  Point set registration is an essential step in many computer vision
applications, such as 3D reconstruction and SLAM. Although there exist many
registration algorithms for different purposes, however, this topic is still
challenging due to the increasing complexity of various real-world scenarios,
such as heavy noise and outlier contamination. In this paper, we propose a
novel probabilistic generative method to simultaneously align multiple point
sets based on the heavy-tailed Laplacian distribution. The proposed method
assumes each data point is generated by a Laplacian Mixture Model (LMM), where
its centers are determined by the corresponding points in other point sets.
Different from the previous Gaussian Mixture Model (GMM) based method, which
minimizes the quadratic distance between points and centers of Gaussian
probability density, LMM minimizes the sparsity-induced L1 distance, thereby it
is more robust against noise and outliers. We adopt Expectation-Maximization
(EM) framework to solve LMM parameters and rigid transformations. We
approximate the L1 optimization as a linear programming problem by exponential
mapping in Lie algebra, which can be effectively solved through the interior
point method. To improve efficiency, we also solve the L1 optimization by
Alternating Direction Multiplier Method (ADMM). We demonstrate the advantages
of our method by comparing it with representative state-of-the-art approaches
on benchmark challenging data sets, in terms of robustness and accuracy.
