Universal Gröbner Bases of (Universal) Multiview Ideals
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916974058012672 |
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| author | Duff, Timothy Kendrick, Jack Thomas, Rekha R. |
| author_facet | Duff, Timothy Kendrick, Jack Thomas, Rekha R. |
| contents | Multiview ideals arise from the geometry of image formation in pinhole cameras, and universal multiview ideals are their analogs for unknown cameras. We prove that a natural collection of polynomials form a universal Gröbner basis for both types of ideals using a criterion introduced by Huang and Larson, and include a proof of their criterion in our setting. Symmetry reduction and induction enable the method to be deployed on an infinite family of ideals. We also give an explicit description of the matroids on which the methodology depends, in the context of multiview ideals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_12376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Gröbner Bases of (Universal) Multiview Ideals Duff, Timothy Kendrick, Jack Thomas, Rekha R. Commutative Algebra Computer Vision and Pattern Recognition Algebraic Geometry Multiview ideals arise from the geometry of image formation in pinhole cameras, and universal multiview ideals are their analogs for unknown cameras. We prove that a natural collection of polynomials form a universal Gröbner basis for both types of ideals using a criterion introduced by Huang and Larson, and include a proof of their criterion in our setting. Symmetry reduction and induction enable the method to be deployed on an infinite family of ideals. We also give an explicit description of the matroids on which the methodology depends, in the context of multiview ideals. |
| title | Universal Gröbner Bases of (Universal) Multiview Ideals |
| topic | Commutative Algebra Computer Vision and Pattern Recognition Algebraic Geometry |
| url | https://arxiv.org/abs/2509.12376 |