Efficient Multilevel Image Thresholding

Thresholding is one of the most widely used image segmentation operations; one application is foreground-background separation. Multilevel thresholding is the extension to segmentation into more than two classes. In order to find the thresholds, which separate the classes, the histogram of the image is analyzed. In most cases, the optimal thresholds are found by the minimazing or maximazing an objective function, which depends on the positions of the thresholds. We identify a class of objective functions for which the optimal thresholds can be found using algorithms with low time complexities. We also show, that two well known objective functions are members of this class. By implementing the algorithms and comparing their execution times, we can make a quantitative statement about their performance.