Framework for efficient optimal multilevel image thresholding

Image thresholding is a very common image processing operation, since almost all image processing schemes need some sort of separation of the pixels into different classes. In order to determine the thresholds, most methods analyze the histogram of the image. The optimal thresholds are often found by either minimizing or maximizing an objective function with respect to the values of the thresholds. By defining two classes of objective functions for which the optimal thresholds can be found by efficient algorithms, this paper provides a framework for determining the solution approach for current and future multilevel thresholding algorithms. We show, for example, that the method proposed by Otsu and other well-known methods have objective functions belonging to these classes. By implementing the algorithms in ANSI C and comparing their execution times, we can also make quantitative statements about their performance.