Accurate segmentation of cerebral vasculature and a quantitative assessment of its morphology is critical to various diagnostic and therapeutic purposes and is pertinent to studying brain health and disease. However, this is still a challenging task due to the complexity of the vascular imaging data. We propose an automated method for cerebral vascular segmentation without the need of any manual intervention as well as a method to skeletonize the binary segmented map to extract vascular geometric features and characterize vessel structure. We combine a Hessian-based probabilistic vessel-enhancing filtering with an active-contour-based technique to segment magnetic resonance and computed tomography angiograms (MRA and CTA) and subsequently extract the vessel centerlines and diameters to calculate the geometrical properties of the vasculature. Our method was validated using a 3D phantom of the Circle-of-Willis region, demonstrating 84% mean Dice similarity coefficient (DSC) and 85% mean Pearson's correlation coefficient (PCC) with minimal modified Hausdorff distance (MHD) error (3 surface pixels at most), and showed superior performance compared to existing segmentation algorithms upon quantitative comparison using DSC, PCC and MHD. We subsequently applied our algorithm to a dataset of 40 subjects, including 1) MRA scans of healthy subjects (n = 10, age = 30 ± 9), 2) MRA scans of stroke patients (n = 10, age = 51 ± 15), 3) CTA scans of healthy subjects (n = 10, age = 62 ± 12), and 4) CTA scans of stroke patients (n = 10, age = 68 ± 11), and obtained a quantitative comparison between the stroke and normal vasculature for both imaging modalities. The vascular network in stroke patients compared to age-adjusted healthy subjects was found to have a significantly (p < 0.05) higher tortuosity (3.24 ± 0.88 rad/cm vs. 7.17 ± 1.61 rad/cm for MRA, and 4.36 ± 1.32 rad/cm vs. 7.80 ± 0.92 rad/cm for CTA), higher fractal dimension (1.36 ± 0.28 vs. 1.71 ± 0.14 for MRA, and 1.56 ± 0.05 vs. 1.69 ± 0.20 for CTA), lower total length (3.46 ± 0.99 m vs. 2.20 ± 0.67 m for CTA), lower total volume (61.80 ± 18.79 ml vs. 34.43 ± 22.9 ml for CTA), lower average diameter (2.4 ± 0.21 mm vs. 2.18 ± 0.07 mm for CTA), and lower average branch length (4.81 ± 1.97 mm vs. 8.68 ± 2.03 mm for MRA), respectively. We additionally studied the change in vascular features with respect to aging and imaging modality. While we observed differences between features as a result of aging, statistical analysis did not show any significant differences, whereas we found that the number of branches were significantly different (p < 0.05) between the two imaging modalities (201 ± 73 for MRA vs. 189 ± 69 for CTA). Our segmentation and feature extraction algorithm can be applied on any imaging modality and can be used in the future to automatically obtain the 3D segmented vasculature for diagnosis and treatment planning as well as to study morphological changes due to stroke and other cerebrovascular diseases (CVD) in the clinic.