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Quantification of the degree of stenosis or vessel dimensions are important for diagnosis of vascular diseases and planning vascular interventions. Although diagnosis from three-dimensional (3-D) magnetic resonance angiograms (MRA's) is mainly performed on two-dimensional (2-D) maximum intensity projections, automated quantification of vascular segments directly from the 3-D dataset is desirable to provide accurate and objective measurements of the 3-D anatomy. A model-based method for quantitative 3-D MRA is proposed. Linear vessel segments are modeled with a central vessel axis curve coupled to a vessel wall surface. A novel image feature to guide the deformation of the central vessel axis is introduced. Subsequently, concepts of deformable models are combined with knowledge of the physics of the acquisition technique to accurately segment the vessel wall and compute the vessel diameter and other geometrical properties. The method is illustrated and validated on a carotid bifurcation phantom, with ground truth and medical experts as comparisons. Also, results on 3-D time-of-flight (TOF) MRA images of the carotids are shown. The approach is a promising technique to assess several geometrical vascular parameters directly on the source 3-D images, providing an objective mechanism for stenosis grading.