A Minimal Solution to the Generalized Pose-and-Scale Problem

We propose a novel solution to the generalized camera pose problem which includes the internal scale of the generalized camera as an unknown parameter. This further generalization of the well-known absolute camera pose problem has applications in multi-frame loop closure. While a well-calibrated camera rig has a fixed and known scale, camera trajectories produced by monocular motion estimation necessarily lack a scale estimate. Thus, when performing loop closure in monocular visual odometry, or registering separate structure-from-motion reconstructions, we must estimate a seven degree-of-freedom similarity transform from corresponding observations. Existing approaches solve this problem, in specialized configurations, by aligning 3D triangulated points or individual camera pose estimates. Our approach handles general configurations of rays and points and directly estimates the full similarity transformation from the 2D-3D correspondences. Four correspondences are needed in the minimal case, which has eight possible solutions. The minimal solver can be used in a hypothesize-and-test architecture for robust transformation estimation. Our solver also produces a least-squares estimate in the overdetermined case. The approach is evaluated experimentally on synthetic and real datasets, and is shown to produce higher accuracy solutions to multi-frame loop closure than existing approaches.