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. 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.

DCPI-Depth: Explicitly Infusing Dense Correspondence Prior to Unsupervised Monocular Depth Estimation

There has been a recent surge of interest in learning to perceive depth from monocular videos in an unsupervised fashion. A key challenge in this field is achieving robust and accurate depth estimation in challenging scenarios, particularly in regions with weak textures or where dynamic objects are present. This study makes three major contributions by delving deeply into dense correspondence priors to provide existing frameworks with explicit geometric constraints. The first novelty is a contextual-geometric depth consistency loss, which employs depth maps triangulated from dense correspondences based on estimated ego-motion to guide the learning of depth perception from contextual information, since explicitly triangulated depth maps capture accurate relative distances among pixels. The second novelty arises from the observation that there exists an explicit, deducible relationship between optical flow divergence and depth gradient. A differential property correlation loss is, therefore, designed to refine depth estimation with a specific emphasis on local variations. The third novelty is a bidirectional stream co-adjustment strategy that enhances the interaction between rigid and optical flows, encouraging the former towards more accurate correspondence and making the latter more adaptable across various scenarios under the static scene hypotheses. DCPI-Depth, a framework that incorporates all these innovative components and couples two bidirectional and collaborative streams, achieves state-of-the-art performance and generalizability across multiple public datasets, outperforming all existing prior arts. Specifically, it demonstrates accurate depth estimation in texture-less and dynamic regions, and shows more reasonable smoothness.