Minimal solutions for pose estimation of a multi-camera system

Abstract In this paper, we propose a novel formulation to solve the pose estimation problem of a calibrated multi-camera system. The non-central rays that pass through the 3D world points and multi-camera system are elegantly represented as Plücker lines. This allows us to solve for the depth of the points along the Plücker lines with a minimal set of 3-point correspondences. We show that the minimal solution for the depth of the points along the Plücker lines is an 8 degree polynomial that gives up to 8 real solutions. The coordinates of the 3D world points in the multi-camera frame are computed from the known depths. Consequently, the pose of the multi-camera system, i.e. the rigid transformation between the world and multi-camera frames can be obtained from absolute orientation. We also derive a closed-form minimal solution for the absolute orientation. This removes the need for the computation-ally expensive Singular Value Decompositions (SVD) during the evaluations of the possible solutions for the depths. We identify the correct solution and do robust es-timation with RANSAC. Finally, the solution is further refined by including all the inlier correspondences in a non-linear refinement step. We verify our approach by showing comparisons with other existing approaches and results from large-scale real-world datasets.