A Faster Method for 3D/2D Medical Image Registration--a Simulation Study

3D/2D 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. Iterative variation of the CT's position between rendering steps finally leads to exact registration. 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 3D/2D 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 requirements 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 n6 to n5. 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 tibia, a pelvis and a skull base. When using one projective image and a discrete full parameter space search for solving the optimization problem, average accuracy was found to be 1.0 +/- 0.6(degrees) and 4.1 +/- 1.9 (mm) for a registration in six parameters, and 1.0 +/- 0.7(degrees) and 4.2 +/- 1.6 (mm) when using the 5 + 1 dof method described in this paper. Time requirements were reduced by a factor 3.1. We conclude that this hardware-independent optimization of 3D/2D registration is a step towards increasing the acceptance of this promising method for a wide number of clinical applications.