The lungs exchange air with the external environment via the pulmonary airways. Computed tomography (CT) scanning can be used to obtain detailed images of the pulmonary anatomy, including the airways. These images have been used to measure airway geometry, study airway reactivity, and guide surgical interventions. Prior to these applications, airway segmentation can be used to identify the airway lumen in the CT images. Airway tree segmentation can be performed manually by an image analyst, but the complexity of the tree makes manual segmentation tedious and extremely time-consuming. We describe a fully automatic technique for segmenting the airway tree in three-dimensional (3-D) CT images of the thorax. We use grayscale morphological reconstruction to identify candidate airways on CT slices and then reconstruct a connected 3-D airway tree. After segmentation, we estimate airway branchpoints based on connectivity changes in the reconstructed tree. Compared to manual analysis on 3-mm-thick electron-beam CT images, the automatic approach has an overall airway branch detection sensitivity of approximately 73%.