This paper addresses the problem of registering a known structured 3D scene, typically a 3D scan, and its metric Structure-from-Motion (SfM) counterpart. The proposed registration method relies on a prior plane segmentation of the 3D scan. Alignment is carried out by solving either the point-to-plane assignment problem, should the SfM reconstruction be sparse, or the plane-to-plane one in case of dense SfM. A Polynomial Sum-of-Squares optimization theory framework is employed for identifying point-to-plane and plane-to-plane mismatches, i.e. outliers, with certainty. An inlier set maximization approach within a Branch-and-Bound search scheme is adopted to iteratively build potential inlier sets and converge to the solution satisfied by the largest number of assignments. Plane visibility conditions and vague camera locations may be incorporated for better efficiency without sacrificing optimality. The registration problem is solved in two cases: (i) putative correspondences (with possibly overwhelmingly many outliers) are provided as input and (ii) no initial correspondences are available. Our approach yields outstanding results in terms of robustness and optimality.

中文翻译：

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通过平方和多项式对图像集和结构化场景进行稳健和优化配准

本文解决了注册已知结构化 3D 场景（通常为 3D 扫描）及其度量运动结构 (SfM) 对应物的问题。所提出的配准方法依赖于 3D 扫描的先验平面分割。对齐是通过解决点到平面分配问题来执行的，如果 SfM 重建是稀疏的，或者在密集 SfM 的情况下解决平面到平面的问题。多项式平方和优化理论框架用于确定地识别点对平面和平面对平面的失配，即异常值。采用分支定界搜索方案中的内点集最大化方法来迭代构建潜在的内点集并收敛到由最大分配数满足的解决方案。可以在不牺牲最优性的情况下合并平面能见度条件和模糊的摄像机位置以提高效率。配准问题在两种情况下得到解决：（i）假定的对应关系（可能有很多异常值）作为输入提供，（ii）没有初始对应关系可用。我们的方法在稳健性和最优性方面产生了出色的结果。