Robust Extrinsic Symmetry Estimation in 3D Point Clouds

TL;DR

This paper introduces a robust statistical estimator-based method for detecting reflection symmetry planes in 3D point clouds, effectively handling outliers and missing data, with improved accuracy over existing methods.

Contribution

It proposes a novel optimization approach on a 2-Sphere combined with heat kernel signature for symmetry-invariant matching, enhancing robustness and efficiency.

Findings

Achieves comparable mean ground-truth error to state-of-the-art methods.

Increases F-score by 4.5% on benchmark datasets.

Robustly handles outliers and missing parts in 3D point clouds.

Abstract

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.