Convex Relaxations for Isometric and Equiareal NRSfM
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866910671429435392 |
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| author | Sengupta, Agniva Bartoli, Adrien |
| author_facet | Sengupta, Agniva Bartoli, Adrien |
| contents | Extensible objects form a challenging case for NRSfM, owing to the lack of a sufficiently constrained extensible model of the point-cloud. We tackle the challenge by proposing 1) convex relaxations of the isometric model up to quasi-isometry, and 2) convex relaxations involving the equiareal deformation model, which preserves local area and has not been used in NRSfM. The equiareal model is appealing because it is physically plausible and widely applicable. However, it has two main difficulties: first, when used on its own, it is ambiguous, and second, it involves quartic, hence highly nonconvex, constraints. Our approach handles the first difficulty by mixing the equiareal with the isometric model and the second difficulty by new convex relaxations. We validate our methods on multiple real and synthetic data, including well-known benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16005 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convex Relaxations for Isometric and Equiareal NRSfM Sengupta, Agniva Bartoli, Adrien Computer Vision and Pattern Recognition Extensible objects form a challenging case for NRSfM, owing to the lack of a sufficiently constrained extensible model of the point-cloud. We tackle the challenge by proposing 1) convex relaxations of the isometric model up to quasi-isometry, and 2) convex relaxations involving the equiareal deformation model, which preserves local area and has not been used in NRSfM. The equiareal model is appealing because it is physically plausible and widely applicable. However, it has two main difficulties: first, when used on its own, it is ambiguous, and second, it involves quartic, hence highly nonconvex, constraints. Our approach handles the first difficulty by mixing the equiareal with the isometric model and the second difficulty by new convex relaxations. We validate our methods on multiple real and synthetic data, including well-known benchmarks. |
| title | Convex Relaxations for Isometric and Equiareal NRSfM |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2211.16005 |