Fuzzy C-Means with Local Membership Based Weighted Pixel Distance and KL Divergence for Image Segmentation

This paper presents a new technique for incorporating local membership information into the standard fuzzy C-means (FCM) clustering algorithm. In this technique, the objective consists of minimizing the classical FCM function with a unity fuzzification exponent plus a weighted proposed fuzzification and regularization term. The pixel to cluster-center distance is weighted using the reciprocal of the local membership average. The regularization term is formulated using the Kullback-Leibler (KL) divergence which measures the proximity between a pixel membership and the local average of this membership in the immediate neighborhood. Therefore, minimizing this KL divergence biases the cluster membership of the pixel toward the local membership average. It is also shown that the proposed weighted distance further leads to assigning a pixel to the cluster more likely existing in the immediate neighborhood. This can provide immunity against noise and results in clustered images with piecewise homogeneous regions. Results of clustering and segmentation of synthetic and real-world images are presented to compare the performance of the proposed local membership based weighted distance and KL divergence FCM (LMWD-KLFCM) and the standard FCM, a local data based information FCM (LDMFCM) and a type of local membership information based FCM (LMFCM) algorithms.