已知两个竖直对齐地标位置，用加速度计辅助求解相机位姿，有唯一或两解。
Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer
- 结合加速度计与两个竖直对齐地标，推导相机位姿求解的数学条件
- 在多数实际场景下（同高地标、相机异高）仅有唯一解
- 适用于移动端实现，且对地标标签无要求
研究配备加速度计的相机，仅通过两个已知坐标系中竖直对齐的标记点位置及传感器图像，恢复相机的位置与姿态。该问题为经典PnP问题的变体，不依赖重力数据。证明了在三类奇异情况下存在无穷多解，一类情况有唯一解，另一类有两解，并精确刻画各类情形。特别地，在两个地标等高而相机高度不同时，总存在唯一解。通过数值模拟和消费级手机实现验证。若地标未标注，则除前述奇异情况外，仍恒有一解或两解。
原文摘要 · Abstract (English)
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.
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