# Hausdorff Distance with Manhattan Distance

I'm applying Hausdorff Distance to understand if two datasets are representing the same subset of the space of a particular problem. The point is that I've read the Hausdorff distance computes the Euclidean distance between 2 subsets, and I would be interested in other distance metric such as Hamming or Manhattan. But I haven't seen any Hausdorff Distance algorithm using this kind of distance metrics. So, my question is: can HD be applied over any other distance metric different from Euclidean distance? As far as I understand Hausdorff Distance, it should be applied over any kind of distance metric, but I'm not sure due I haven't seen anything like this.

Thank you so much guys!!