Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignment
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909934556282880 |
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| author | Sarker, Anik Asbeck, Alan T. |
| author_facet | Sarker, Anik Asbeck, Alan T. |
| contents | We address the correspondence-free alignment of two rotation sets on \(SO(3)\), a core task in calibration and registration that is often impeded by missing time alignment, outliers, and unknown axis conventions. Our key idea is to decompose each rotation into its \emph{Transformed Basis Vectors} (TBVs)-three unit vectors on \(S^2\)-and align the resulting spherical point sets per axis using fast, robust matchers (SPMC, FRS, and a hybrid). To handle axis relabels and sign flips, we introduce a \emph{Permutation-and-Sign Invariant} (PASI) wrapper that enumerates the 24 proper signed permutations, scores them via summed correlations, and fuses the per-axis estimates into a single rotation by projection/Karcher mean. The overall complexity remains linear in the number of rotations (\(\mathcal{O}(n)\)), contrasting with \(\mathcal{O}(N_r^3\log N_r)\) for spherical/\(SO(3)\) correlation. Experiments on EuRoC Machine Hall simulations
(axis-consistent) and the ETH Hand-Eye benchmark (\texttt{robot\_arm\_real})
(axis-ambiguous) show that our methods are accurate, 6-60x faster than traditional methods, and robust under extreme outlier ratios (up to 90\%), all without correspondence search. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignment Sarker, Anik Asbeck, Alan T. Robotics Computational Geometry Computer Vision and Pattern Recognition We address the correspondence-free alignment of two rotation sets on \(SO(3)\), a core task in calibration and registration that is often impeded by missing time alignment, outliers, and unknown axis conventions. Our key idea is to decompose each rotation into its \emph{Transformed Basis Vectors} (TBVs)-three unit vectors on \(S^2\)-and align the resulting spherical point sets per axis using fast, robust matchers (SPMC, FRS, and a hybrid). To handle axis relabels and sign flips, we introduce a \emph{Permutation-and-Sign Invariant} (PASI) wrapper that enumerates the 24 proper signed permutations, scores them via summed correlations, and fuses the per-axis estimates into a single rotation by projection/Karcher mean. The overall complexity remains linear in the number of rotations (\(\mathcal{O}(n)\)), contrasting with \(\mathcal{O}(N_r^3\log N_r)\) for spherical/\(SO(3)\) correlation. Experiments on EuRoC Machine Hall simulations (axis-consistent) and the ETH Hand-Eye benchmark (\texttt{robot\_arm\_real}) (axis-ambiguous) show that our methods are accurate, 6-60x faster than traditional methods, and robust under extreme outlier ratios (up to 90\%), all without correspondence search. |
| title | Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignment |
| topic | Robotics Computational Geometry Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2512.00659 |