each point is assigned to one of the two subclusters depending on which side of the *mean* point its projection falls to. It should be noted that the choice of this threshold is primarily motivated by computational convenience. Here, we propose a better alternative based on discriminant analysis.

The projections of the points on the partitioning axis can be viewed as a discrete probability distribution, which can be conveniently represented by a histogram. The problem of dividing a histogram into two partitions is a well studied one in the field of image processing. A plethora of histogram partitioning, a.k.a. thresholding, methods has been proposed in the literature with the early ones dating back to the 1960s [@Sezgin04]. Among these, Otsu’s method [@Otsu79] has become the method of choice as confirmed by numerous comparative studies [@Sahoo88; @Lee90; @Trier95; @Sezgin04; @Medina05; @Celebi13b].

Given an image represented by $L$ gray levels $\left\{ 0, 1, \dotsc, L - 1\right\}$, a thresholding method partitions the image pixels into two classes $\mathcal{C}_0 = \left\{ 0, 1, \dotsc, t \right\}$ and $\mathcal{C}_1 = \{ t + 1, t + 2,$ $\dotsc, L - 1 \}$ (object and background, or vice versa) at gray level $t$. In other 