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difficulty 2/5

Intersection over union

Definition

The area two regions share divided by the area they cover between them. It is read as "how correct is this box", and it is stricter and scale-blind in ways that number hides.

Formula
IoU(A,B)=∣A∩B∣∣A∪B∣\mathrm{IoU}(A, B) = \frac{|A \cap B|}{|A \cup B|}

Intuition

Two regions are drawn on an image — one is what a model predicted, one is what was actually there. IoU is the single number that decides whether those count as the same thing.

It is the shared area divided by the area they cover between them [1, §14.4.2]. The division is what makes it strict: anything one region covers and the other does not is absent from the top of the fraction and present at the bottom, so every disagreement is charged twice. That is why the number runs lower than intuition expects, and why 0.5 is a much weaker claim than "half right".

Formal definition

How it works

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Why & when

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3 questions

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Sources

  1. Zhang, Lipton, Li, Smola. Dive into Deep Learning — Anchor Boxesbook · retrieved 2026-09-20https://d2l.ai/chapter_computer-vision/anchor.html
  2. Rezatofighi, Tsoi, Gwak, Sadeghian, Reid, Savarese. Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression (2019)paper · retrieved 2026-09-20https://ar5iv.labs.arxiv.org/html/1902.09630

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