Briefly, the Coherent Point Drift regards the points in Y as Gaussian mixture model centroids that generate the points in X . The soft correspondences between points, i.e. the probability that a given point in X was generated by a Gaussian centered at a given point in Y, are automatically inferred in Coherent Point Drift. The likelihood is maximized by the expectation-maximization (EM) algorithm: the E-step estimates probabilities of correspondence between the points given the current estimate for the rotation matrix and Gaussian variance; the M-step chooses the rotation matrix to minimize the distances between the points in X and transformed points in Y, weighted by current estimates of the probabilities of correspondence, in addition to making the Gaussians as narrow as possible.