PLMP -- Point-Line Minimal Problems for Projective SfM
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912512504496128 |
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| author | Kiehn, Kim Ahlbäck, Albin Kohn, Kathlén |
| author_facet | Kiehn, Kim Ahlbäck, Albin Kohn, Kathlén |
| contents | We completely classify all minimal problems for Structure-from-Motion (SfM) where arrangements of points and lines are fully observed by multiple uncalibrated pinhole cameras. We find 291 minimal problems, 73 of which have unique solutions and can thus be solved linearly. Two of the linear problems allow an arbitrary number of views, while all other minimal problems have at most 9 cameras. All minimal problems have at most 7 points and at most 12 lines. We compute the number of solutions of each minimal problem, as this gives a measurement of the problem's intrinsic difficulty, and find that these number are relatively low (e.g., when comparing with minimal problems for calibrated cameras). Finally, by exploring stabilizer subgroups of subarrangements, we develop a geometric and systematic way to 1) factorize minimal problems into smaller problems, 2) identify minimal problems in underconstrained problems, and 3) formally prove non-minimality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04351 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PLMP -- Point-Line Minimal Problems for Projective SfM Kiehn, Kim Ahlbäck, Albin Kohn, Kathlén Computer Vision and Pattern Recognition Algebraic Geometry We completely classify all minimal problems for Structure-from-Motion (SfM) where arrangements of points and lines are fully observed by multiple uncalibrated pinhole cameras. We find 291 minimal problems, 73 of which have unique solutions and can thus be solved linearly. Two of the linear problems allow an arbitrary number of views, while all other minimal problems have at most 9 cameras. All minimal problems have at most 7 points and at most 12 lines. We compute the number of solutions of each minimal problem, as this gives a measurement of the problem's intrinsic difficulty, and find that these number are relatively low (e.g., when comparing with minimal problems for calibrated cameras). Finally, by exploring stabilizer subgroups of subarrangements, we develop a geometric and systematic way to 1) factorize minimal problems into smaller problems, 2) identify minimal problems in underconstrained problems, and 3) formally prove non-minimality. |
| title | PLMP -- Point-Line Minimal Problems for Projective SfM |
| topic | Computer Vision and Pattern Recognition Algebraic Geometry |
| url | https://arxiv.org/abs/2503.04351 |