  In this paper, we address the problem of registering multiple point clouds
corrupted with high anisotropic localization noise. Our approach follows the
widely used framework of Gaussian mixture model (GMM) reconstruction with an
expectation-maximization (EM) algorithm. Existing methods are based on an
implicit assumption of space-invariant isotropic Gaussian noise. However, this
assumption is violated in practice in applications such as single molecule
localization microscopy (SMLM). To address this issue, we propose to introduce
an explicit localization noise model that decouples shape modeling with the GMM
from noise handling. We design a stochastic EM algorithm that considers
noise-free data as a latent variable, with closed-form solutions at each EM
step. The first advantage of our approach is to handle space-variant and
anisotropic Gaussian noise with arbitrary covariances. The second advantage is
to leverage the explicit noise model to impose prior knowledge about the noise
that may be available from physical sensors. We show on various simulated data
that our noise handling strategy improves significantly the robustness to high
levels of anisotropic noise. We also demonstrate the performance of our method
on real SMLM data.
