Efficient closed-form approaches for pose estimation using Sylvester forms
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| Format: | Preprint |
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2026
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| _version_ | 1866908969933471744 |
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| author | Vráblíková, Jana Malis, Ezio Busé, Laurent |
| author_facet | Vráblíková, Jana Malis, Ezio Busé, Laurent |
| contents | Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the optimization problem can be reduced to the solution of a~system of polynomial equations and solved in closed form. Recent advances in efficient closed form solvers utilizing resultant matrices have shown a promising research direction to decrease the computation time while preserving the estimation accuracy. In this paper, we propose a new class of resultant-based solvers that exploit Sylvester forms to further reduce the complexity of the resolution. We demonstrate that our proposed methods are numerically as accurate as the state-of-the-art solvers, and outperform them in terms of computational time. We show that this approach can be applied for pose estimation in two different types of problems: estimating a pose from 3D to 3D correspondences, and estimating a pose from 3D points to 2D points correspondences. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14747 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient closed-form approaches for pose estimation using Sylvester forms Vráblíková, Jana Malis, Ezio Busé, Laurent Computer Vision and Pattern Recognition Robotics Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the optimization problem can be reduced to the solution of a~system of polynomial equations and solved in closed form. Recent advances in efficient closed form solvers utilizing resultant matrices have shown a promising research direction to decrease the computation time while preserving the estimation accuracy. In this paper, we propose a new class of resultant-based solvers that exploit Sylvester forms to further reduce the complexity of the resolution. We demonstrate that our proposed methods are numerically as accurate as the state-of-the-art solvers, and outperform them in terms of computational time. We show that this approach can be applied for pose estimation in two different types of problems: estimating a pose from 3D to 3D correspondences, and estimating a pose from 3D points to 2D points correspondences. |
| title | Efficient closed-form approaches for pose estimation using Sylvester forms |
| topic | Computer Vision and Pattern Recognition Robotics |
| url | https://arxiv.org/abs/2604.14747 |