Maximum likelihood estimation of the distribution of target registration error

Estimating the alignment accuracy is an important issue in rigid-body point-based registration algorithms. The registration accuracy depends on the level of the noise perturbing the registering data sets. The noise in the data sets arises from the fiducial (point) localization error (FLE) that may have an identical or inhomogeneous, isotropic or anisotropic distribution at each point in each data set. Target registration error (TRE) has been defined in the literature, as an error measure in terms of FLE, to compute the registration accuracy at a point (target) which is not used in the registration process. In this paper, we mathematically derive a general solution to approximate the distribution of TRE after registration of two data sets in the presence of FLE having any type of distribution. The Maximum Likelihood (ML) algorithm is proposed to estimate the registration parameters and their variances between two data sets. The variances are then used in a closed-form solution, previously presented by these authors, to derive the distribution of TRE at a target location. Based on numerical simulations, it is demonstrated that the derived distribution of TRE, in contrast to the existing methods in the literature, accurately follows the distribution generated by Monte Carlo simulation even when FLE has an inhomogeneous isotropic or anisotropic distribution.