Noun
Hausdorff metric (plural Hausdorff metrics)
(mathematical analysis) In the abstract metric space of all compact subsets of
R
n
{\displaystyle \mathbb {R} ^{n}}
, given a pair of compact sets A and B, the Hausdorff metric is
h
(
A
,
B
)
=
max
{
ρ
(
A
,
B
)
,
ρ
(
B
,
A
)
}
{\displaystyle h(A,B)={\mbox{max}}\{\rho (A,B),\rho (B,A)\}}
where
ρ
(
A
,
B
)
=
sup
a
∈
A
inf
b
∈
B
d
(
a
,
b
)
{\displaystyle \rho (A,B)=\sup _{a\in A}\inf _{b\in B}\,d(a,b)}
, where d is the Euclidean metric in
R
n
{\displaystyle \mathbb {R} ^{n}}
.
Synonyms: Hausdorff distance, Pompeiu-Hausdorff distance