Elastic Correspondence between Triangle Meshes
We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an elastic deformation of the source and its projection on the target. The...
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| Veröffentlicht in: | Computer graphics forum Jg. 38; H. 2; S. 121 - 134 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Blackwell Publishing Ltd
01.05.2019
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an elastic deformation of the source and its projection on the target. The elastic energy we minimize is invariant to rigid body motions, and its non‐linear membrane energy component favors locally injective maps. Symmetrizing this model enables feature aligned correspondences even for non‐isometric meshes. We demonstrate the advantage of our approach over state of the art methods on isometric and non‐isometric datasets, where we improve the geodesic distance from the ground truth, the conformal and area distortions, and the mismatch of the mean curvature functions. Finally, we show that our computed maps are applicable for surface interpolation, consistent cross‐field computation, and consistent quadrangular remeshing of a set of shapes. |
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| AbstractList | We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match
crease
features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an
elastic
deformation of the source and its projection on the target. The elastic energy we minimize is invariant to rigid body motions, and its non‐linear membrane energy component favors locally injective maps. Symmetrizing this model enables feature aligned correspondences even for non‐isometric meshes. We demonstrate the advantage of our approach over state of the art methods on isometric and non‐isometric datasets, where we improve the geodesic distance from the ground truth, the conformal and area distortions, and the mismatch of the mean curvature functions. Finally, we show that our computed maps are applicable for surface interpolation, consistent cross‐field computation, and consistent quadrangular remeshing of a set of shapes. We propose a novel approach for shape matching between triangular meshes that, in contrast to existing methods, can match crease features. Our approach is based on a hybrid optimization scheme, that solves simultaneously for an elastic deformation of the source and its projection on the target. The elastic energy we minimize is invariant to rigid body motions, and its non‐linear membrane energy component favors locally injective maps. Symmetrizing this model enables feature aligned correspondences even for non‐isometric meshes. We demonstrate the advantage of our approach over state of the art methods on isometric and non‐isometric datasets, where we improve the geodesic distance from the ground truth, the conformal and area distortions, and the mismatch of the mean curvature functions. Finally, we show that our computed maps are applicable for surface interpolation, consistent cross‐field computation, and consistent quadrangular remeshing of a set of shapes. |
| Author | Rumpf, M. Heeren, B. Ezuz, D. Azencot, O. Ben‐Chen, M. |
| Author_xml | – sequence: 1 givenname: D. surname: Ezuz fullname: Ezuz, D. – sequence: 2 givenname: B. surname: Heeren fullname: Heeren, B. – sequence: 3 givenname: O. surname: Azencot fullname: Azencot, O. – sequence: 4 givenname: M. surname: Rumpf fullname: Rumpf, M. – sequence: 5 givenname: M. surname: Ben‐Chen fullname: Ben‐Chen, M. |
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| Copyright | 2019 The Author(s) Computer Graphics Forum © 2019 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. 2019 The Eurographics Association and John Wiley & Sons Ltd. |
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| SubjectTerms | CCS Concepts Computing methodologies → Mesh models Curvature Elastic deformation Energy conservation Ground truth Interpolation Optimization Rigid structures |
| Title | Elastic Correspondence between Triangle Meshes |
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