Recovering projection geometry: how a cheap camera can outperform an expensive stereo system

Recovering the projection geometry of an X-ray system or an augmented reality video see-through Head Mounted Display (HMD) are mathematically quite similar. Recent work in both medical imaging and augmented reality use external optical sensors in order to recover the motion of the imaging system. In this paper, we take the example of the recovery of an X-ray projection geometry. We show that the mathematical problem, which needs to be solved, is equivalent to the hand-eye calibration well studied in both computer vision and robotics community. We present a comparative study for the recovery of the motion and therefore projection geometry using five different hand-eye calibration methods proposed in the literature. We compare the motion estimation results using expensive external stereo-based tracking systems with one obtained by using an integrated optical camera. The paper concludes by showing that even if the motion estimation is more accurate when using an external sensor, the projection geometry is better estimated by the integrated optical camera. These results are of crucial importance to both medical imaging and augmented reality communities.