In this paper, a methodology, based on 3D geometry extracted from Contract-Enhanced MR Angiograms, is presented to identify and segment the internal carotid arteries for stenosis quantification. The internal carotid artery is automatically identified by tracking the carotid bifurcation and selecting the artery branch with no further arterial branches. To avoid the problems encountered using global thresholding, the artery segmentation is carried out using local adaptive thresholding based on cross-sectional slices perpendicular to the arterial central axis. The crosssectional areas for normal and stenotic regions are then measured. Initial results for eight internal carotid arteries are included, to demonstrate the performance of the method. Further experiments with various levels of additive Gaussian noise give only small variations in the cross-sectional area measurements for values of up to 40.