Hausdorff metric

English

Noun

Hausdorff metric (plural Hausdorff metrics)

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

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