Definify.com

Definition 2024

Hausdorff_metric

Hausdorff metric

English

Noun

Hausdorff metric ‎(plural Hausdorff metrics)

(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