Detailed segmentation of the vertebrae is an important pre-requisite in various applications of image-based spine assessment, surgery and biomechanical modeling. In particular, accurate segmentation of the processes is required for image-guided interventions, for example for optimal placement of bone grafts between the transverse processes. Furthermore, the geometry of the processes is now required in musculoskeletal models due to their interaction with the muscles and ligaments. In this paper, we present a new method for detailed segmentation of both the vertebral bodies and processes based on statistical shape decomposition and conditional models. The proposed technique is specifically developed with the aim to handle the complex geometry of the processes and the large variability between individuals. The key technical novelty in this work is the introduction of a part-based statistical decomposition of the vertebrae, such that the complexity of the subparts is effectively reduced, and model specificity is increased. Subsequently, in order to maintain the statistical and anatomic coherence of the ensemble, conditional models are used to model the statistical inter-relationships between the different subparts. For shape reconstruction and segmentation, a robust model fitting procedure is used to exclude improbable inter-part relationships in the estimation of the shape parameters. Segmentation results based on a dataset of 30 healthy CT scans and a dataset of 10 pathological scans show a point-to-surface error improvement of 20% and 17% respectively, and the potential of the proposed technique for detailed vertebral modeling.