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Osteoporosis is a bone disease characterized by a reduction in bone mass, resulting in an increased risk of fractures. To diagnose the osteoporosis accurately, bone mineral density (BMD) measurements and fracture analysis (FA) of the Vertebral bodies (VBs) are required. In this paper, we propose a robust and 3D shape based method to segment VBs in clinical computed tomography (CT) images in order to make BMD measurements and FA accurately. In this experiment, image appearance and shape information of VBs are used. In the training step, 3D shape information is obtained from a set of data sets. Then, we estimate the shape variations using a distance probabilistic model which approximates the marginal densities of the VB and background in the variability region. In the segmentation step, the Matched filter is used to detect the VB region automatically. We align the detected volume with 3D shape prior in order to be used in distance probabilistic model. Then, the graph cuts method which integrates the linear combination of Gaussians (LCG), Markov Gibbs Random Field (MGRF), and distance probabilistic model obtained from 3D shape prior is used.