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We present a novel adaptive mean shift (AMS) algorithm for the segmentation of tissues in magnetic resonance (MR) brain images. In particular we introduce a novel Bayesian approach for the estimation of the adaptive kernel bandwidth and investigate its impact on segmentation accuracy. We studied the three class problem where the brain tissues are segmented into white matter, gray matter and cerebrospinal fluid. The segmentation experiments were performed on both multi-modal simulated and real patient TI-weighted MR volumes with different noise characteristics and spatial inhomogeneities. The performance of the algorithm was evaluated relative to several competing methods using real and synthetic data. Our results demonstrate the efficacy of the proposed algorithm and that it can outperform competing methods, especially when the noise and spatial intensity inhomogeneities are high.