Globally Optimal Consensus Maximization for Relative Pose Estimation with Known Gravity Direction

Relative pose estimation is a core task in robotic vision, and it is the basis of many high-level applications (e.g., visual odometry). In this letter, we focus on a quite common case in which the gravity direction is known in advance with the help of IMUs. Commonly, incorrect feature matches (a.k.a. outliers) are unavoidable, and they will impair the accuracy significantly. RANSAC is the de facto standard to suppress the outliers and obtain a robust solution. However, RANSAC is a non-deterministic algorithm, which means it produces a reasonable result only with a certain probability, and it cannot guarantee the global optimality to meet the safety demand in many life-critical applications. Therefore, we propose a globally optimal algorithm for relative pose estimation with known gravity direction. Specifically, the proposed method employs the branch-and-bound algorithm to solve a consensus maximization problem, and thus it is able to obtain the global solution with a provable guarantee. To verify the feasibility of our proposed method, both synthetic and real-data experiments are conducted. The experimental results support the global optimality of the proposed method and show that the method performs more robustly than existing methods.