Detecting the reflection symmetry plane of an object represented by a 3D point cloud is a fundamental problem in 3D computer vision and geometry processing due to its various applications, such as compression, object detection, robotic grasping, 3D surface reconstruction, etc. There exist several efficient approaches for solving this problem for clean 3D point clouds. However, it is a challenging problem to solve in the presence of outliers and missing parts. The existing methods try to overcome this challenge mostly by voting-based techniques but do not work efficiently. In this work, we proposed a statistical estimator-based approach for the plane of reflection symmetry that is robust to outliers and missing parts. We pose the problem of finding the optimal estimator for the reflection symmetry as an optimization problem on a 2-Sphere that quickly converges to the global solution for an approximate initialization. We further adapt the heat kernel signature for symmetry invariant matching of mirror symmetric points. This approach helps us to decouple the chicken-and-egg problem of finding the optimal symmetry plane and correspondences between the reflective symmetric points. The proposed approach achieves comparable mean ground-truth error and 4.5\% increment in the F-score as compared to the state-of-the-art approaches on the benchmark dataset.

翻译：检测由三维点云表示的物体的反射对称平面是三维计算机视觉和几何处理中的一个基本问题，其应用广泛，例如压缩、物体检测、机器人抓取、三维表面重建等。对于无噪的三维点云，已有多种高效方法可解决此问题。然而，在存在离群点和缺失部分的情况下，这是一个具有挑战性的问题。现有方法大多通过基于投票的技术来克服这一挑战，但效率不高。在本工作中，我们提出了一种基于统计估计器的反射对称平面方法，该方法对离群点和缺失部分具有鲁棒性。我们将反射对称的最优估计器寻找问题建模为定义在二维球面上的优化问题，该问题在近似初始化下能快速收敛到全局解。我们进一步采用热核签名进行镜像对称点的对称不变匹配。该方法有助于解耦寻找最优对称平面与对称点对应关系之间的"鸡与蛋"问题。在基准数据集上，与最先进方法相比，所提方法实现了相当的平均真实误差，并将F分数提高了4.5%。