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For many orthopaedic, neurological, and oncological applications, an exact segmentation of the vertebral column including an identification of each vertebra is essential. However, although bony structures show high contrast in CT images, the segmentation and labelling of individual vertebrae is challenging. In this paper, we present a comprehensive solution for automatically detecting, identifying, and segmenting vertebrae in CT images. A framework has been designed that takes an arbitrary CT image, e.g., head-neck, thorax, lumbar, or whole spine, as input and provides a segmentation in form of labelled triangulated vertebra surface models. In order to obtain a robust processing chain, profound prior knowledge is applied through the use of various kinds of models covering shape, gradient, and appearance information. The framework has been tested on 64 CT images even including pathologies. In 56 cases, it was successfully applied resulting in a final mean point-to-surface segmentation error of 1.12+/-1.04mm. One key issue is a reliable identification of vertebrae. For a single vertebra, we achieve an identification success of more than 70%. Increasing the number of available vertebrae leads to an increase in the identification rate reaching 100% if 16 or more vertebrae are shown in the image.