Purpose: Detailed characterization of pulmonary vascular anatomy has important applications for the diagnosis and management of a variety of vascular diseases. Prior efforts have emphasized using vessel segmentation to gather information on the number or branches, number of bifurcations, and branch length and volume, but accurate traversal of the vessel tree to identify and repair erroneous interconnections between adjacent branches and neighboring tree structures has not been carefully considered. In this study, we endeavor to develop and implement a successful approach to distinguishing and characterizing individual vascular trees from among a complex intermingling of trees. Methods: We developed strategies and parameters in which the algorithm identifies and repairs false branch inter-tree and intra-tree connections to traverse complicated vessel trees. A series of two-dimensional (2D) virtual datasets with a variety of interconnections were constructed for development, testing, and validation. To demonstrate the approach, a series of real 3D computed tomography (CT) lung datasets were obtained, including that of an anthropomorphic chest phantom; an adult human chest CT; a pediatric patient chest CT; and a micro-CT of an excised rat lung preparation. Results: Our method was correct in all 2D virtual test datasets. For each real 3D CT dataset, the resulting simulated vessel tree structures faithfully depicted the vessel tree structures that were originally extracted from the corresponding lung CT scans. Conclusion: We have developed a comprehensive strategy for traversing and labeling interconnected vascular trees and successfully implemented its application to pulmonary vessels observed using 3D CT images of the chest.