A Generalized 2-Point Solution for Absolute Camera Pose With Known Rotation Axis

The perspective-n-point problem (PnP) is one of the most fundamental problems in photogrammetry and computer vision. Recently, prior motion knowledge has been applied to help solve the problem, generating a perspective-two-point (P2P) problem, also known as the absolute camera pose problem with a known rotation axis. This paper provides a simple, generalized, closed-form solution to the P2P problem. The rotation axis can be the gravity direction from IMU, the upward direction from the vanishing points in the images, or the vertical direction of the ground plane where a vehicle is moving. The current state-of-art P2P solver finds roots of a depth-based equation. However, as can be seen from the perspective-three-point (P3P) problem, there are two categories of solvers, one formulating a quartic equation about the rotation and the other formulating the equation about the depth. The former is more numerically stable than the latter one. Activated by this, we obtain a quadratic polynomial involving one variable about the rotation from the geometric constraints, which can be solved quickly. Subsequent back substitution directly gives a linear solution to the translation. Moreover, we extend our idea to the generalized camera model, which makes our solver work for a single camera or a multi-camera rig. We ran several synthetic experiments demonstrating that our algorithm has high accuracy and robustness and needs less computational time than other state-of-the-art algorithms. Further experiments with real data show that our solver provides state-of-the-art performance and works well with the RANSAC-outlier-rejection scheme.