Last Updated
：2025/11/24
Hausdorff metric
Noun
Japanese Meaning
Hausdorff距離：数学解析の文脈で、ℝⁿ上のすべてのコンパクト集合の抽象的距離空間において、2つのコンパクト集合AとBに対して定義される距離。具体的には、h(A,B) = max{ρ(A,B), ρ(B,A)}と表され、ρ(A,B)はA内の各点aについて、B内の最も近い点bとの距離d(a,b)の下限の上限として定義される。ここで、dはℝⁿにおけるユークリッド距離である。
（ plural ）
Quizzes for review
(mathematical analysis) In the abstract metric space of all compact subsets of ℝⁿ, given a pair of compact sets A and B, the Hausdorff metric is h(A,B)= mbox max𝜌(A,B),𝜌(B,A) where 𝜌(A,B)= sup _(a∈A) inf _(b∈B),d(a,b), where d is the Euclidean metric in ℝⁿ.
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Hausdorff metric
When comparing two compact subsets of ℝⁿ, the Hausdorff metric quantifies their difference by taking the maximum of the directed distances between the sets.
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When comparing two compact subsets of ℝⁿ, the Hausdorff metric quantifies their difference by taking the maximum of the directed distances between the sets.
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