In this paper, the standard hard C-means (HCM) clustering approach to image segmentation is modified by incorporating weighted membership Kullback–Leibler (KL) divergence and local data information into the HCM objective function. The membership KL divergence, used for fuzzification, measures the proximity between each cluster membership function of a pixel and the locally-smoothed value of the membership in the pixel vicinity. The fuzzification weight is a function of the pixel to cluster-centers distances. The used pixel to a cluster-center distance is composed of the original pixel data distance plus a fraction of the distance generated from the locally-smoothed pixel data. It is shown that the obtained membership function of a pixel is proportional to the locally-smoothed membership function of this pixel multiplied by an exponentially distributed function of the minus pixel distance relative to the minimum distance provided by the nearest cluster-center to the pixel. Therefore, since incorporating the locally-smoothed membership and data information in addition to the relative distance, which is more tolerant to additive noise than the absolute distance, the proposed algorithm has a threefold noise-handling process. The presented algorithm, named local data and membership KL divergence based fuzzy C-means (LDMKLFCM), is tested by synthetic and real-world noisy images and its results are compared with those of several FCM-based clustering algorithms.
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 fuzzifier exponent plus the Kullback-Leibler (KL) information distance acting as a fuzzification and regularization term. The KL distance is proposed to measure the proximity between cluster membership function of a pixel and an average of the cluster membership functions of immediate neighborhood pixels. Therefore, minimizing this KL distance biases the cluster membership of the pixel toward this smoothed membership function of the local neighborhoods. 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 medical images are presented to compare the performance of the proposed local membership KL information based FCM (LMKLFCM) and the standard FCM, a local data information based FCM (LDFCM) and a type of local membership information based FCM (LMFCM) algorithms.
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