How do I measure the distances between all pixels in a letter T

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I have an image like this: letter T

and would need to measure the distance of all black pixels (which make up the letter T) from each other. Can anyone recommend the best way? I am particularly interested in the distance between pixels that make up the 'border' of the T, essentially this:

letter T edge

would you advise that I first turn the T into its own perimeter only (as in the second figure) and then map? Or is there a clever way to say "just map distances between pixels at the edge)? many thanks

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