Scattered bright points, some lying on a hidden line, some just noise — how does a machine find the line? Every point VOTES for all the lines that could pass through it; the true line is the one that collects votes from all its points at once. Democracy for geometry. Slide the noise and watch the peak hold.
Each edge point (x,y) is mapped to the sinusoid ρ = x·cosθ + y·sinθ in (ρ,θ) space and votes along it; collinear points’ sinusoids all cross at the single (ρ,θ) of their common line, making a peak in the accumulator. The instrument builds the real accumulator live. A fail-loud self-check places 10 exactly-collinear points and throws unless the peak cell collects at least 9 votes — the line recovered from scattered points by agreement, not by fitting.
The accumulator is quantised (2° angle bins here), so near-collinear points can miss the peak and heavy noise raises a false floor; real pipelines pre-detect edges and smooth the accumulator. The voting geometry and the collinear-peak are exact.