Providing an in-vivo and non-invasive tool for 3D reconstruction of anatomical tree structures (vascular networks and bronchial tree) from 2D or pseudo-3D data acquisition remains today a key and challenging issue for computer vision in medical imaging. In this paper, we address this issue within the specific framework of airways. Our contribution consists of a realistic 3D modeling of the bronchial tree structure. Mathematical and physical principles here involved refer to 3D mathematical morphology (3DMM), Diffusion Limited Aggregation (DLA), energy-based modeling and fractal representations. Here, a model-based 3D reconstruction of the bronchial tree is achieved in a fully-automated way. The tree segmentation is performed by applying a DLA-based propagation. The initialization results from the 3DMM procedure. Energy modeling and fractals are used to overcome the well- known cases of subdivision ambiguities and artifact generation related to such a complex topological structure. Therefore, the proposed method is robust with respect to anatomical variabilities. The 3D bronchial tree reconstruction is finally visualized by using a semi-transparent volume rendering technique which provides brochogram- like representations. The developed method was applied to a data set acquired within a clinical framework by using both double- and multiple- detector CT scanners (5 patients corresponding to 1500 axial slices, including both normal and strong pathological cases). Results thus obtained, compared with a previously-developed 2D/3D technique, show significant improvements and accuracy increase of the 3D reconstructions.