<title>Multiresolution spline-based 3D/2D registration of CT volume and C-arm images for computer-assisted surgery</title>

We propose an algorithm for aligning a preoperative computed tomography (CT) volume and intraoperative C-arm images, with applications in computer-assisted spinal surgery. Our three-dimensional (3D)/two-dimensional (2D) registration algorithm is based on splines and is tuned to a multiresolution strategy. Its goal is to establish the mutual relations of locations in the real-world scene to locations in the 3D CT and in the 2D C-arm images. The principle of the solution is to simulate a series of C-arm images, using CT data only. Each numerical simulation of a C-arm image is defined by its pose. Our registration algorithm then adjusts this pose until the given C-arm projections and the simulated projections exhibit the greatest degree of similarity. We show the performance of the algorithm for the experiments in a controlled environment which allows for an objective validation of the quality of our algorithm. For each of 100 randomly generated disturbances around the optimum solution, the 3D/2D registration algorithm was successful and resulted in image registration with subpixel error.