Extraction, segmentation and analysis of pulmonary vessels from computed tomography (CT) images of the human chest is an important topic for a wide range of applications in medical image analysis. We present a pulmonary vessel extraction and segmentation algorithm which is fast, fully automatic and robust against noise. It uses a segmentation of the airway tree and a left and right lung labeled volume to restrict the response of an offset medialness vessel enhancement filter. We test our algorithm on phantom data as well as on the VESSEL12 challenge dataset. Our clinical focus is on the detection of pulmonary hypertension (PH), which is a chronic disorder of the pulmonary circulation, marked by an elevated mean pulmonary arterial pressure (mPAP). On a dataset containing 24 patients from a clinical pulmonary hypertension pilot study, we show that quantitative indices derived from the segmented pulmonary vessels correlate with the mPAP and are applicable to distinguish patients with and without PH.