Accuracy analysis for RSA: a computer simulation study on 3D marker reconstruction

In this paper, error analysis of three-dimensional marker coordinates reconstructed from noisy two-dimensional measurement in RSA was performed. Mathematical models to predict error propagation of focus position and object points were derived and computer simulations were performed to validate these models. Two clinical calibration cages were compared by testing the error propagation at each RSA step. The results revealed that errors of reconstructed object points were related to the focus position error, two-dimensional measurement error, position of focus and positions of object points, while errors of reconstructed focus position were determined by the two-dimensional measurement error, number of control points and location of the focus. The maximum difference between the mathematical model and the simulation for the assessment of errors of focus position was 14 μm and the maximum difference of object point positions was 1.1 μm. These differences were small and judged irrelevant, hence the simulations indicated that our models were accurate.