Robust 2D/3D registration for fast-flexion motion of the knee joint using hybrid optimization

Previously, we proposed a 2D/3D registration method that uses Powell’s algorithm to obtain 3D motion of a knee joint by 3D computed-tomography and bi-plane fluoroscopic images. The 2D/3D registration is performed consecutively and automatically for each frame of the fluoroscopic images. This method starts from the optimum parameters of the previous frame for each frame except for the first one, and it searches for the next set of optimum parameters using Powell’s algorithm. However, if the flexion motion of the knee joint is fast, it is likely that Powell’s algorithm will provide a mismatch because the initial parameters are far from the correct ones. In this study, we applied a hybrid optimization algorithm (HPS) combining Powell’s algorithm with the Nelder–Mead simplex (NM-simplex) algorithm to overcome this problem. The performance of the HPS was compared with the separate performances of Powell’s algorithm and the NM-simplex algorithm, the Quasi-Newton algorithm and hybrid optimization algorithm with the Quasi-Newton and NM-simplex algorithms with five patient data sets in terms of the root-mean-square error (RMSE), target registration error (TRE), success rate, and processing time. The RMSE, TRE, and the success rate of the HPS were better than those of the other optimization algorithms, and the processing time was similar to that of Powell’s algorithm alone.