Automatic segmentation of structures with missing or invisible borders is a challenging task. Since structures in the lungs are related, humans use contextual and shape information to infer the position of invisible borders. An example of a task in which the borders are often incomplete or invisible is the segmentation of the pulmonary lobes. In this paper, a fully automatic segmentation of the pulmonary lobes in chest CT scans is presented. The method is especially designed to be robust to incomplete fissures by incorporating contextual information from automatic lung, fissure, and bronchial tree segmentations, as well as shape information. Since the method relies on the result of automatic segmentations, it is important that the method is robust against failure of one or more of these segmentation methods. In an extensive experiment on 10 chest CT scans with manual segmentations, the robustness of the method to incomplete fissures and missing input segmentations is shown. In a second experiment on 100 chest CT scans with incomplete fissures, the method is shown to perform well.