We describe a method for automatic detection and localisation of vertebrae in clinical images that was designed to avoid making a priori assumptions of how many vertebrae are visible. Multiple random forest regressors were trained to identify vertebral end-plates, providing estimates of both the location and pose of the vertebrae. The highest-weighted responses from each model were combined using a Hough-style voting array. A graphical approach was then used to extract contiguous sets of detections representing neighbouring vertebrae, by finding a path linking modes of high weight, subject to pose constraints. The method was evaluated on 320 lateral dual-energy X-ray absorptiometry spinal images with a high prevalence of osteoporotic vertebral fractures, and detected 92% of the vertebrae between T7 and L4 with a mean localisation error of 2.36 mm. When used to initialise a constrained local model segmentation of the vertebrae, the method increased the incidence of fit failures from 1.5 to 2.1% compared to manual initialisation, and produced no difference in fracture classification using a simple classifier.