A Theoretical Comparison of Different Target Registration Error Estimators

Estimation of target registration error (TRE), a common measure of the registration accuracy, is an important issue in computer assisted surgeries. Within the last decade, several new approaches have been developed to estimate either the mean squared value of TRE or the distribution of TRE under different noise conditions. In this paper, we theoretically demonstrate that all the proposed algorithms converge to a general Maximum Likelihood (ML) solution. Numerical simulations are performed to validate our derivations. Using experimentally measured fiducial localization error, we provide an example of TRE prediction in the presence of anisotropic noise.