Lexic.us

Definition of Hausdorff metric

1. Noun. (analysis) 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 $\backslash mathbb\{R\}^n$. ¹

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