We present a method that significantly improves magnetic resonance imaging (MRI) based brain tissue segmentation by modeling the topography of boundaries between tissue compartments. Edge operators are used to identify tissue interfaces and thereby more realistically model tissue label dependencies between adjacent voxels on opposite sides of an interface. When applied to a synthetic MRI template corrupted by additive noise, it provided more consistent tissue labeling across noise levels than two commonly used methods (FAST and SPM5). When applied to longitudinal MRI series it provided lesser variability in individual trajectories of tissue change, suggesting superior ability to discriminate real tissue change from noise. These results suggest that this method may be useful for robust longitudinal brain tissue change estimation.