beginning of the connected line, the middle of the connected line, and when a connected line ends. The same rules for this, when applied to noise (the lone 1's), would just ignore the lone 1's.

The output I want is basically:

   b=
      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 1 1 0
      0 0 0 0 0 0 0
      0 0 0 0 0 0 0

[Guillaume]

Have you got the image processing toolbox? It's easy if you do.

Answer 1

[Guillaume]

If you have the image processing toolbox, use bwconncomp:

a = [0 0 0 0 0 0 0; 0 1 0 1 0 0 0; 0 0 0 0 0 0 0; 0 0 0 0 0 0 0; 0 0 1 1 1 1 0; 0 0 0 0 0 0 0; 1 1 0 0 0 0 0];

b = zeros(size(a));
cc = bwconncomp(a, 8);
for pidx = cc.PixelIdxList
    if numel(pidx{1}) >= 3
      b(pidx{1}) = 1;
    end
end
b