A Birotation Solution for Relative Pose Problems

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. This article breaks the mold by tackling this traditional problem with a novel birotation solution. Three basis transformations are first introduced to bridge general relative pose estimation and birotation optimization. Since each basis transformation induces a distinct geometric constraint, three corresponding geometric metrics are derived to quantify the distances between the relative pose to be estimated and these basis transformations. Based on these metrics, three energy functions are constructed and minimized on the Riemannian manifold SO(3) by iteratively updating 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 the proposed birotation solution. Source code, demo video, and created datasets will be available at mias.group/birotation-solution upon publication.