Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916449616920576 |
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| author | Pruss, Alexander R. |
| author_facet | Pruss, Alexander R. |
| contents | We consider the problem of recovering the position and orientation of a camera equipped with an accelerometer from sensor images of two labeled landmarks whose positions in a coordinate system aligned in a known way with gravity are known. This a variant on the much studied P$n$P problem of recovering camera position and orientation from $n$ points without any gravitational data. It is proved that in three types of singular cases there are infinitely many solutions, in another type of case there is one, and in a final type of case there are two. A precise characterization of each type of case. In particular, there is always a unique solution in the practically interesting case where the two landmarks are at the same altitude and the camera is at a different altitude. This case is studied by numerical simulation and an implementation on a consumer cellphone. It is also proved that if the two landmarks are unlabeled, then apart from the same singular cases, there are still always one or two solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer Pruss, Alexander R. Computer Vision and Pattern Recognition We consider the problem of recovering the position and orientation of a camera equipped with an accelerometer from sensor images of two labeled landmarks whose positions in a coordinate system aligned in a known way with gravity are known. This a variant on the much studied P$n$P problem of recovering camera position and orientation from $n$ points without any gravitational data. It is proved that in three types of singular cases there are infinitely many solutions, in another type of case there is one, and in a final type of case there are two. A precise characterization of each type of case. In particular, there is always a unique solution in the practically interesting case where the two landmarks are at the same altitude and the camera is at a different altitude. This case is studied by numerical simulation and an implementation on a consumer cellphone. It is also proved that if the two landmarks are unlabeled, then apart from the same singular cases, there are still always one or two solutions. |
| title | Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2410.17997 |