Detecting Approximate Reflection Symmetry in a Point Set Using Optimization on Manifold
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Publication:4628321
DOI10.1109/TSP.2019.2893835zbMATH Open1415.94348arXiv1706.08801OpenAlexW2895823967WikidataQ114830531 ScholiaQ114830531MaRDI QIDQ4628321
Author name not available (Why is that?)
Publication date: 6 March 2019
Published in: (Search for Journal in Brave)
Abstract: We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to 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.
Full work available at URL: https://arxiv.org/abs/1706.08801
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