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We present a novel three dimensional (3D) region-based hidden Markov model (rbHMM) for unsupervised image segmentation. Our contributions are twofold. First, our rbHMM employs a more efficient representation of the image than approaches based on a rectangular lattice or grid; thus, resulting in a faster optimization process. Second, our proposed novel tree-structured parameter estimation algorithm for the rbHMM provides a locally optimal data labeling that is invariant to object rotation. We demonstrate the advantages of our segmentation technique by validating on synthetic images of geometric shapes as well as both simulated and clinical magnetic resonance imaging (MRI) data of the brain. For the geometric shape data, we show that our method produces more accurate results in less time than a grid-based HMM framework using a similar optimization strategy. For the brain MRI data, our white and gray matter segmentation results in substantially greater accuracy than both block-based 3D HMM estimation and expectation-maximization hidden Markov random field (HMRF-EM) approaches.