Image segmentation based on weak fuzzy partition entropy

Fuzzy partition entropy-based method is an effective way for image segmentation. In this paper a segmentation method based on a weak fuzzy partition is presented. Firstly, we propose a method to construct generalized fuzzy complement, and moreover construct a generalized fuzzy complement operator which has a nice property for parameter optimization in real application. Then, a one-dimensional (1D) weak fuzzy partition, a two-dimensional (2D) weak fuzzy partition being obtained by a Cartesian product of two 1D fuzzy partitions, are defined using the proposed generalized fuzzy complement. With these concepts, a weak fuzzy partition entropy-based image segmentation method is proposed. The method is described in the 1D and 2D cases by modeling the 1D and 2D histograms. The 2D approach allows us to ensure a spatial regularity of the fuzzy classification. Finally, a nested optimization method is developed, based on an improved uniformity measure, to search for the optimal threshold in the image segmentation method. Empirical results show that the proposed weak fuzzy partition entropy-based method is capable of achieving better segmentation results than several state-of-the-art methods that are based on or not based on fuzzy entropy. The proposed 2D weak fuzzy partition entropy-based method is especially effective for noisy images.