Projections of Curves and Conic Multiview Varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909160415690752 |
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| author | Rydell, Felix Sundelius, Isak |
| author_facet | Rydell, Felix Sundelius, Isak |
| contents | We present an algebraic study of the projection of plane curves and twisted cubics in space onto multiple images of pinhole cameras. The Zariski closure of the image of the projection of conics is a conic multiview varieties. Extending previous work for point and line multiview varieties, we use back-projected cones to describe these varieties. For two views, we provide the defining ideal of the multiview variety. For any number of views, we state when the simplest possible set-theoretic description is achieved based on the geometry of the camera centers. Finally, we investigate the complexity of the associated triangulation problem and conjecture the Euclidean distance degree for the conic multiview variety for two cameras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projections of Curves and Conic Multiview Varieties Rydell, Felix Sundelius, Isak Algebraic Geometry 14H10, 14H99 (Primary) We present an algebraic study of the projection of plane curves and twisted cubics in space onto multiple images of pinhole cameras. The Zariski closure of the image of the projection of conics is a conic multiview varieties. Extending previous work for point and line multiview varieties, we use back-projected cones to describe these varieties. For two views, we provide the defining ideal of the multiview variety. For any number of views, we state when the simplest possible set-theoretic description is achieved based on the geometry of the camera centers. Finally, we investigate the complexity of the associated triangulation problem and conjecture the Euclidean distance degree for the conic multiview variety for two cameras. |
| title | Projections of Curves and Conic Multiview Varieties |
| topic | Algebraic Geometry 14H10, 14H99 (Primary) |
| url | https://arxiv.org/abs/2404.03063 |