A Minimal Solution for Non-Perspective Pose Estimation from Line Correspondences

Abstract

In this paper, we study and propose solutions to the relatively un-investigated non-perspective pose estimation problem from line correspondences. Specifically, we represent the 2D and 3D line correspondences as Plücker lines and derive the minimal solution for the minimal problem of three line correspondences with Gröbner basis. Our minimal 3-Line algorithm that gives up to eight solutions is well-suited for robust estimation with RANSAC. We show that our algorithm works as a least-squares that takes in more than three line correspondences without any reformulation. In addition, our algorithm does not require initialization in both the minimal 3-Line and least-squares n-Line cases. Furthermore, our algorithm works without a need for reformulation under the special case of perspective pose estimation when all line correspondences are observed from one single camera. We verify our algorithms with both simulated and real-world data.