Abstract
Hard C-means (HCM) and fuzzy C-means (FCM) algorithms are among the most popular ones for data clustering including image data. The HCM algorithm offers each data entity with a cluster membership of 0 or 1. This implies that the entity will be assigned to only one cluster. On the contrary, the FCM algorithm provides an entity with a membership value between 0 and 1, which means that the entity may belong to all clusters but with different membership values. The main disadvantage of both HCM and FCM algorithms is that they cluster an entity based on only its self-features and do not incorporate the influence of the entity’s neighborhoods, which makes clustering prone to additive noise. In this chapter, Kullback-Leibler (KL) membership divergence is incorporated into the HCM for image data clustering. This HCM-KL-based clustering algorithm provides twofold advantage. The first one is that it offers a fuzzification approach to the HCM clustering algorithm. The second one is that by incorporating a local spatial membership function into the HCM objective function, additive noise can be tolerated. Also spatial data is incorporated for more noise-robust clustering.
Highlights
Hard C-means (HCM) called K-means clustering algorithm is an unsupervised approach in which data is basically partitioned based on locations and distances between various data points [4–6]
From (8), it is clear that the Local spatial data-based FCM (LDFCM) aims at minimizing the standard fuzzy C-means (FCM) objective function plus another weighted modified FCM function acting as a regularization function
It is obvious so far that the membership function of the nth entities provided by FCM, HCM and membership entropy-based FCM (MEFCM) algorithms depends upon the inverse of the square of the Euclidean distance din 1⁄4 kxn À vik2 which is a function of only xn with no data or membership information of the clustering entity’s neighbors are involved
Summary
Image segmentation is a principle process in many image, video, scene analysis and computer vision applications [1–3]. One disadvantage of the standard FCM is not incorporating any spatial or local information in image context, making it very sensitive to additive noise and other imaging artifacts. To handle this problem, different techniques have been developed [9–13]. These techniques have involved spatial or local data information for the enhancement and regularization of the performance of the standard FCM algorithm. HCM clustering algorithm is modified by incorporating local spatial data and Kullback-Leibler (KL) membership divergence [18–22]. The local data information is incorporated via an additional weighted HCM function in which the smoothed image data is used for the distance computation.
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