Automatic Fuzzy Algorithms for Reliable Image Segmentation

The problem of classifying an image into different homogeneous regions is viewed as the task of clustering the pixels in the intensity space. In particular, medical image segmentation is complex, and automatically detecting regions or clusters of such widely varying sizes is a challenging task. In this paper, we present automatic fuzzy k-means, and kernelized fuzzy c-means algorithms by considering some spatial constraints on the objective function. The proposed algorithm incorporates spatial information into the membership function and the validity procedure for clustering. It starts by partitioning the given data into an arbitrary number of clusters. These clusters are considered as an initial partition of the data. The similar clusters that satisfy the validity function are merged into one cluster. The proposed validity function is based on the intra-cluster distance measure, which is simply the distance between the center of the cluster and its neighbor cluster center multiplied by the objective function. A first cluster is fetched; the second cluster is selected if it has the shortest distance between their two centers. These clusters are merged together into one cluster if they satisfy the validity function; else the next cluster is fetched, and so on. The process stops only when all clusters are checked. The number of clusters increases automatically according to the decision of validity function. The most important aspect of the proposed algorithms is actually to work automatically to improve automatic image segmentation. The proposed methods are evaluated and compared with the existing methods by applying them on various test images, including synthetic images corrupted with noise of varying levels and simulated volumetric Magnetic Resonance Image (MRI) datasets.