Minimal solutions for the multi-camera pose estimation problem

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 Plu¨cker lines. This allows us to solve for the depth of the points along the Plu¨cker lines with a minimal set of three-point correspondences. We show that the minimal solution for the depth of the points along the Plu¨cker lines is an eight-degree polynomial that gives up to eight 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 computationally expensive singular value decompositions during the evaluations of the possible solutions for the depths. We identify the correct solution and do robust estimation with RANSAC. Finally, the solution is further refined by including all the inlier correspondences in a nonlinear refinement step. We verify our approach by showing comparisons with other existing approaches and results from large-scale real-world datasets.