Characterization of the multiplicity of solutions for camera pose given two vertically-aligned landmarks and accelerometer
This work addresses camera localization for robotics or AR applications, but it is incremental as it builds on the well-studied PnP problem by incorporating gravitational data.
The paper tackles the problem of recovering camera pose using two vertically-aligned landmarks and an accelerometer, proving that in most cases there are one or two solutions, with a unique solution when landmarks are at the same altitude and the camera at a different altitude, as validated by numerical simulation and cellphone implementation.
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.