Determining the number of clusters for kernelized fuzzy C-means algorithms for automatic medical image segmentation

In this paper, we determine the suitable validity criterion of kernelized fuzzy C-means and kernelized fuzzy C-means with spatial constraints for automatic segmentation of magnetic resonance imaging (MRI). For that; the original Euclidean distance in the FCM is replaced by a Gaussian radial basis function classifier (GRBF) and the corresponding algorithms of FCM methods are derived. The derived algorithms are called as the kernelized fuzzy C-means (KFCM) and kernelized fuzzy C-means with spatial constraints (SKFCM). These methods are implemented on eighteen indexes as validation to determine whether indexes are capable to acquire the optimal clusters number. The performance of segmentation is estimated by applying these methods independently on several datasets to prove which method can give good results and with which indexes. Our test spans various indexes covering the classical and the rather more recent indexes that have enjoyed noticeable success in that field. These indexes are evaluated and compared by applying them on various test images, including synthetic images corrupted with noise of varying levels, and simulated volumetric MRI datasets. Comparative analysis is also presented to show whether the validity index indicates the optimal clustering for our datasets.