Hausdorff metric

Hausdorff metric (plural Hausdorff metrics)

1. (mathematical analysis) In the abstract metric space of all compact subsets of ${\displaystyle \mathbb {R} ^{n}}$ , given a pair of compact sets A and B, the Hausdorff metric is ${\displaystyle h(A,B)={\mbox{max}}\{\rho (A,B),\rho (B,A)\}}$ where ${\displaystyle \rho (A,B)=\sup _{a\in A}\inf _{b\in B}\,d(a,b)}$ , where d is the Euclidean metric in ${\displaystyle \mathbb {R} ^{n}}$ .

   h(A,B) = 0 iff A = B