Reliable segmentation of 3D magnetic resonance angiography (MRA) is fundamental for planning and performing neurosurgical procedures, but also for detecting vascular pathologies. We propose here a method for brain vessel segmentation based on mathematical morphology tools. This method, devoted to phase-contrast MRA (PC-MRA) performs vessel segmentation by applying an adaptive set of grey-level hit-or-miss operators on each point of the MR data. High level anatomical knowledge modeled by a vascular atlas is used in order to adapt the parameters of these operators (number, size, and orientation) to the current position. The method has been performed on 30 PC-MRA cases composed of both phase and magnitude images. The results have been validated and compared to segmented data obtained by applying a region-growing algorithm on the same database. They tend to prove that the method is reliable for brain vessel detection and additionnally provides information on vessel size and orientation without requiring any post-processing step.