Detecting Approximate Reflection Symmetry in a Point Set Using Optimization on Manifold

Nagar, Rajendra; Raman, Shanmuganathan

doi:10.1109/tsp.2019.2893835

Cited by 28 publications

(23 citation statements)

References 65 publications

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“…Another concern is the limited invariance properties (only with respect to axial symmetry symmetry in our case). Nevertheless, we expect that such a cost can be of interest in cases where invariance to symmetry is a desired property, such as in [44].…”

Section: Discussionmentioning

confidence: 99%

Subspace Detours Meet Gromov–Wasserstein

et al. 2021

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In the context of optimal transport (OT) methods, the subspace detour approach was recently proposed by Muzellec and Cuturi. It consists of first finding an optimal plan between the measures projected on a wisely chosen subspace and then completing it in a nearly optimal transport plan on the whole space. The contribution of this paper is to extend this category of methods to the Gromov–Wasserstein problem, which is a particular type of OT distance involving the specific geometry of each distribution. After deriving the associated formalism and properties, we give an experimental illustration on a shape matching problem. We also discuss a specific cost for which we can show connections with the Knothe–Rosenblatt rearrangement.

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Section: Discussionmentioning

confidence: 99%

Subspace Detours Meet Gromov–Wasserstein

et al. 2021

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Section: Discussionmentioning

confidence: 99%

Subspace Detours Meet Gromov-Wasserstein

Bonet¹,

Courty²,

Septier³

et al. 2021

Preprint

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In the context of optimal transport methods, the subspace detour approach was recently presented by Muzellec and Cuturi (2019). It consists in building a nearly optimal transport plan in the measures space from an optimal transport plan in a wisely chosen subspace, onto which the original measures are projected. The contribution of this paper is to extend this category of methods to the Gromov-Wasserstein problem, which is a particular type of transport distance involving the inner geometry of the compared distributions. After deriving the associated formalism and properties, we also discuss a specific cost for which we can show connections with the Knothe-Rosenblatt rearrangement. We finally give an experimental illustration on a shape matching problem.Preprint. Under review.

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“…Advances in Multimedia symmetry detection approach for CAD models, but this approach mainly works for regular CAD models. Nagar and Raman [31] develop a generic framework to detect approximate reflection symmetry in a volumetric set of points in R d using optimization on Riemannian manifold. ey show the effectiveness of the method by applying it to the problem of 2D and 3D reflection symmetry detection.…”

Section: Related Workmentioning

confidence: 99%

Dominant Symmetry Plane Detection for Point-Based 3D Models

Wang

Zhang

et al. 2020

Advances in Multimedia

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In this paper, a symmetry detection algorithm for three-dimensional point cloud model based on weighted principal component analysis (PCA) is proposed. The proposed algorithm works as follows: first, using the point element’s area as the initial weight, a weighted PCA is performed and a plane is selected as the initial symmetry plane; and then an iterative method is used to adjust the approximate symmetry plane step by step to make it tend to perfect symmetry plane (dominant symmetry plane). In each iteration, we first update the weight of each point based on a distance metric and then use the new weights to perform a weighted PCA to determine a new symmetry plane. If the current plane of symmetry is close enough to the plane of symmetry in the previous iteration or if the number of iterations exceeds a given threshold, the iteration terminates. After the iteration is terminated, the plane of symmetry in the last iteration is taken as the dominant symmetry plane of the model. As shown in experimental results, the proposed algorithm can find the dominant symmetry plane for symmetric models and it also works well for nonperfectly symmetric models.

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Detecting Approximate Reflection Symmetry in a Point Set Using Optimization on Manifold

Cited by 28 publications

References 65 publications

Subspace Detours Meet Gromov–Wasserstein

Subspace Detours Meet Gromov–Wasserstein

Subspace Detours Meet Gromov-Wasserstein

Dominant Symmetry Plane Detection for Point-Based 3D Models

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