Low-dose computed tomography (CT) imaging provides a method for obtaining accurate anatomical information without the full radiation exposure inherent in standard CT protocols, and is primarily used in lung cancer screening. Segmentation of the pulmonary arteries from low-dose chest CT images is a vital first step in improving computer-aided detection of frequently missed pulmonary nodules near major arteries. This thesis presents the first fully automated method for segmenting the main pulmonary arterial trees in low-dose CT images. The correlation between the arterial and airway trees was used to develop an automated pulmonary artery seed point detector. The main basal pulmonary arteries are identified by searching for candidate vessels near known airways, using a progressive morphological opening method. The arteries are tracked into the lungs by means of a cylindrical vessel tracker that iteratively fits model cylinders to the CT image. Vessel bifurcations are detected by measuring the rate of change of vessel radii. Subsequent vessels are segmented by initiating new cylinder trackers at bifurcation points. Quantitative analysis of both the number of arteries and veins segmented, as well as the error per vessel, was accomplished with a novel evaluation metric called the Sparse Surface (SS) metric. The SS metric was developed to capture the details of the true vessel surface while reducing the ground-truth marking burden on the human user. This metric is a unique new tool for ground truth marking and segmentation validation, with particular importance in problems with complex geometries. The segmentation method and SS metric were applied to a dataset of seven CT images, and achieved an overall sensitivity of 0.62 and specificity of 0.90 of all manually identified vessels. The average root mean square error between the vessel surface and the segmentation surface was 0.63 mm, or less than 1 voxel. Additionally, seed points were detected automatically for a majority (80%) of cases with labeled airways. This method is an important first step towards robust pulmonary artery segmentation and artery/vein separation in low-dose chest CT, and is the first fully automated method designed for accomplishing this task.