A Birotation Solution for Relative Pose Problems

Abstract: Relative pose estimation, a fundamental computer vision problem, has been extensively studied for decades. Existing methods either estimate and decompose the essential matrix or directly estimate the rotation and translation to obtain the solution. In this article, we break the mold by tackling this traditional problem with a novel birotation solution. We first introduce three basis transformations, each associated with a geometric metric to quantify the distance between the relative pose to be estimated and its corresponding basis transformation. Three energy functions, designed based on these metrics, are then minimized on the Riemannian manifold $\mathrm{SO(3)}$ by iteratively updating the two rotation matrices. The two rotation matrices and the basis transformation corresponding to the minimum energy are ultimately utilized to recover the relative pose. Extensive quantitative and qualitative evaluations across diverse relative pose estimation tasks demonstrate the superior performance of our proposed birotation solution. Source code, demo video, and datasets will be available at \href{https://mias.group/birotation-solution}{mias.group/birotation-solution} upon publication.