Central Perturbation-based Interval Type-2 Fuzzy C-Means Clustering for Image Segmentation

Abstract

In fuzzy c-means (FCM) clustering algorithm, when assigning membership degree to a data point, the calculation of fuzzy membership degree contains various uncertain factors, such as fuzzifier, distance metric and cluster center, etc. Although the interval type-2 FCM (IT2FCM) clustering algorithm and its improved algorithms consider the uncertainty about the fuzzifier, it suffers from falling into the local optimum because of ignoring the uncertainty of the cluster center. To address the issue, a central perturbation-based interval type-2 fuzzy c-means (CPIT2FCM) clustering algorithm for image segmentation is proposed by representing the uncertainty of the cluster center in this paper. In the proposed algorithm, the traditional crisp center is extended to the interval fuzzy center utilizing central perturbation, and the upper and lower membership functions are constructed by the interval fuzzy center, thus the type-l fuzzy set is extended to the interval type-2 fuzzy set. At the same time, the Mahalanobis distance is introduced into the CPIT2FCM algorithm to improve the clustering performance for the datasets and the color image. Finally, experiments are conducted on synthetic datasets and real images respectively, and the effectiveness of the proposed algorithm was verified by combining visual effects and evaluation indices.