Correspondence label and coordinates' points

Question

How to obtain the coordinates of the first and the last appearances (under column-major ordering) of each label present in a matrix?

Example of a label matrix (where labels are 1 to 4):

L = [    
     1 1 1 1 0 0 0 0
     0 0 0 0 2 2 0 0
     0 0 0 0 0 0 2 0
     0 0 0 0 0 0 0 0
     0 0 0 0 0 3 0 0
     0 0 0 0 0 0 3 3
     0 0 0 4 0 0 0 0
     4 4 4 0 0 0 0 0
    ];

For the above example L, I would like to obtain a matrix of coordinates like:

M = [
    1 1 1
    1 4 1
    2 5 2
    3 7 2
    5 6 3
    6 8 3
    8 1 4
    7 4 4 ];

Where the 1^st column of M contains horizontal coordinates, the 2^nd contains vertical coordinates, and the 3^rd column contains the label. There should be 2 rows for each label.

Answer 1

With for-loop you can do it like that:

M=zeros(2*max(L(:)),3);
for k=1:max(L(:))
   [r,c]=find(L==k);
   s=sortrows([r c],2);
   M(k*2-1:k*2,:)=[s(1,:) k; s(end,:) k];
end

M =
 1     1     1
 1     4     1
 2     5     2
 3     7     2
 5     6     3
 6     8     3
 8     1     4
 7     4     4

Maybe somehow with regionprops options you can do it without the loop...