We have developed an algorithm for the rigid-body registration of a 3D CT to a set of C-arm images by matching them to computed cone-beam projections of the CT (DRRs). We precomputed rescaled versions (pyramid) of the CT volume and of the C-arm images. We perform the registration of the CT to the C-arm images starting from their coarsest resolution until we reach some finer resolution that offers a good compromise between time and accuracy. To achieve precision, we use a cubic-spline data model to compute the data pyramids, the DRRs, and the gradient and the Hessian of the cost function. We validate our algorithm on a 3D CT and on C-arm images of a cadaver spine using fiducial markers. When registering the CT to two C-arm images, our algorithm operates safely if the angle between the two image planes is larger than 10°. It achieves an accuracy with a mean and a standard deviation of approximately 2.0±1.0 mm.
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.