A level set based method is presented for cerebral vascular tree segmentation from computed tomography angiography (CTA) data. The method starts with bone masking by registering a contrast enhanced scan with a low-dose mask scan in which the bone has been segmented. Then an estimate of the background and vessel intensity distributions is made based on the intensity histogram which is used to steer the level set to capture the vessel boundaries. The relevant parameters of the level set evolution are optimized using a training set. The method is validated by a diameter quantification study which is carried out on phantom data, representing ground truth, and 10 patient data sets. The results are compared to manually obtained measurements by two expert observers. In the phantom study, the method achieves similar accuracy as the observers, but is unbiased whereas the observers are biased, i.e., the results are 0.00+/-0.23 vs. -0.32+/-0.23 mm. Also, the method's reproducibility is slightly better than the inter-and intra-observer variability. In the patient study, the method is in agreement with the observers and also, the method's reproducibility -0.04+/-0.17 mm is similar to the inter-observer variability 0.06+/-0.17 mm. Since the method achieves comparable accuracy and reproducibility as the observers, and since the method achieves better performance than the observers with respect to ground truth, we conclude that the level set based vessel segmentation is a promising method for automated and accurate CTA diameter quantification.