Interval type-2 outlier-robust picture fuzzy clustering and its application in medical image segmentation

Based on picture fuzzy set theory, picture fuzzy clustering has achieved good results on some data as more information is involved in the clustering process. However, current picture fuzzy clustering methods still suffer from two common weaknesses, i.e., the sensitivity to outliers and the neglect of the uncertainty caused by different fuzzy degrees, which influence their performance in practical applications like medical image segmentation. To solve these issues, we present two new picture fuzzy clustering methods in this paper. First, to improve immunity to outliers, we propose an outlier-robust picture fuzzy clustering method named ORPFC by using a robust distance measurement, which treats the data objects far away from cluster prototypes as outliers and limits their effects on the prototype update. Second, to handle the uncertainty caused by fuzzy degrees, we further present an interval type-2 enhanced method called IT2ORPFC by incorporating the interval type-2 fuzzy set theory into ORPFC. In each iteration, IT2ORPFC estimates positive memberships, neutral memberships, and refusal memberships according to different fuzzification coefficients and then conducts type reduction for reliable type-1 clustering results. In the experiments, the proposed methods obtain robust and reliable results on eleven datasets. Specifically, ORPFC and IT2ORPFC achieve rewarding performance on segmenting medical images with noise.