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How can I segment and label edges in a binary matrix?

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I have a binary matrix that contains a polygon with different edges and vertices. Edges are false, non-edges are true. I would like to detect the edges of the polygon (i.e. lines with different orientations) like this:
The aim would be to get an output Matrix, the same size as my input one, where the edge values are labelled according to which edge they correspond to.
I have looked through Matlab's segmentation and edge detection functions but can't seem to find anything that does this.
Thanks for any help.

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