Recently, we proposed marginal space learning (MSL) as a generic approach for automatic detection of 3D anatomical structures in many medical imaging modalities. To accurately localize a 3D object, we need to estimate nine parameters (three for position, three for orientation, and three for anisotropic scaling). Instead of uniformly searching the original nine-dimensional parameter space, only low-dimensional marginal spaces are uniformly searched in MSL, which significantly improves the speed. In many real applications, a strong correlation may exist among parameters in the same marginal spaces. For example, a large object may have large scaling values along all directions. In this paper, we propose constrained MSL to exploit this correlation for further speed-up. As another major contribution, we propose to use quaternions for 3D orientation representation and distance measurement to overcome the inherent drawbacks of Euler angles in the original MSL. The proposed method has been tested on three 3D anatomical structure detection problems in medical images, including liver detection in computed tomography (CT) volumes, and left ventricle detection in both CT and ultrasound volumes. Experiments on the largest datasets ever reported show that constrained MSL can improve the detection speed up to 14 times, while achieving comparable or better detection accuracy. It takes less than half a second to detect a 3D anatomical structure in a volume.