In image processing What is Hausdorff’s distance's unit if we don't know the scale?

I have medical images that I resized to fit into my CNN for semantic segmentation, now to evaluate I calculated the DICE coeffitients, and the Hausdorff’s distance, now comparing to the litretures all papers reported their results in length unit (usually mm). However, I am not convenced as I think it should be pixel in my case, I used the scipy function (scipy.spatial.distance.directed_hausdorff)

So is it true to report results in pixels?

Tried to google it, but all are explaining the HD from mathmaticle point of view, without mentioning the unint, even the documentation of the function itself,


  • In the docs you can see that it returns ''the directed Hausdorff distance between two 2-D arrays of coordinates'' so if your inputs are pixel coordinates - and only then - the distance will be in pixels.

    In papers this distance is usually given in mm by multiplying the pixel distance with the pixel size.