Cycle-Sync: Robust Global Camera Pose Estimation through Enhanced Cycle-Consistent Synchronization

TL;DR

Cycle-Sync presents a robust global framework for camera pose estimation that jointly recovers rotations and locations without bundle adjustment. It introduces a Welsh-type objective and an MPLS-based cycle-consistency strategy to solve location estimation, along with a plug-and-play outlier rejection module and an integrated rotation synchronization via MPLS-cycle. Theoretical guarantees establish deterministic exact recovery under adversarial corruption with improved sample complexity, and extensive synthetic and real-data experiments show Cycle-Sync outperforming state-of-the-art pose estimators and full SfM pipelines. The approach enhances robustness to highly corrupted and variable-distance measurements, enabling accurate 3D reconstruction in challenging SfM scenarios with practical efficiency gains.

Abstract

We introduce Cycle-Sync, a robust and global framework for estimating camera poses (both rotations and locations). Our core innovation is a location solver that adapts message-passing least squares (MPLS) -- originally developed for group synchronization -- to camera location estimation. We modify MPLS to emphasize cycle-consistent information, redefine cycle consistencies using estimated distances from previous iterations, and incorporate a Welsch-type robust loss. We establish the strongest known deterministic exact-recovery guarantee for camera location estimation, showing that cycle consistency alone -- without access to inter-camera distances -- suffices to achieve the lowest sample complexity currently known. To further enhance robustness, we introduce a plug-and-play outlier rejection module inspired by robust subspace recovery, and we fully integrate cycle consistency into MPLS for rotation synchronization. Our global approach avoids the need for bundle adjustment. Experiments on synthetic and real datasets show that Cycle-Sync consistently outperforms leading pose estimators, including full structure-from-motion pipelines with bundle adjustment.

Figures (10)

• Figure 1: Comparison of different losses. Our loss combines the advantages of the $L_1$ and Welsch losses. Specifically, it suppresses the influence of large $x$ values (like Welsch), while retaining a nonsmooth corner at the origin (like $L_1$), which introduces a singular point in the reweighting function $f(x)$ and enables exact recovery.
• Figure 2: Illustration of Cycle-Sync. The algorithm solves the weighted least squares (WLS) in \ref{['eq:wls_2']} to estimate the locations $\{\boldsymbol{t}_i\}_{i\in [n]}$. The weights for WLS are iteratively updated in two ways. The main one is a cycle-edge message passing procedure (bottom unit, where green elements represent cleaner information, and red elements indicate corrupted information). Each cycle weight $q_{ij,k}^t$ is updated using the two residuals $r_{ik,t}$ and $r_{jk,t}$. The bar length surrounding $q_{ij,k}^t$ reflects its magnitude. The theory indicates higher weights for good (green) cycles. The quantity $h_{ij,t}$ is a weighted average of $d_{ijk,t}$, defined in \ref{['eq:dijk']}) and updated at each iteration using the estimated locations. The theory guarantees that $h_{ij,t}$ is a good estimate for the corruption level at edge $ij$. The weights are obtained by applying the function $f(x)$ in \ref{['eq:f']}. The weights are also computed by IRLS (top unit). The final weights combine the two procedures with $\lambda_t \to 1$, so the message-passing unit progressively takes over.
• Figure 3: Median camera location error versus corruption probability. Left to right: (1) uniform corruption without noise, (2) uniform corruption with mild noise ($\sigma = 0.05$), (3) cycle-consistent (adversarial) corruption without noise, and (4) cycle-consistent corruption with mild noise. Error bars indicate standard deviation over 10 independent trials. No error bars are shown in plots with logarithmic scale.
• Figure 4: Median translation errors using ETH3D. Each column represents a dataset, the last one shows the average median error across all datasets. Different methods are presented per column. Upper: comparison of all pipelines. Unlike Theia and GLOMAP, Cycle-Sync (ours) estimates locations without bundle adjustment. Middle: comparison for different camera location algorithms; all methods preprocessed by STE and MPLS-cycle for fair comparison. Lower: Ablation studies.
• Figure 5: Visualization of camera location estimations and ground truth on the courtyard dataset. Top left: ground truth. Top right: Cycle-Sync. Bottom left: GLOMAP. Bottom right: Theia.

Theorems & Definitions (2)

• Theorem 2.1
• Theorem A.1