Definition
Let X and Y be two non-empty subsets of a metric space (M, d). We define their Hausdorff distance d H(X, Y) by
where sup represents the supremum and inf the infimum.
Equivalently
- ,
where
- ,
that is, the set of all points within of the set (sometimes called the -fattening of or a generalized ball of radius around ).
Read more about this topic: Hausdorff Distance
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