Automatically extracting vertebra regions from a spinal magnetic resonance image is normally required as the first step to an intelligent spinal MR image diagnosis system. In this work, we develop a fully automatic vertebra detection and segmentation method. Our system consists of three stages; namely, AdaBoost-based vertebra detection, detection refinement via robust curve fitting, and vertebra segmentation by an iterative normalized cut algorithm. We proposed an efficient and effective vertebra detector, which is trained by the improved AdaBoost algorithm, to locate the initial vertebra positions. Then, a robust estimation procedure is applied to fit all the vertebrae as a polynomial spinal curve to refine the vertebra detection results. Finally, an iterative segmentation algorithm based on normalized-cut energy minimization is applied to extract the precise vertebra regions from the detected windows. The experimental results show our system can achieve high accuracy on a number of testing 3D spinal MRI data sets.