The Quadrifocal Variety
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866911212279693312 |
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| author | Oeding, Luke |
| author_facet | Oeding, Luke |
| contents | Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering several flatlander cameras. The ideal of the quadrifocal variety is computed up to degree 8 (and partially in degree 9) using the representations of $\operatorname{GL}(3)^{\times 4}$ in the polynomial ring on the space of $3 \times 3 \times 3 \times 3$ tensors. Further representation-theoretic analysis gives a lower bound for the number of minimal generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1501_01266 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | The Quadrifocal Variety Oeding, Luke Algebraic Geometry Computer Vision and Pattern Recognition 13Pxx, 14Qxx (Primary), 15A69, 15A72, 68T45 (Secondary) Multi-view Geometry is reviewed from an Algebraic Geometry perspective and multi-focal tensors are constructed as equivariant projections of the Grassmannian. A connection to the principal minor assignment problem is made by considering several flatlander cameras. The ideal of the quadrifocal variety is computed up to degree 8 (and partially in degree 9) using the representations of $\operatorname{GL}(3)^{\times 4}$ in the polynomial ring on the space of $3 \times 3 \times 3 \times 3$ tensors. Further representation-theoretic analysis gives a lower bound for the number of minimal generators. |
| title | The Quadrifocal Variety |
| topic | Algebraic Geometry Computer Vision and Pattern Recognition 13Pxx, 14Qxx (Primary), 15A69, 15A72, 68T45 (Secondary) |
| url | https://arxiv.org/abs/1501.01266 |