  In this note, we propose an approach to initialize the Iterative Closest
Point (ICP) algorithm to match unlabelled point clouds related by rigid
transformations. The method is based on matching the ellipsoids defined by the
points' covariance matrices and then testing the various principal half-axes
matchings that differ by elements of a finite reflection group. We derive
bounds on the robustness of our approach to noise and numerical experiments
confirm our theoretical findings.
