Detecting Approximate Reflection Symmetry in a Point Set using Optimization on Manifold
This addresses the problem of symmetry detection in computer vision and geometry processing, offering a descriptor-independent method that is robust to distortions, though it appears incremental as it builds on existing optimization frameworks.
The authors tackled the problem of detecting approximate reflection symmetry in point sets by formulating it as an optimization on a manifold, achieving state-of-the-art performance on a standard benchmark dataset.
We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb{R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting approximate reflection symmetry as the problem of establishing correspondences between the points which are reflections of each other and we determine the reflection symmetry transformation. We formulate an optimization framework in which the problem of establishing the correspondences amounts to solving a linear assignment problem and the problem of determining the reflection symmetry transformation amounts to solving an optimization problem on a smooth Riemannian product manifold. The proposed approach estimates the symmetry from the geometry of the points and is descriptor independent. We evaluate the performance of the proposed approach on the standard benchmark dataset and achieve the state-of-the-art performance. We further show the robustness of our approach by varying the amount of distortion in a perfect reflection symmetry pattern where we perturb each point by a different amount of perturbation. We demonstrate the effectiveness of the method by applying it to the problem of 2-D and 3-D reflection symmetry detection along with comparisons.