  We investigate a variation of the 3D registration problem, named multi-model
3D registration. In the multi-model registration problem, we are given two
point clouds picturing a set of objects at different poses (and possibly
including points belonging to the background) and we want to simultaneously
reconstruct how all objects moved between the two point clouds. This setup
generalizes standard 3D registration where one wants to reconstruct a single
pose, e.g., the motion of the sensor picturing a static scene. Moreover, it
provides a mathematically grounded formulation for relevant robotics
applications, e.g., where a depth sensor onboard a robot perceives a dynamic
scene and has the goal of estimating its own motion (from the static portion of
the scene) while simultaneously recovering the motion of all dynamic objects.
We assume a correspondence-based setup where we have putative matches between
the two point clouds and consider the practical case where these
correspondences are plagued with outliers. We then propose a simple approach
based on Expectation-Maximization (EM) and establish theoretical conditions
under which the EM approach converges to the ground truth. We evaluate the
approach in simulated and real datasets ranging from table-top scenes to
self-driving scenarios and demonstrate its effectiveness when combined with
state-of-the-art scene flow methods to establish dense correspondences.
