Efficient Minimal Solvers for Relative Pose Estimation With Known Rotation Angle

In this letter, we propose novel minimal solvers for calibrated relative pose estimation with a known rotation angle. This scenario is particularly relevant for devices such as smartphones, tablets, and camera-IMU (Inertial Measurement Unit) systems, where gyroscopes provide precise measurements of the rotation angle. By leveraging the prior knowledge of the rotation angle from the gyroscope, the relative rotation between two views can be reduced to 2 degrees of freedom (DOF), and the relative pose estimation problem is simplified to 4-DOF. This reduction enables the estimation of the relative pose using only four-point correspondences. Unlike previous approaches, we address both cases where the four points are in general positions or coplanar. For points in general positions, we present a straightforward yet effective method to eliminate specific monomials in the equations, leading to a more computationally efficient solution. For coplanar points, we establish a connection between the homography matrix and the essential matrix, introducing new constraints on the homography matrix. Based on these constraints, we derive a new solver for homography-based relative pose estimation with a known rotation angle. We provide comprehensive analyses and comparisons against state-of-the-art algorithms, demonstrating the superior efficiency and effectiveness of our proposed method. Our results highlight the practical applicability of our solvers in real-world scenarios, particularly for devices equipped with IMUs.