Relative Pose from a Calibrated and an Uncalibrated Smartphone Image

In this paper, we propose a new minimal and a non-minimal solver for estimating the relative camera pose together with the unknown focal length of the second camera. This configuration has a number of practical benefits, e.g., when processing large-scale datasets. Moreover, it is resistant to the typical degenerate cases of the traditional six-point algorithm. The minimal solver requires four point correspondences and exploits the gravity direction that the built-in IMU of recent smart devices recover. We also propose a linear solver that enables estimating the pose from a larger-than-minimal sample extremely efficiently which then can be improved by, e.g., bundle adjustment. The methods are tested on 35654 image pairs from publicly available real-world and new datasets. When combined with a recent robust estimator, they lead to results superior to the traditional solvers in terms of rotation, translation and focal length accuracy, while being notably faster.