Globally Optimal Solution to the Generalized Relative Pose Estimation Problem using Affine Correspondences

TL;DR

This paper presents a globally optimal method for generalized relative pose estimation using affine correspondences, improving accuracy in multi-camera and inertial systems like self-driving cars.

Contribution

The authors introduce a novel solver that optimally estimates relative pose with known vertical direction by transforming the problem into polynomial eigenvalue equations.

Findings

Outperforms state-of-the-art methods in accuracy on synthetic and real data

Provides a new linear solution for small relative rotations

Demonstrates robustness and efficiency in practical scenarios

Abstract

Mobile devices equipped with a multi-camera system and an inertial measurement unit (IMU) are widely used nowadays, such as self-driving cars. The task of relative pose estimation using visual and inertial information has important applications in various fields. To improve the accuracy of relative pose estimation of multi-camera systems, we propose a globally optimal solver using affine correspondences to estimate the generalized relative pose with a known vertical direction. First, a cost function about the relative rotation angle is established after decoupling the rotation matrix and translation vector, which minimizes the algebraic error of geometric constraints from affine correspondences. Then, the global optimization problem is converted into two polynomials with two unknowns based on the characteristic equation and its first derivative is zero. Finally, the relative rotation angle can be solved using the polynomial eigenvalue solver, and the translation vector can be obtained from the eigenvector. Besides, a new linear solution is proposed when the relative rotation is small. The proposed solver is evaluated on synthetic data and real-world datasets. The experiment results demonstrate that our method outperforms comparable state-of-the-art methods in accuracy.