We study the problem of aligning two sets of 3D geometric primitives given known correspondences. Our first contribution is to show that this primitive alignment framework unifies five perception problems including point cloud registration, primitive (mesh) registration, category-level 3D registration, absolution pose estimation (APE), and category-level APE. Our second contribution is to propose DynAMical Pose estimation (DAMP), the first general and practical algorithm to solve primitive alignment problem by simulating rigid body dynamics arising from virtual springs and damping, where the springs span the shortest distances between corresponding primitives. We evaluate DAMP in simulated and real datasets across all five problems, and demonstrate (i) DAMP always converges to the globally optimal solution in the first three problems with 3D-3D correspondences; (ii) although DAMP sometimes converges to suboptimal solutions in the last two problems with 2D-3D correspondences, using a scheme for escaping local minima, DAMP always succeeds. Our third contribution is to demystify the surprising empirical performance of DAMP and formally prove a global convergence result in the case of point cloud registration by charactering local stability of the equilibrium points of the underlying dynamical system.

翻译：我们研究如何将已知通信中的两组三维几何原始体相匹配的问题。 我们的第一个贡献是显示这个原始的校准框架将五个感知问题统一起来,包括点云登记、原始(黑)登记、3D类登记、3D类登记、和解包含估计(APE)和APE。我们的第二个贡献是提出Dynamical Pose估计(DAMP),这是通过模拟虚拟泉源产生的僵硬身体动态来解决原始对齐问题的第一个一般和实用的算法,这里的弹簧跨越相应的原始体之间的最短距离。我们在模拟和真实的数据集中评估DAMP在所有五个问题中都评估DAMP,并展示:(一) DAMP在前三个问题中,D3D通信中总是与全球最佳解决办法一致;(二) 虽然DAMP有时在最后两个问题中与2D-3D对应体的次最佳解决办法相匹配,使用一个逃离当地迷你马的计划,DMP总是成功。我们的第三个贡献是消除DAMP的惊人实证性表现,并正式证明在稳定点上的全球结果。