General approach to error prediction in point registration

A method for the first-order analysis of the point registration problem is presented and validated. The method is a unified approach to the problem that allows for inhomogeneous and anisotropic fiducial localization error (FLE) and arbitrary weighting in the registration algorithm. Cross-covariance matrices are derived both for target registration error (TRE) and for weighted fiducial registration error (FRE). Furthermore, it is shown that for ideal weighting, in which the weighting matrix for each fiducial equals the inverse of the square root of the cross covariance of the two-space FLE for that fiducial, fluctuations of FRE and TRE are independent. These results are validated by comparison with previously published expressions for special cases and by simulation and shown to be correct. Furthermore, simulations for randomly generated fiducial positions and FLEs are presented that show that correlation is negligible (correlation coefficient < 0.1) for uniform weighting (i.e., no weighting) as well. From these results we conclude that measures of the goodness of fit of the fiducials, e.g., FRE, are unreliable estimators of registration accuracy, i.e., TRE, and should be avoided.