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The study of the architecture of the optic nerve head (ONH) may provide valuable information about the development and progression of glaucoma. To this end, we have generated three-dimensional datasets from monkey eyes under controlled intraocular pressure (IOP). Segmentation of the connective tissues in this area is crucial to obtain an accurate measurement of geometrical parameters and to build mechanical models. However, this segmentation is made difficult by the complicated geometry and the artifacts introduced in the dataset building process. We present a novel segmentation algorithm, based on expectation-maximization, which incorporates an anisotropic Markov random field (MRF) to introduce prior knowledge about the geometry of the structure. The structure tensor is used to characterize the predominant structure direction and the spatial coherence at each point. The algorithm, which has been validated on an artificial validation dataset that mimics our ONH datasets, shows significant improvement over an isotropic MRF. Results on the real datasets demonstrate the ability of the new algorithm to obtain accurate, spatially consistent segmentations of this structure.