Hausdorff distance: Difference between revisions

Latest revision as of 01:57, 20 February 2009

Definition

Suppose $A$ and $B$ are two subsets of a metric space $(X, d)$ . The Hausdorff distance between $A$ and $B$ , denoted $d_{H} (A, B)$ , is defined as:

$d_{H} (A, B) = inf {ε ∣ A \in B_{ε} (B), B \in B_{ε} (A)}$ .

Here $B_{ε} (M)$ denotes the union of balls of radius $ε$ about all points in $M$ .

Related notions

Gromov-Hausdorff distance

Facts

Hausdorff distance is a metric on closed subsets of a compact metric space

Revision as of 01:56, 20 February 2009 (view source) Vipul (talk \| contribs) (New page: ==Definition== Suppose <math>A</math> and <math>B</math> are two subsets of a metric space <math>(X,d)</math>. The '''Hausdorff distance''' between <math>A</math> and <math>B</math>, ...)		Latest revision as of 01:57, 20 February 2009 (view source) Vipul (talk \| contribs) No edit summary
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	==Facts==		==Facts==

	* [[Hausdorff distance is a metric on closed subsets of a metric space]]		* [[Hausdorff distance is a metric on closed subsets of a compact metric space]]