# Label connected components in binary image using non-standard pixel connectivity

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Jori Selen on 23 Mar 2020
Commented: Sean de Wolski on 23 Mar 2020
Assume I have the following binary image
BW = [ 1 0 0 0;
0 0 0 0;
0 1 1 0;
0 0 0 0;
0 0 0 0
0 1 1 0 ];
I would like to find all connected components in this binary image, where 2 points are connected if they are at most 2 rows and at most 1 column away from each other and both have the value 1. The function bwlabeln seems to be useful for this task, but it does not provide me the flexibility of specifying the desired pixel connectivity. My problem statement seems to translate to a 5-by-3 pixel connectivity of all ones. Is there any function that can help me here?
The desired labeling of connected components is
L = [ 1 0 0 0;
0 0 0 0;
0 1 1 0;
0 0 0 0;
0 0 0 0
0 2 2 0 ];
and the number of connected components is 2.

Sean de Wolski on 23 Mar 2020
Edited: Sean de Wolski on 23 Mar 2020
Call imdilate with a custom structuring element of your size. This will then expand the regions so they overlap and bwlabel can then do its thing.
After, do a logical index to remove the added values from imdilate.
Id = imdilate(I, custom_element)
L = bwlabel(Id);
L(~I) = 0;

Jori Selen on 23 Mar 2020
Thanks! I cannot seem to get this to work for the MWE I provided above. It is not clear to me what custom_element should be so that I get the 5-by-3 pixel connectivity.
Sean de Wolski on 23 Mar 2020
Hi,
This should work but I may be off by 1 (i.e. test it under other conditions!). More on structuring elements here https://www.mathworks.com/help/images/structuring-elements.html:
BW = [ 1 0 0 0;
0 0 0 0;
0 1 1 0;
0 0 0 0;
0 0 0 0
0 1 1 0 ];
Id = imdilate(BW, ones(2,1));
L = bwlabel(Id);
L(~BW) = 0