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

TL;DR

This paper analyzes the solution multiplicity in camera pose estimation using two landmarks and an accelerometer, providing a detailed classification of cases and practical validation on a cellphone.

Contribution

It offers a comprehensive characterization of solution counts in a landmark-based camera pose problem with gravity data, including singular cases and unlabeled landmarks.

Findings

Infinitely many solutions in certain singular cases

Unique solutions in the case of landmarks at the same altitude

Numerical validation and implementation on a consumer cellphone

Abstract

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.