Automated detection and segmentation of vertebral bodies from spinal computed tomography (CT) images is usually a prerequisite step for numerous spine-related medical applications, such as diagnosis, surgical planning and follow-up assessment of spinal pathologies. However, automated detection and segmentation are challenging tasks due to a relatively high degree of anatomical complexity, presence of unclear boundaries and articulation of vertebrae with each other. In this paper, we describe a sparse representation error minimization (SEM) framework for joint detection and segmentation of vertebral bodies in CT images. By minimizing the sparse representation error of sampled intensity values, we are able to recover the oriented bounding box (OBB) and segmentation binary mask for each vertebral body in the CT image. The performance of the proposed SEM framework was evaluated on five CT images of the thoracolumbar spine. The resulting Euclidean distance of 1:75±1:02 mm, computed between the center points of recovered and corresponding reference OBBs, and Dice coefficient of 92:3±2:7%, computed between the resulting and corresponding reference segmentation binary masks, indicate that the proposed framework can successfully detect and segment vertebral bodies in CT images of the thoracolumbar spine.