Rotation invariance principles in 2D/3D registration

2D/3D patient-to-computed tomography (CT) registration is a method to determine a transformation that maps two coordinate systems by comparing a projection image rendered from CT to a real projection image. Applications include exact patient positioning in radiation therapy, calibration of surgical robots, and pose estimation in computer-aided surgery. One of the problems associated with 2D/3D registration is the fact that finding a registration includes solving a minimization problem in six degrees-of-freedom (dof) in motion. This results in considerable time expenses since for each iteration step at least one volume rendering has to be computed. We show that by choosing an appropriate world coordinate system and by applying a 2D/2D registration method in each iteration step, the number of iterations can be grossly reduced from n(6) to n(5). Here, n is the number of discrete variations around a given coordinate. Depending on the configuration of the optimization algorithm, this reduces the total number of iterations necessary to at least 1/3 of it's original value. The method was implemented and extensively tested on simulated X-ray images of a pelvis. We conclude that this hardware-independent optimization of 2D/3D registration is a step towards increasing the acceptance of this promising method for a wide number of clinical applications.