Knowledge of vertebra location, shape, and orientation is crucial in many medical applications such as orthopedics or interventional procedures. Computed tomography (CT) offers a high contrast between bone and soft tissues, but automatic vertebra segmentation remains difficult. Hence, the wide range of shapes, aging, and degenerative joint disease alterations as well as the variety of pathological cases encountered in an aging population make automatic segmentation sometimes challenging. Besides, daily practice implies a need for affordable computation time. This paper aims to present a new automated vertebra segmentation method (using a first bounding box for initialization) for CT 3D data which tackles these problems. This method is based on two consecutive steps. The first one is a new coarse-to-fine method efficiently reducing the data amount to obtain a coarse shape of the vertebra. The second step consists in a hidden Markov chain (HMC) segmentation using a specific volume transformation within a Bayesian framework. Our method does not introduce any prior on the expected shape of the vertebra within the bounding box and thus deals with the most frequent pathological cases encountered in daily practice. We experiment this method on a set of standard lumbar, thoracic, and cervical vertebrae and on a public dataset, on pathological cases, and in a simple integration example. Quantitative and qualitative results show that our method is robust to changes in shapes and luminance and provides correct segmentation with respect to pathological cases