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Two segmentation methods, one atlas-based and one neural-network-based, were compared to see how well they can each automatically segment the brain stem and cerebellum in Displacement Encoding with Stimulated Echoes Magnetic Resonance Imaging (DENSE-MRI) data. The segmentation is a pre-requisite for estimating the average displacements in these regions, which have recently been proposed as biomarkers in the diagnosis of Chiari Malformation type I (CMI). In numerical experiments, the segmentations of both methods were similar to manual segmentations provided by trained experts. It was found that, overall, the neural-network-based method alone produced more accurate segmentations than the atlas-based method did alone, but that a combination of the two methods -- in which the atlas-based method is used for the segmentation of the brain stem and the neural-network is used for the segmentation of the cerebellum -- may be the most successful.