Interval Type-2 Fuzzy Set and Theory of Weak Continuity Constraints for Accurate Multiclass Image Segmentation

Abstract

Multiclass image segmentation is a challenging task due to the uncertainties involved with the process of segmentation. To handle those uncertainties, we propose an automatic multiclass image segmentation method based on an interval type-2 fuzzy set (IT2FS). In the proposed method in this article, the accurate multiclass segmentation is achieved by minimizing an energy function. This energy function is based on IT2FS and weak continuity constraints present in the membership values. The theory of weak continuity constraints helps to localize the segmentation boundaries between the classes accurately with the minimization of the energy. The proper localization of segmentation boundaries helps to minimize the uncertainties in the segmentation process. We also theoretically show that the minimization of the energy function reduces the uncertainties present in the segmentation process. Furthermore, the method automatically determines the number of clusters without a priori knowledge. The proposed method is found to be superior to the existing conventional, fuzzy type-1 and fuzzy type-2 based segmentation techniques. The superiority is verified using synthetic and benchmark datasets. The noise immunity of the proposed method is found to be better than that of the state-of-the-art methods when benchmark against the modified Cramer–Rao bound.