# Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer

arXiv: https://arxiv.org/abs/2410.17997 · HTML: https://mlsanity.com/paper/2410.17997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 10 references that are in the map.
- First posted on arXiv 23 Oct 2024.

## Builds on (most cited first, 1 of 1)

- [New insights on Multi-Solution Distribution of the P3P Problem](https://mlsanity.com/paper/1901.11464/) (2019)

## Abstract (arXiv)

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 PnP 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.