This invention relates generally to medical imaging and, in particular, to a method and system for reconstructing a model path through a branched tubular organ. Novel methodologies and systems segment and define accurate endoluminal surfaces in airway trees, including small peripheral bronchi. An automatic algorithm is described that searches the entire lung volume for airway branches and poses airway-tree segmentation as a global graph-theoretic optimization problem. A suite of interactive segmentation tools for cleaning and extending critical areas of the automatically segmented result is disclosed. A model path is reconstructed through the airway tree.