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Bone mineral density (BMD) measurements and fracture analysis of the spine bones are restricted to the Vertebral bodies (VBs), especially the trabecular bones (TBs). In this paper, we propose a novel, fast, and robust 3D framework to segment VBs and trabecular bones in clinical computed tomography (CT) images without any user intervention. The Matched filter is employed to detect the VB region automatically. To segment the whole VB, the graph cuts method which integrates a linear combination of Gaussians (LCG) and Markov Gibbs Random Field (MGRF) is used. Then, the cortical and trabecular bones are segmented using local volume growing methods. Validity was analyzed using ground truths of data sets (expert segmentation) and the European Spine Phantom (ESP) as a known reference. Experiments on the data sets show that the proposed segmentation approach is more accurate than other known alternatives.