## Does anyone know how I could find out the number of ends an arbitrary shape has e.g. an 'x' that is displayed in an image.

### MP (view profile)

on 13 Jul 2017
Latest activity Commented on by Guillaume

### Guillaume (view profile)

on 14 Jul 2017
Does anyone know how I could find out the number of ends an arbitrary shape has e.g. an 'x' or a straight line. I use regionprops -> pixelList to extract a the points describing the shape from a BW image.

### Guillaume (view profile)

on 13 Jul 2017

sum(bwmorph(bwmorph(yourbinaryimage, 'skel'), 'endpoints'))
Should give you what you want. For more information, see bwmorph.

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Guillaume

### Guillaume (view profile)

on 13 Jul 2017
In your question you say you have a binary image.. I have no idea what you mean by x and y vectors. What do these x and y vectors represent, where do they come from.
Jan

### Jan (view profile)

on 13 Jul 2017
The values are coming from regionprops->PixelList .
@MP: And now you are looking for coordinates in X and Y, which have less then 2 4- or 8-connected neighbors only. Correct?
Guillaume

### Guillaume (view profile)

on 14 Jul 2017
Ah, alright. If the binary image has not been skeletonised before the call to regionprop then it's going to be very difficult to find the end points from the coordinate vectors. If the image has beem skeletonised before regionprops then the end points are those pixels with just one neighbours.
One way of finding pixels with just one neighbours would be to compute the cheesboard distance matrix between all the pixels (with pdist2 if you have the stats toolbox, manually otherwise), keep only the ones in that matrix. The end points are those pixels with just one one in the row (or column), e.g.:
pixels = [1 1;1 2; 2 3; 3 3];
chessdist = max(abs(pixels(:, 1) - pixels(:, 1)'), abs(pixels(:, 2) - pixels(:, 2)')); %requires R2016b or later, or use pdist2
endpoints = pixels(sum(chessdist == 1) == 1, :)
But honestly, using bwmorph would be simpler. If the image is no longer available, I would recreate it from the list of pixels:
img = zeros(max(pixels(:, 2)), max(pixels(:, 1)));
img(sub2ind(size(img), pixels(:, 2), pixels(:, 1))) = 1;
[endpoints(:, 2), endpoints(:, 1)] = find(bwmorph(bwmorph(img, 'skel'), 'endpoints'))