Regularized Pointwise Map Recovery from Functional Correspondence
The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point‐to‐point correspondence from a given functional map has...
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| Published in: | Computer graphics forum Vol. 36; no. 8; pp. 700 - 711 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Oxford
Blackwell Publishing Ltd
01.12.2017
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| ISSN: | 0167-7055, 1467-8659 |
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| Abstract | The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point‐to‐point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly‐isometric, and easily extends to recovering the point‐to‐point correspondence in part‐to‐whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases.
The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point‐to‐point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly‐isometric, and easily extends to recovering the point‐to‐point correspondence in part‐to‐whole shape matching problems. |
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| AbstractList | The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point‐to‐point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly‐isometric, and easily extends to recovering the point‐to‐point correspondence in part‐to‐whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases. The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point‐to‐point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly‐isometric, and easily extends to recovering the point‐to‐point correspondence in part‐to‐whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases. The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point‐to‐point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly‐isometric, and easily extends to recovering the point‐to‐point correspondence in part‐to‐whole shape matching problems. |
| Author | Moeller, M. Cremers, D. Rodolà, E. |
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| Cites_doi | 10.1109/3DV.2016.10 10.1109/34.491619 10.1145/2897824.2925913 10.1109/CVPR.2017.707 10.1145/2185520.2185526 10.1111/cgf.12066 10.1111/cgf.12435 10.1109/TPAMI.2010.46 10.1002/nav.3800020109 10.1007/BF00126430 10.1111/cgf.12970 10.1145/1015706.1015811 10.1111/cgf.12797 10.1109/TPAMI.2010.223 10.1145/2461912.2461959 10.1111/cgf.12064 10.1111/j.2517-6161.1977.tb01600.x 10.1145/258734.258849 10.1145/2601097.2601111 10.1109/34.121791 10.1080/10586458.1993.10504266 10.1111/j.1467-8659.2011.01884.x 10.1109/CVPR.2015.7298692 10.1145/2010324.1964974 10.1111/cgf.12429 |
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| Copyright | 2017 The Authors Computer Graphics Forum © 2017 The Eurographics Association and John Wiley & Sons Ltd. 2017 The Eurographics Association and John Wiley & Sons Ltd. |
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| SubjectTerms | 3D shape matching Deformation effects Formability I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling—Shape Analysis Matching |
| Title | Regularized Pointwise Map Recovery from Functional Correspondence |
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