Efficient polynomial implementation of several multithresholding methods for gray-level image segmentation

Abstract

Multithresholding consists of segmenting a histogram of image in classes by using thresholds. Many researchers avoid the exponential space problem of possible thresholds combinations of a given criteria function. In this work, we present a polynomial easy-to-implement dynamic programming algorithm to find the exact optimum thresholds of three well-known criteria functions for multithresholding: the maximum of histogram between class-variance (Otsu’s method); the maximum histogram entropy (Kapur et al.‘s method), and minimum histogram error (Kittler and Illingworth’s method). The algorithm, that has been used to optimum quantization, has O((K -1)L2) time complexity, where K and L stand for the number of desired classes and the number of gray levels in the image, respectively. Experiments showed that the exact optimum thresholds for gray-level image segmentation can be found in less than 160 milliseconds in a Pentium 4-2GHz, in whatever the number of classes.