Globally Optimal Relative Pose Estimation for Multi-Camera Systems with Known Gravity Direction

Multiple-camera systems have been widely used in self-driving cars, robots, and smartphones. In addition, they are typically also equipped with IMUs (inertial measurement units). Using the gravity direction extracted from the IMU data, the y-axis of the body frame of the multi-camera system can be aligned with this common direction, reducing the original three degree-of-freedom(DOF) relative rotation to a single DOF one. This paper presents a novel globally optimal solver to compute the relative pose of a generalized camera. Existing optimal solvers based on LM (Levenberg-Marquardt) method or SDP (semidefinite program) are either iterative or have high computational complexity. Our proposed optimal solver is based on minimizing the algebraic residual objective function. According to our derivation, using the least-squares algorithm, the original optimization problem can be converted into a system of two polynomials with only two variables. The proposed solvers have been tested on synthetic data and the KITTI benchmark. The experimental results show that the proposed methods have competitive robustness and accuracy compared with the existing state-of-the-art solvers.