A novel fuzzy clustering algorithm by minimizing global and spatially constrained likelihood-based local entropies for noisy 3D brain MR image segmentation

Abstract

In this paper, we propose a novel fuzzy clustering algorithm by minimizing global and spatially constrained likelihood-based local entropies (FCMGsLE) for segmenting noisy 3D brain magnetic resonance (MR) image volumes. For each voxel, in order to measure uncertainties that arise while identifying its class, two different entropies are defined. In particular, they measure the amount of uncertainties in terms of global entropy using fuzzifier weighted global membership function and spatially constrained likelihood-based local entropy using fuzzifier weighted local membership function. To mitigate the effect of noise and intensity inhomogeneity (IIH) or radio frequency (RF) inhomogeneity, the local membership function is induced by spatially constrained likelihood measure. These entropies are minimized through a fuzzy objective function to obtain the cluster prototypes and membership functions. The final membership function is obtained by integrating these global and local membership functions using weighted parameters. The algorithm is assessed both qualitatively and quantitatively on ten 3D volumes of simulated and clinical brain MR image data having high levels of noise and intensity inhomogeneity and a synthetic 3D image volume with Rician noise. The simulation results reveal that the proposed algorithm outperforms several state-of-the-art algorithms devised in recent past when evaluated in terms of segmentation accuracy, Dice similarity coefficient, partition coefficient, and partition entropy