Nagar, Rajendra

Reflection symmetry is a very commonly occurring feature in both natural and man-made objects, which helps in understanding objects better and makes them visually pleasing. Detection of reflection symmetry is a fundamental problem in the field of computer vision and computer graphics which aids in understanding and representing reflective symmetric objects. In this work, we attempt the problem of detecting the 3D global reflection symmetry of a 3D object represented as a point cloud. The main challenge is to handle outliers, missing parts, and perturbations from the perfect reflection symmetry. We propose a descriptor-free approach, in which, we pose the problem of reflection symmetry detection as an optimization problem and provide a closed-form solution. We show that the proposed method achieves state-of-the-art performance on the standard dataset.

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. Several approaches exist to solve 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 primarily 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.