Metric Multiview Geometry -- a Catalogue in Low Dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910314611605504 |
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| author | Duff, Timothy Rydell, Felix |
| author_facet | Duff, Timothy Rydell, Felix |
| contents | We systematically compile an exhaustive catalogue of multiview varieties and anchored multiview varieties arising from projections of points and lines in 1, 2, and 3-dimensional projective space. We say that two such varieties are ED-equivalent if there is a linear isomorphism between that that preserve ED-critical points. This gives rise to fourteen equivalence classes, and we determine various properties - dimension, set-theoretic equations, and multidegrees - for all varieties featured in our catalogue. In the case of points, we also present a complementary study of resectioning varieties and their singular loci. Finally, we propose conjectures for the Euclidean distance degrees of all varieties appearing in our comprehensive compilation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Metric Multiview Geometry -- a Catalogue in Low Dimensions Duff, Timothy Rydell, Felix Algebraic Geometry 14Nxx, 14Qxx We systematically compile an exhaustive catalogue of multiview varieties and anchored multiview varieties arising from projections of points and lines in 1, 2, and 3-dimensional projective space. We say that two such varieties are ED-equivalent if there is a linear isomorphism between that that preserve ED-critical points. This gives rise to fourteen equivalence classes, and we determine various properties - dimension, set-theoretic equations, and multidegrees - for all varieties featured in our catalogue. In the case of points, we also present a complementary study of resectioning varieties and their singular loci. Finally, we propose conjectures for the Euclidean distance degrees of all varieties appearing in our comprehensive compilation. |
| title | Metric Multiview Geometry -- a Catalogue in Low Dimensions |
| topic | Algebraic Geometry 14Nxx, 14Qxx |
| url | https://arxiv.org/abs/2402.00648 |