The Euclidean distance degree of one-parameter anchored multiview varieties
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912950173827072 |
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| author | Finkel, Bella Rodriguez, Jose Israel |
| author_facet | Finkel, Bella Rodriguez, Jose Israel |
| contents | Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as their Euclidean distance (ED) degree, which measures the algebraic complexity of determining the 3D features that minimize the reprojection error when computing the scene structure by triangulation. In this article, we prove a formula for the ED degree of curves parameterized by rational functions with mild genericity assumptions. We apply our results to resolve conjectures on one-dimensional line multiview varieties from computer vision proposed by Duff and Rydell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Euclidean distance degree of one-parameter anchored multiview varieties Finkel, Bella Rodriguez, Jose Israel Algebraic Geometry Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as their Euclidean distance (ED) degree, which measures the algebraic complexity of determining the 3D features that minimize the reprojection error when computing the scene structure by triangulation. In this article, we prove a formula for the ED degree of curves parameterized by rational functions with mild genericity assumptions. We apply our results to resolve conjectures on one-dimensional line multiview varieties from computer vision proposed by Duff and Rydell. |
| title | The Euclidean distance degree of one-parameter anchored multiview varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.18521 |