Distinguish a simply connected figures?

Question

So I have a binary matrix in Matlab. It is basically a blob (pixels of value 1) surrounded by a neutral background (value 0).

I want to figure out whether this blob is simply connected or not. Figure below is a straightforward example.

How can this be achieved? Notably I understand that every path in a pixelated image can be created by choosing from 4 adjacent elements (up, down, left, right) or 8 adjacent elements etc - it doesn't matter in this case.

Answer 1

Code

%// Assuming bw1 is the input binary matrix

[L,num] = bwlabel( ~bw1 );
counts = sum(bsxfun(@eq,L(:),1:num));
[~,ind] = max(counts);
bw2 = ~(L==ind);

%// Output decision
[L,num] = bwlabel( bw1 );
if ~nnz(bw1~=bw2) && num==1
    disp('Yes it is a simply connected blob.')
else
    disp('Nope, not a simply connected blob.')
end