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- W2895823967 abstract "We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to ℝ <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>d</sup> 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-theart 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 (two-dimensional) and 3-D reflection symmetry detection along with comparisons." @default.
- W2895823967 created "2018-10-26" @default.
- W2895823967 creator A5060041957 @default.
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- W2895823967 date "2019-03-15" @default.
- W2895823967 modified "2023-10-02" @default.
- W2895823967 title "Detecting Approximate Reflection Symmetry in a Point Set Using Optimization on Manifold" @default.
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- W2895823967 doi "https://doi.org/10.1109/tsp.2019.2893835" @default.
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