Estimation of target registration error considering small inhomogeneous and anisotropic bias in fiducial localizer error

Rigid point-based registration is commonly used in many aspects of image-guided surgery (IGS). The registration task is usually performed by first identifying corresponding fiducials (markers) in two spaces. Since the localization of fiduicals is imprecise, the performed registration is not perfect and has some error inevitably. Extensive work has been done to estimate the registration error when the FLE (fiducial localization error) has zero-mean Gaussian distribution over the entire set of fiducials. The effect of homogeneous bias has been first well explored in [1]. If FLE has inhomogeneous bias, the effect of bias on registration accuracy has not been investigated so well. In this work, we derive formulation that relate inhomogeneous and anisotropic bias in FLE to the rms (root-mean-square) of TRE (target registration error) of the performed registration. The new statistical model is verified through a Monte Carlo simulation with optically tracked instrument tool. The simulation results show that in most cases of various instrument tool designs and FLE models, the theoretical estimation can serve as an upper bound for the real TRE rms value in rigid point-based registration.