Hausdorff metric

E608816
distance function mathematical concept metric

The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (2)

Surface form Occurrences
Gromov–Hausdorff convergence 1
Hausdorff distance 1

Statements (46)

Predicate Object
instanceOf distance function ⓘ
mathematical concept ⓘ
metric ⓘ
alternativeName Hausdorff distance NERFINISHED ⓘ
Pompeiu–Hausdorff metric NERFINISHED ⓘ
applicableTo closed and bounded subsets of a complete metric space ⓘ
compact subsets of Euclidean space ⓘ
category metric on sets ⓘ
codomain nonnegative real numbers ⓘ
construction based on supremum of point-to-set distances ⓘ
definedOn set of compact subsets of a metric space ⓘ
set of nonempty closed subsets of a metric space ⓘ
domain subsets of a metric space ⓘ
enables definition of completeness of hyperspaces ⓘ
study of stability of attractors in dynamical systems ⓘ
field computer vision ⓘ
functional analysis ⓘ
image processing ⓘ
metric geometry ⓘ
shape analysis ⓘ
topology ⓘ
mathematicalArea general topology ⓘ
metric space theory ⓘ
measures distance between subsets ⓘ
how far two subsets are from each other ⓘ
namedAfter Felix Hausdorff NERFINISHED ⓘ
property equals zero if and only if sets are equal (for closed sets) ⓘ
nonnegative ⓘ
satisfies triangle inequality ⓘ
symmetric ⓘ
relatedConcept Gromov–Hausdorff distance NERFINISHED ⓘ
Kuratowski convergence of sets NERFINISHED ⓘ
Vietoris topology NERFINISHED ⓘ
requires underlying metric space ⓘ
symbol d_H ⓘ
topologicalRole induces topology on hyperspace of closed subsets ⓘ
turns space of nonempty compact subsets into a metric space ⓘ
usedIn approximation of sets by polyhedra ⓘ
continuity of set-valued maps ⓘ
convergence of sets ⓘ
fractal geometry ⓘ
geometric modeling ⓘ
object matching in images ⓘ
pattern recognition ⓘ
shape comparison ⓘ
uses supremum over one set of infimum distances to the other set ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Felix Hausdorff → knownFor → Hausdorff metric ⓘ
Felix Hausdorff → notableConcept → Hausdorff metric ⓘ
Felix Hausdorff → notableConcept → Hausdorff metric ⓘ
this entity surface form: Hausdorff distance
Mikhail Gromov → notableFor → Hausdorff metric ⓘ
this entity surface form: Gromov–Hausdorff convergence