Three-level image segmentation based on maximum fuzzy partition entropy of 2-D histogram and quantum genetic algorithm

Abstract

A method is presented for three-level image segmentation through maximizing the fuzzy partition entropy of two-dimensional histogram. Two groups, each including three member functions, namely Z-function, Π-function and S-function, are used for fuzzy division of two-dimensional histogram to get nine fuzzy sets. And the nine fuzzy sets are classified to three parts, corresponding to dark, gray and white part of the image, respectively, while a fuzzy partition is obtained for the two-dimensional space. Then a fuzzy partition entropy is defined based on multi-dimensional fuzzy partition and entropy theory. The parameters of the six membership functions can be determined by maximizing fuzzy partition entropy of two-dimensional histogram and the procedure for finding the optimal combination of all the fuzzy parameters is implemented by quantum genetic algorithm with an appropriate coding method. The experiment results show that the proposed method gives better performance than onedimensional three-level thresholding method under noise case. © 2008 Springer-Verlag Berlin Heidelberg.