A pulmonary fissure is a boundary between the lobes in the lungs. Its segmentation is of clinical interest as it facilitates the assessment of lung disease on a lobar level. This paper describes a new approach for segmenting the major fissures in both lungs on thin-section computed tomography (CT). An image transformation called "ridge map" is proposed for enhancing the appearance of fissures on CT. A curve-growing process, modeled by a Bayesian network, is described that is influenced by both the features of the ridge map and prior knowledge of the shape of the fissure. The process is implemented in an adaptive regularization framework that balances these influences and reflects the causal dependencies in the Bayesian network using an entropy measure. The method effectively alleviates the problem of inappropriate weights of regularization terms, an effect that can occur with static regularization methods. The method was applied to segment and visualize the lobes of the lungs on chest CT of 10 patients with pulmonary nodules. Only 78 out of 3286 left or right lung regions with fissures (2.4%) required manual correction. The average distance between the automatically segmented and the manually delineated "ground-truth" fissures was 1.01 mm, which was similar to the average distance of 1.03 mm between two sets of manually segmented fissures. The method has a linear-time worst-case complexity and segments the upper lung from the lower lung on a standard computer in less than 5 min.