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.

我们研究了 3D 注册问题的一个变种，名为多模型 3D 注册。在多模型注册问题中，我们给出两个描绘了不同姿态下一组物体（可能包括属于背景的点）的点云，并且我们希望同时重建出这两个点云之间所有物体的运动。该方法通用于标准的 3D 注册，其中需要重建出单个姿态，例如传感器描绘静态场景的运动。此外，它为相关的机器人应用提供了数学上的基础，例如，机器人上的深度传感器感知动态场景，并且目标是在同时恢复出自身的运动（从静态部分场景中）以及所有动态物体的运动。我们假设一个基于对应关系的设置，在两个点云之间存在着匹配关系，同时考虑了这些对应关系受到异常值干扰的实际情况。然后，我们提出了一种基于期望最大化（Expectation-Maximization）的简单方法，并建立了 EM 方法收敛到真实结果的理论条件。我们在从桌面场景到自动驾驶场景的模拟和实际数据集上评估了该方法，并证明其与最先进的场景流方法相结合时的有效性。