In the framework of computer-aided diagnosis, pulmonary airway investigation based on multi-detector computerized tomography (MDCT) requires the development of specific tools for data interaction and analysis. The 3D segmentation of the bronchial tree provides radiologists with appropriate examination modalities such as CT bronchography, for a global analysis, or virtual endoscopy, for a local endoluminal diagnosis. Focusing on the latter modality, this paper proposes a set of advanced navigation and investigation tools based on the automatic extraction of the central axis (CA) of the 3D segmented airways. In the case of complex branching structures, such as the bronchial tree, the automatic CA computation is a challenging problem raising several difficulties related to geometry and topology preservation. In this respect, an original approach is presented, combining 3D distance map information and geodesic front propagation in order to accurately detect branching points and to preserve the original 3D topology of the airways, irrespective to both caliber variability with the bronchial order and to bronchial wall irregularities. The CA information is represented as a multi-valued and hierarchic tree structure, making possible automatic trajectory computation between two given points, bronchial caliber estimation in the plane orthogonal to the bronchus axis at a given location, branch indexation, and so on. These applications are illustrated on clinical data including both normal and pathological airway morphologies.