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Daniel Stanley Tan added section_Otsu_s_Method_The__.tex
over 8 years ago
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\section{Otsu's Method}
The simplest property that pixels in a region can share is intensity. Therefore, a natural way to segment such regions is to find a threshold that would separate the light and dark regions. This creates binary images from gray-level ones by turning all pixels below some threshold to zero (background pixels) and all pixels above that threshold to one (foreground pixels).
A simple way to find a suitable threshold is to find each of the modes (local maxima) and then find the valley (minimum) between them. One way to think of it is to consider the values in the two regions as two clusters. Our goal is to make each cluster as tight as possible, thus minimizing the overlap.
We can't change the distribution but we can adjust where we separate them (the threshold). As we adjust the threshold one way, we increase the spread of one and decrease the spread of the other. The goal then is to select the threshold that minimizes the combined spread.
We can define the within-class variance as the weighted sum of the variances of each cluster:
$$\sigma^2_{\text{Within}}(2) = n_B(T)\sigma^2_B(T)+n_O(T)\sigma^2_O(T)$$
