The segmentation of the human airway tree from volumetric computed tomography (CT) images builds an important step for many clinical applications and for physiological studies. Previously proposed algorithms suffer from one or several problems: leaking into the surrounding lung parenchyma, the need for the user to manually adjust parameters, excessive runtime. Low-dose CT scans are increasingly utilized in lung screening studies, but segmenting them with traditional airway segmentation algorithms often yields less than satisfying results. In this paper, a new airway segmentation method based on fuzzy connectivity is presented. Small adaptive regions of interest are used that follow the airway branches as they are segmented. This has several advantages. It makes it possible to detect leaks early and avoid them, the segmentation algorithm can automatically adapt to changing image parameters, and the computing time is kept within moderate values. The new method is robust in the sense that it works on various types of scans (low-dose and regular dose, normal subjects and diseased subjects) without the need for the user to manually adjust any parameters. Comparison with a commonly used region-grow segmentation algorithm shows that the newly proposed method retrieves a significantly higher count of airway branches. A method that conducts accurate cross-sectional airway measurements on airways is presented as an additional processing step. Measurements are conducted in the original gray-level volume. Validation on a phantom shows that subvoxel accuracy is achieved for all airway sizes and airway orientations.