Hausdorff metric

Noun

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