  This paper addresses the problem of registering multiple point sets.
Solutions to this problem are often approximated by repeatedly solving for
pairwise registration, which results in an uneven treatment of the sets forming
a pair: a model set and a data set. The main drawback of this strategy is that
the model set may contain noise and outliers, which negatively affects the
estimation of the registration parameters. In contrast, the proposed
formulation treats all the point sets on an equal footing. Indeed, all the
points are drawn from a central Gaussian mixture, hence the registration is
cast into a clustering problem. We formally derive batch and incremental EM
algorithms that robustly estimate both the GMM parameters and the rotations and
translations that optimally align the sets. Moreover, the mixture's means play
the role of the registered set of points while the variances provide rich
information about the contribution of each component to the alignment. We
thoroughly test the proposed algorithms on simulated data and on challenging
real data collected with range sensors. We compare them with several
state-of-the-art algorithms, and we show their potential for surface
reconstruction from depth data.
