Illustration of the method used to identify the optimal tolerance <i>τ</i>_<i>b</i>.

On the interval [τs, τf], the proportion of selected pixels χ (solid black) is non-decreasing and reaches the maximum value 1 for τ ≥ τu. The best binary image occurs at the tolerance τb, which occurs just before the rapid increase in χ. For each τm ∈ [τs + 1, τc − 1], a piecewise linear function pm (purple) is fit to χ on the intervals [τs, τm] and [τm + 1, τc], for some critical value τc such that χ(τc) is close to unity. The point τb is taken to be the threshold that minimises the mean error between χ and the piecewise linear interpolant.