MATLAB: Calculating perimeter/circumfrence of regions in a binary image through a different approach than regionprops(BW, ‘perimeter’) *UPDATED*

binary imagecircumfrenceimage processingImage Processing Toolboxperimeterregionprops

Suppose I have a binary image with many different regions in it. One region in the image may look like this:
Using regionprops and the 'perimeter' property, Matlab would calculate the green marked perimeter, which for this region would be 17.9460.
Now, what I want to calculate is a little bit different. It's basically the length of the lines forming the region (marked red in the image). Or in other words, the number of green marked "pixels" in the following image, although the blue marked pixles would have to be counted twice to get the length of the lines:
So this would get a length of all lines (or count of pixels) of 24.
Is there a way to do this using some build in Matlab functions in the Image Processing Toolbox?
Thanks in advance, Best Regards

Best Answer

I tried out a lot of different approaches in the last days and I finally managed to solve this problem. I did this by using Look-Up-Tables and a selfwritten function, that I pass to the Look-Up-Table. So, I basically did this by counting the 'edges' that a single pixel has (not sure if that makes it clear, but here is an image showing this):
Using the following code, I managed to do exactly what the image is showing:
 % create T-Shape:
 mtrx = zeros(7,9);
 mtrx(2, 2:8) = 1;
 mtrx(3:6, 4:6) = 1;
 % create LUT 
 lut = makelut(@checkForPixelEdges, 3);
 % apply LUT to matrix
 out = bwlookup(mtrx, lut);
 % get perimeter
 perimeter = sum(out(:));
the variable out is a matrix containing the numbers shown in the image above, all other matrix positions are equal to zero. Therefore the sum(out(:)) returns the total length of the lines forming the region (shown red in the images in the question above), which in this case means perimeter = 24 (pixels).
The function checkForPixelEdges() looks like this:
 function num = checkForPixelEdges( nhood )
 %   checkForPixelEdges:
 %   This function counts the "edges" surrounding a pixel, by checking the
 %   pixels 4-Neighbourhood-Connectivity.
 %   Input-Arguments:
 %   nhood: Neighbourhood defined by makelut()-function. Either a
 %   2-by-2-Neighbourhood or a 3-by-3-Neighbourhood
 %   Output-Arguments:
 %   num: Number of "edges" surrounding a Pixel, or the number of
 %   4-Connected-Neighbourhood-Pixles that are 0
 % Example: 0 0 1  --> In this case num = 2, because there are two zero
 %          1 1 1      pixels in the 4-Connected-Neighbourhood of the center pixel  
 %          0 0 1
 % check if pixel in the center is 1 or 0
 if(nhood(2,2) == 1) % center pixel = 1
    % get sum of 4-Connected-Neighbourhood around center pixel
    sum_4_nhood = nhood(1,2) + nhood(2,1) + nhood(3,2) + nhood(2,3);
    % 3 Neighbours --> 1 edge
    if (sum_4_nhood == 3)
        num = 1; 
    % 2 Neighbours --> 2 edges
    elseif (sum_4_nhood == 2)
        num = 2;
    % 1 Neighbour --> 3 edges   
    elseif (sum_4_nhood == 1)
        num = 3;
    % isolated pixel with no neighbours (8-Connected-Neighbourhood)
    % --> 4 edges
    elseif((sum(nhood(:))-nhood(2,2)) == 0)
        num = 4;
    else % 4 Neighbours --> 0 edges
        num = 0;
    end
 else % center pixel = 0
    num = 0;
 end
 end
This code even works for any arbitrary shape! (as long as the shape doesn't have any holes)
I really want to thank both of you ( Image Analyst and Amith) for commenting on this question and providing some solutions that brought me to my solution!
I'm going to mark my answer as the definitve answer, since it solves the whole problem.
Related Question