Improving Fuzzy Algorithms for Automatic Magnetic Resonance Image Segmentation

In this paper, we present reliable algorithms for fuzzy k-means and C-means that could improve MRI segmentation. Since the k-means or FCM method aims to minimize the sum of squared distances from all points to their cluster centers, this should result in compact clusters. Therefore the distance of the points from their cluster centre is used to determine whether the clusters are compact. For this purpose, we use the intra-cluster distance measure, which is simply the median distance between a point and its cluster centre. The intra-cluster is used to give us the ideal number of clusters automatically; i.e a centre of the first cluster is used to estimate the second cluster, while an intra-cluster of the second cluster is obtained. Similar, the third cluster is estimated based on the second cluster information (centre and intra cluster), so on, and only stop when the intra-cluster is smaller than a prescribe value. The proposed algorithms are evaluated and compared with established fuzzy kmeans and C-means methods by applying them on simulated volumetric MRI and real MRI data to prove their efficiency. These evaluations, which are not easy to specify in the absence of any prior knowledge about resulted clusters, for real MRI dataset are judged visually by specialists since a real MRI dataset cannot give us a quantitative measure about how much they are successful.