Gravity-aligned Rotation Averaging with Circular Regression

TL;DR

This work introduces a principled approach that integrates gravity direction into the rotation averaging phase of global pipelines, enhancing camera orientation accuracy and reducing the degrees of freedom, and proposes a mechanism to refine error-prone gravity.

Abstract

Reconstructing a 3D scene from unordered images is pivotal in computer vision and robotics, with applications spanning crowd-sourced mapping and beyond. While global Structure-from-Motion (SfM) techniques are scalable and fast, they often compromise on accuracy. To address this, we introduce a principled approach that integrates gravity direction into the rotation averaging phase of global pipelines, enhancing camera orientation accuracy and reducing the degrees of freedom. This additional information is commonly available in recent consumer devices, such as smartphones, mixed-reality devices and drones, making the proposed method readily accessible. Rooted in circular regression, our algorithm has similar convergence guarantees as linear regression. It also supports scenarios where only a subset of cameras have known gravity. Additionally, we propose a mechanism to refine error-prone gravity. We achieve state-of-the-art accuracy on four large-scale datasets. Particularly, the proposed method improves upon the SfM baseline by 13 AUC@$1^\circ$ points, on average, while running eight times faster. It also outperforms the standard planar pose graph optimization technique by 23 AUC@$1^\circ$ points. The code is at https://github.com/colmap/glomap.

Figures (9)

• Figure 1: Gravity-aligned rotation averaging. Given a set of cameras and their gravity directions (left), orientation estimation becomes a 1-degree-of-freedom optimization of the viewing angle (right). Circular regression tackles the periodicity of the problem.
• Figure 2: Datasets. Reconstruction examples from EuRoC burri2016euroc, LaMAR sarlin2022lamar, and 1DSfM wilson2014robust; and trajectories from KITTI geiger2013vision. Our method consistently outperforms baselines across these diverse datasets, showcasing its generalization ability.
• Figure 3: The cumulative distribution functions (CDFs) of the absolute rotation errors ($^\circ$). Estimated by the Levenberg-Marquardt more2006levenberg method solving the 3-DoF (LM 3DoF) and 1-DoF (LM 1DoF) problems, by LAGO carlone2014fast, by CPL-Sync fan2019efficient, by the rotation averaging in the Theia library theia-manualchatterjee2013efficient, by Theia with an additional penalty term (Theia$^\text{reg}$crandall2012sfm), by COLMAP schoenberger2016sfm, and by the proposed method. Curve "Gravity" stands for the approximate upper bound achievable by using gravity direction. A method being accurate is interpreted by its curve close to the top-left corner. Different metrics for the datasets are reported in Tables \ref{['tbl:euroc']}, \ref{['tbl:KITTI']}, \ref{['tbl:lamar_map']}, \ref{['tbl:1dsfm']}.
• Figure 4: Avg. $\log_{10}$ time (secs) as a function of image number in synthetic pose graphs: sequential (left) and grid-like (right) cameras.
• Figure : Solve optimization for \ref{['eq:R_err_1dof_k']}