Recovering the X-ray projection geometry for three-dimensional tomographic reconstruction with additional sensors: attached camera versus external navigation system

Three-dimensional tomographic reconstruction using intra-operative mobile C-arms could provide physicians with new and exciting tools for image-guided surgery. Recovery of the projection geometry of mobile X-ray systems is a crucial step for such reconstruction procedures. Recent work on medical imaging describes the use of optical or electro-magnetic sensor systems in order to navigate surgical instruments. These systems can also be used for the estimation of C-arm motion, and therefore for the recovery of the projection geometry of the X-ray C-arm. In this case, the mathematical problem that needs to be solved is equivalent to the hand-eye calibration well studied by both the computer vision and robotics community. We first study the recovery of the motion and projection geometry using five different hand-eye calibration methods proposed in the literature. The optical navigation system POLARIS from Northern Digital Inc. was used in our experiments. The results of the estimated motion and projection geometry using the five hand-eye calibration methods are compared with the same results obtained using an off-the-shelf CCD camera attached to the mobile C-arm. The experimental results include three-dimensional tomographic reconstruction results using our mobile C-arm. We show that even though the motion of the C-arm is more precisely recovered using the navigation system, the projection geometry is better estimated using the attached CCD camera.