# Hausdorff metric

## English

### Noun

Hausdorff metric (plural Hausdorff metrics)

1. (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
Last modified on 14 April 2009, at 02:59