To match anatomical trees such as airways, we propose a graph-based strategy combined with an appropriate distance function. The strategy was devised to cope with topological and geometrical differences that may arise between trees corresponding to the same subject, but extracted from images acquired in different conditions. The proposed distance function, called father/family distance, combines topological and geometrical information in a single measure, by calculating a sum of path-to-path distances between sub-trees of limited extent. To use it successfully, the branches of these sub-trees need to be brought closer, which is obtained by successively translating the roots of these sub-trees prior to their actual matching. The work herein presented contributes to a study of the acute respiratory distress syndrome, where a series of pulmonary CT images from the same subject is acquired at varying settings (pressure and volume) of the mechanical ventilation. The method was evaluated on 45 combinations of synthetic trees, as well as on 15 pairs of real airway trees: nine corresponding to end-expiration and end-inspiration with the same pressure, and six corresponding to end-inspiration with significantly different pressures. It achieved a high rate of successful matches with respect to a hand-made reference containing a total of 2391 matches in real data: sensitivity of 94.3% and precision of 92.8%, when using the basic parameter settings of the algorithm.