Hausdorff Distance

The Hausdorff distance, also called the Hausdorff metric or the Pompeiu-Hausdorff distance, measures how far two subsets of a metric space are from each other. It can be described as the longest distance an adversary could force someone to travel by choosing a point in one of the two sets from which they must then reach the other set, so it captures the greatest distance from any point in one set to the nearest point in the other. It is named after Felix Hausdorff, who introduced it in his 1914 book Grundzuge der Mengenlehre, building on a related idea in Maurice Frechet's 1906 doctoral thesis, and after Dimitrie Pompeiu. The Hausdorff distance turns the collection of non-empty compact subsets of a metric space into a metric space in its own right, making it a standard tool for comparing geometric shapes and sets. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/