  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.
