To split an image into figure and ground you need a cutoff — but where? Otsu’s method finds it with no human: try every possible threshold and keep the one that carves the pixel histogram into the two tightest, most-separated groups. The machine picks its own line. Slide a manual cut and see how far off you are from Otsu’s.
Otsu (1979) maximises between-class variance σ² = w₀w₁(μ₀−μ₁)², where w and μ are the weight and mean of the two groups a threshold t makes. Maximising the separation between the groups is equivalent to minimising the spread within them. The instrument sweeps all 256 thresholds live and marks the winner. A fail-loud self-check throws unless, on a bimodal histogram with peaks at 60 and 190, Otsu’s threshold lands in the valley strictly between them — the automatic cut, not a set number.
Otsu assumes a bimodal histogram; on flat or multi-modal images it still returns a number but a poor split (adaptive/local thresholding fixes that). The σ² formula and the valley-finding are exact.