Multiresolution-based registration of a volume to a set of its projections

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 of approximately 2.0±1.0 mm.