Multi-scale EM-ICP: A Fast and Robust Approach for Surface Registration

Abstract

We investigate in this article the rigid registration of large sets of points, generally sampled from surfaces. We formulate this problem as a general Maximum-Likelihood (ML) estimation of the transformation and the matches. We show that, in the specific case of a Gaussian noise, it corresponds to the Iterative Closest Point algorithm (ICP) with the Mahalanobis distance.

Then, considering matches as a hidden variable, we obtain a slightly more complex criterion that can be efficiently solved using Expectation-Maximization (EM) principles. In the case of a Gaussian noise, this new methods corresponds to an ICP with multiple matches weighted by normalized Gaussian weights, giving birth to the EM-ICP acronym of the method.

The variance of the Gaussian noise is a new parameter that can be viewed as a “scale or blurring factor” on our point clouds. We show that EM-ICP robustly aligns the barycenters and inertia moments with a high variance, while it tends toward the accurate ICP for a small variance. Thus, the idea is to use a multi-scale approach using an annealing scheme on this parameter to combine robustness and accuracy. Moreover, we show that at each “scale”, the criterion can be efficiently approximated using a simple decimation of one point set, which drastically speeds up the algorithm.

Experiments on real data demonstrate a spectacular improvement of the performances of EM-ICP w.r.t. the standard ICP algorithm in terms of robustness (a factor of 3 to 4) and speed (a factor 10 to 20), with similar performances in precision. Though the multiscale scheme is only justified with EM, it can also be used to improve ICP, in which case the performances reaches then the one of EM when the data are not too noisy.