A Hard C-Means Clustering Algorithm Incorporating Membership KL Divergence and Local Data Information for Noisy Image Segmentation

Abstract

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.

Incorporating Local Data and KL Membership Divergence into Hard C-Means Clustering for Fuzzy and Noise-Robust Data Segmentation

“…In [18], an approach to incorporating local spatial membership information into HCM algorithm has been presented. By adding Kullback-Leibler (KL) divergence between the membership function of an entity and the locally-smoothed membership in the immediate spatial neighborhood, the modified objective function, called the local membership KL divergencebased FCM (LMKLFCM), is given by [18][19][20][21][22].…”

“…where γ is a weighting parameter experimentally selected to control the fuzziness induced by the second term in (19), u in ¼ 1 À u in is the complement of the membership function u in , π in and π in are the spatial local or moving averages of membership u in and the complement membership u in , functions respectively. These local membership and membership complement averages are computed by [18][19][20][21][22].…”

“…Other windows can be used such as Gaussian one provided that the weight of the windowcenter is 0 and the rest weights are summed to unity. The first term in (19) provides hardcluster labeling. It pushes the membership function toward 0 or 1.…”

“…In this chapter, HCM clustering algorithm is modified by incorporating local spatial data and Kullback-Leibler (KL) membership divergence [18][19][20][21][22]. The local data information is incorporated via an additional weighted HCM function in which the smoothed image data is used for the distance computation.…”

Kernel-Based Robust Bias-Correction Fuzzy Weighted C-Ordered-Means Clustering Algorithm

“…Clustering analysis is a significant technique in data analysis, which covers a wide range of applications in many areas such as data mining [1,2], image processing [3][4][5], computer vision [6] and artificial intelligence [7,8]. Generally, the clustering methods can be divided into four types, namely hierarchical clustering, graph theory, Density-based clustering and minimization objective function [9].…”