We propose a completely automated algorithm for the detection of the spinal centreline and the centres of vertebral bodies and intervertebral discs in images acquired by computed tomography (CT) and magnetic resonance (MR) imaging. The developed methods are based on the analysis of the geometry of spinal structures and the characteristics of CT and MR images and were evaluated on 29 CT and 13 MR images of lumbar spine. The overall mean distance between the obtained and the ground truth spinal centrelines and centres of vertebral bodies and intervertebral discs were 1.8 +/- 1.1 mm and 2.8 +/- 1.9 mm, respectively, and no considerable differences were detected among the results for CT, T(1)-weighted MR and T(2)-weighted MR images. The knowledge of the location of the spinal centreline and the centres of vertebral bodies and intervertebral discs is valuable for the analysis of the spine. The proposed method may therefore be used to initialize the techniques for labelling and segmentation of vertebrae.