Hausdorff metric



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 20 June 2013, at 20:51