The analysis of pulmonary vessels provides better insights into the lung physio-pathology and offers the basis for a functional investigation of the respiratory system. In order to be performed in clinical routine, such analysis has to be compatible with the general protocol for thorax imaging based on multi-slice CT (MSCT), which does not involve the use of contrast agent for vessels enhancement. Despite the fact that a visual assessment of the pulmonary vascular tree is facilitated by the natural contrast existing between vessels and lung parenchyma, a quantitative analysis becomes quickly tedious due to the high spatial density and subdivision complexity of these anatomical structures. In this paper, we develop an automated 3D approach for the segmentation of the pulmonary vessels in MSCT allowing further quantification facilities for the lung function. The proposed approach combines mathematical morphology and discrete geometry operators in order to reach distal small caliber blood vessels and to preserve the border with the wall of the bronchial tree which features identical intensity values. In this respect, the pulmonary field is first roughly segmented using thresholding, and the trachea and the main bronchi removed. The lung shape is then regularized by morphological alternate filtering and the high opacities (vessels, bronchi, and other eventual pathologic features) selected. After the attenuation of the bronchus wall for large and medium airways, the set of vessel candidates are obtained by morphological grayscale reconstruction and binarization. The residual bronchus wall components are then removed by means of a geometrical shape filtering which includes skeletonization and cylindrical shape estimation. The morphology of the reconstructed pulmonary vessels can be visually investigated with volume rendering, by associating a specific color code with the local vessel caliber. The complement set of the vascular tree among the high intensity structures in the lung may also inform on lung pathological conditions (inflammation, interstitial disease, nodular patterns,...). The results obtained on normal and pathological subjects or in inspiration vs. expiration, are presented and discussed.