P3P and P2P problems with known camera and object vertical directions

In this paper the problem of estimating the relative orientation and position between a camera and an object is considered. It is assumed that both the camera and the object are provided with an IMU capable to give their inclinations with respect to the gravity vector. It is moreover assumed that the object contains a feature of 3 points whose position in the object coordinate frame is known. Using the image provided by the camera and the information on the gravity vector by the IMUs we propose an algorithm capable of estimating the relative pose of the object in the camera reference frame by solving a modified P2P or P3P problem. It will be shown that the P2P problem always gives 2 solutions, except in a few singular configurations, while the P3P problem usually gives a single solution. The effectiveness of the proposed approach will be shown by contrasting it with other algorithms presented in the literature.