We propose a top-down fully automatic 3D vertebra segmentation algorithm using global shape-related as well as local appearance-related prior information. The former is brought into the system by a global statistical shape model built from annotated training data, i.e., annotated CT volumes. The latter is handled by a machine learning-based component, i.e., a boundary detector, providing a strong discriminative model for vertebra surface appearance by making use of local context-encoding features. This boundary detector, which is essentially a probabilistic boosting-tree classifier, is also learnt from annotated training data. Contextual information is taken into account by representing vertebra surface candidate voxels with high-dimensional vectors of 3D steerable features derived from the observed volume intensities. Our system does not only consider the body of the individual vertebrae but also the spinal processes. Before segmentation, the image parts depicting individual vertebrae are spatially normalized with respect to their bounding box information in terms of translation, orientation, and scale leading to more accurate results. We evaluate segmentation accuracy on 7 CT volumes each depicting 22 vertebrae. The results indicate a symmetric point-to-mesh surface error of 1.37 ± 0.37 mm, which matches the current state-of-the-art.