An Efficient Solution to the Homography-Based Relative Pose Problem With a Common Reference Direction

Yaqing Ding, Jian Yang, Jean Ponce, Hui Kong; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2019, pp. 1655-1664

In this paper, we propose a novel approach to two-view minimal-case relative pose problems based on homography with a common reference direction. We explore the rank-1 constraint on the difference between the Euclidean homography matrix and the corresponding rotation, and propose an efficient two-step solution for solving both the calibrated and partially calibrated (unknown focal length) problems. We derive new 3.5-point, 3.5-point, 4-point solvers for two cameras such that the two focal lengths are unknown but equal, one of them is unknown, and both are unknown and possibly different, respectively. We present detailed analyses and comparisons with existing 6 and 7-point solvers, including results with smart phone images.