Otsu's method — when it shines: Total Area is where Otsu's method works best. The algorithm assumes a bimodal histogram (two populations: positive and negative pixels) and finds the threshold that minimizes within-class variance — equivalently, maximizes between-class variance. For well-separated staining (strong positive vs. clear negative), Otsu reliably finds the valley between the two histogram peaks. This is a "clean" application because the assumption of two populations closely matches reality for binary staining patterns.
When Otsu fails: Gonzalez & Woods identify several failure modes: (1) when the object area is very small compared to background, the histogram becomes unimodal and Otsu finds an arbitrary threshold; (2) when noise fills the valley between peaks, the optimal threshold becomes unstable; (3) when illumination is non-uniform, a single global threshold cannot correctly classify all regions. For Total Area, failure modes (1) and (3) are the most common — sparse positive staining or uneven illumination. Background Removal before Total Area mitigates mode (3).
Area measurement precision: At the pixel level, area measurement has inherent discretization error. A circular object of true area A covers approximately A pixels, but the discrete boundary introduces error proportional to the perimeter (the "staircase" effect). For large objects this is negligible, but for small objects the relative error can be significant. Total Area, by measuring aggregate area rather than individual objects, averages these errors across thousands of boundary pixels, making the aggregate percentage measurement more precise than any individual object's area measurement.
Otsu's method works best here because staining coverage naturally creates a two-peaked histogram: positive pixels and negative pixels. The algorithm finds the valley between the peaks and uses it as the cutoff. It struggles when positive staining is sparse (the positive peak is tiny) or when illumination is uneven (correctable with Background Removal first).
