An efficient EM-ICP algorithm for non-linear registration of large 3D point sets

Abstract

In this paper, we present a new method for non-linear pairwise registration of 3D point sets. In this method, we consider the points of the first set as the draws of a Gaussian mixture model whose centres are the displaced points of the second set. Next we perform a maximum a posteriori estimation of the parameters (which include the unknown transformation) of this model using the expectation–maximisation (EM) algorithm. Compared to other methods using the same “EM-ICP” framework, we propose four key modifications leading to an efficient algorithm allowing for fast registration of large 3D point sets: (1) truncation of the cost function; (2) symmetrisation of the point-to-point correspondences; (3) specification of priors on these correspondences using differential geometry; (4) efficient encoding of deformations using the RKHS theory and the Fourier analysis. We evaluate the added value of these modifications and compare our method to the state-of-the-art CPD algorithm on real and simulated data.