how to find the midpoint in between end point and branch point

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i am working on hand written word images, i want to represent the word image in the form of graph. i want to find the mid points in between two key points and two branch points
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Raghu Rao
Raghu Rao 2017-3-24
编辑:Raghu Rao 2017-3-24
this is my output image, i already find out the end points and branch points but my problems is i want to add a node in between two end points and branch points

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Image Analyst
Image Analyst 2017-3-24
I'd think taking the average of the x and y values for each endpoint would do it:
xMiddle = (x1+x2)/2;
yMiddle = (y1+y2)/2;
or am I overlooking something?
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Image Analyst
Image Analyst 2019-12-12
Look at bwmorph()
epImage = bwmorph(skeletonImage, 'EndPoints');
bpImage = bwmorph(skeletonImage, 'BranchPoints');
[epRows, epColumns] = find(epImage); % Get location of end points.
hold on;
plot(epColumns, epRows, 'r.', 'MarkerSize', 30);
[bpRows, bpColumns] = find(bpImage); % Get location of branch points.
plot(bpColumns, bpRows, 'ro', 'MarkerSize', 40);

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