We propose two types of novel morphological metrics for quantifying the geometry of tubular structures on computed tomography (CT) images. We apply our metrics to identify irregularities in the airway of patients with chronic obstructive pulmonary disease (COPD) and demonstrate that they provide complementary information to the conventional metrics used to assess COPD, such as the tissue density distribution in lung parenchyma and the wall area ratio of the segmented airway. The three-dimensional shape of the airway and its abstraction as a rooted tree with the root at the trachea carina are automatically extracted from a lung CT volume, and the two metrics are computed based on a mathematical tool called persistent homology; treeH0 quantifies the distribution of branch lengths to assess the complexity of the tree-like structure and radialH0 quantifies the irregularities in the luminal radius along the airway. We show our metrics are associated with clinical outcomes.