Magnetic resonance imaging (MRI) is used to identify the major tissues within a subject's brain. Classification is usually based on a single image providing one measurement for each volume element, or voxel, in a discretization of the brain. A simple model views each voxel as homogeneous, belonging entirely to one of the three major tissue types (gray matter, white matter, and cerebro-spinal fluid); the measurements are normally distributed with means and variances depending on the tissue types

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... of their voxels. Since nearby voxels tend to be of the same tissue type, a Markov random field model can be used to capture the spatial similarity of voxels. A more realistic model would take into account the fact that some voxels are not homogeneous and contain tissues of more than one type. Our approach to this problem is to construct a higher resolution image in which each voxel is divided into subvoxels, and subvoxels are in turn assumed to be homogeneous and follow a Markov random field model. This paper uses a Bayesian hierarchical model to conduct MRI tissue classification. Conditional independence is exploited to improve the speed of sampling. The subvoxel approach provides more accurate tissue classification and also allows more effective estimation of the proportion of major tissue types present in each voxel for both simulated and real data sets. KEY WORDS: Markov random field; Conditional independence; Markov chain Monte Carlo; Brain imaging; Partial volume effect; 3