Why is it called 'multi-level thresholding', if only the best threshold is selected? I'm referring to Otsu's thresholding, and saw this from his paper:


When he says he's trying to maximize the between class variance of thresholds k* 1 and 2, is it the threshold with maximum value that is chosen? Is that what the "max" means? If it was just about selecting one threshold, why is it called multi-level thresholding?  

On the other hand, if multiple thresholds are chosen, then why do we need to find the "max" of it?  

ps: I'm trying to implement Otsu's method in a computational intelligence algorithm (Differential Evolution and Particle Swarm Optimization), and not a single research paper has explained clearly, how the thresholds are to be used for multi-thresholding. Not even the original Otsu paper.
Also, after implementing the algorithm, the image with the best fitness threshold is a different (much darker) threshold than what Matlab's greythresh threshold returns.
Using k1 and k2 you can calculate a between class variance value using the Otsu formula. However, there may be many combinations of k1 and k2 for which you have to calculate between class variance values to see which of them gives the highest between class variance value. That's what 'max' means. So whichever k1 and k2 gives you the highest between class variance, you choose those values of k1 and k2 as your thresholds. Same can be done if you want more thresholds.