The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of symmetry. By reflecting the points of each set with respect to the plane of symmetry, we can largely increase the overlap between the sets and therefore boost the registration process. However, prior knowledge about the plane of symmetry is generally unavailable or at least very hard to find, especially with limited partial views. Finding this plane could strongly benefit from a prior alignment of the partial point sets. We solve this chicken-and-egg problem by jointly optimizing the relative pose and symmetry plane parameters. We present a globally optimal solver by employing the branch-and-bound paradigm and thereby demonstrate that joint symmetry plane fitting leads to a great improvement over the current state of the art in globally optimal point set registration for common objects. We conclude with an interesting application of our method to dense 3D reconstruction of scenes with repetitive objects.

本工作提出了一种解决难题的解决方案，该难题是以非常有限的重叠来记录同一对象的两个部分点集。我们利用一个事实，即在人造环境中发现的大多数对象都包含一个对称平面。通过相对于对称平面反映每个集合的点，我们可以大大增加集合之间的重叠，从而加快配准过程。然而，关于对称平面的现有知识通常是不可用的，或者至少很难找到，特别是在局部视图有限的情况下。找到该平面可以极大地受益于部分点集的事先对齐。我们通过共同优化相对姿态和对称平面参数来解决此“鸡与蛋”问题。我们通过采用分支定界范式介绍了一种全局最优解器，从而证明了联合对称平面拟合在共同对象的全局最优点集配准方面导致了当前技术水平上的巨大进步。最后，我们将我们的方法有趣地应用于具有重复对象的场景的密集3D重建中。