Organizations: GNSS Research Center, Wuhan University, Wuhan 430079, China · Electronic Information School, Wuhan University, Wuhan 430079, China · Hubei Technology Innovation Center for Spatiotemporal Information and Positioning Navigation, Wuhan 430079, China · Hubei Luojia Laboratory, Wuhan 430079, China
Most existing visual odometry (VO) systems treat feature correspondences as deterministic measurements or assign uniform uncertainty, ignoring the inherent localization ambiguity of different observations. However, correspondence uncertainty is often anisotropic due to image structures such as edges, repetitive patterns, and motion blur, which can significantly affect geometric optimization. In this work, we propose MomentBA, a geometry-aware bundle adjustment framework that derives anisotropic correspondence uncertainty from second-order spatial moments of local similarity responses. Instead of introducing additional covariance prediction networks, the proposed method directly converts matching response distributions into interpretable covariance estimates and incorporates them into bundle adjustment as correspondence-specific information matrices for uncertainty-aware residual weighting. Furthermore, the proposed formulation is integrated into a differentiable optimization framework, establishing a direct connection between correspondence uncertainty and geometric estimation. Experiments on the EuRoC MAV and TartanAir v1 Hard datasets demonstrate that MomentBA improves monocular visual odometry accuracy compared with existing feature-based and learning-based approaches. The proposed anisotropic covariance model achieves lower rotational errors and more robust trajectory estimation than fixed and isotropic uncertainty models, validating the effectiveness of geometry-induced uncertainty modeling for challenging visual environments.
Figures & tables
Fig. 1: We present MomentBA , a differentiable bundle adjustment framework that models anisotropic correspondence uncertainty from similarity responses via second-order spatial moments. The left shows correspondence images and uncertainty visualization, the middle illustrates geometry-induced uncertainty estimation and its integration into bundle adjustment, and the right demonstrates improved trajectory estimation under challenging scenes.
Fig. 2: Overview of MomentBA. Similarity responses from the tracking network are used to derive anisotropic covariances via spatial moments, which are incorporated into bundle adjustment for uncertainty-aware optimization and learning.
Fig. 3: Statistics of MomentBA covariance across feature types. Distributions of anisotropy ratio λ1/λ2 , covariance trace tr(Σ) , and similarity entropy H(P) show increasing geometric ambiguity from corners to edges and repetitive regions.
Method
MH03
MH05
V102
V103
V202
V203
Avg.
trel
rrel
trel
rrel
trel
rrel
trel
rrel
trel
rrel
trel
rrel
trel
rrel
VO
TartanVO
0.0302
0.2791
0.0193
0.0604
0.0251
0.1244
0.0263
0.1552
0.0171
0.1251
0.0303
0.2986
0.0247
0.1738
MAC-VO
0.0023
0.0238
0.0025
0.0216
0.0029
0.0434
0.0032
0.0580
0.0018
0.0406
0.0049
0.1284
0.0029
0.0526
Feature
ORB
0.0064
0.0200
0.0085
0.0147
0.0067
0.0406
0.0186
0.0481
0.0061
0.0411
0.0123
0.0628
0.0098
0.0379
TABLE I: Relative pose error comparison on EuRoC dataset. trel denotes translational error and rrel denotes rotational error.
Method
H01
H03
H05
H07
H09
H011
Avg.
trel
rrel
trel
rrel
trel
rrel
trel
rrel
trel
rrel
trel
rrel
trel
rrel
VO
TartanVO
0.2918
0.0877
0.3275
0.1391
0.3644
0.1899
0.2605
0.0338
0.6182
0.0731
0.2204
0.0287
0.3471
0.0921
MAC-VO
0.3440
0.1052
0.2507
0.0778
0.1485
0.0352
0.0985
0.0418
0.3848
0.0628
0.1292
0.1414
0.2260
0.0774
Feature
ORB
0.1163
0.0667
0.2212
0.0241
0.2464
0.0298
0.2613
0.0325
0.3454
0.0416
0.1826
0.0438
0.2289
0.0398
TABLE II: Relative pose error comparison on TartanAir v1 Hard dataset. trel denotes translational error and rrel denotes rotational error.
Fig. 4: Visualization of the estimated anisotropic correspondence covariance on the EuRoC MAV dataset.
Fig. 5: Trajectory comparison of different methods on the TartanAir v1 Hard dataset.
Relative Translation Error ( trel , m/frame)
Trajectory
K01
K03
K05
K07
K09
constant
0.1089
0.0321
0.1820
0.1252
0.1224
isotropic
0.2499
0.0344
0.1916
0.0779
0.1424
anisotropic
0.0802
0.0290
0.1394
0.0650
0.0996
TABLE III: Performance comparison of different ablation setups on the KITTI Dataset.
Most existing image keypoint detection and description methods rely on datasets with accurate pose and depth annotations, limiting scalability and generalization, and often degrading navigation and localization performance. We propose ViBA, a sustainable learning framework that integrates geometric optimization with feature learning for continuous online training on unconstrained video streams. Embedded in a standard visual odometry pipeline, it consists of an implicitly differentiable geometric residual framework: (i) an initial tracking network for inter-frame correspondences, (ii) depth-based outlier filtering, and (iii) differentiable global bundle adjustment that jointly refines camera poses and feature positions by minimizing reprojection errors. By combining geometric consistency from BA with long-term temporal consistency across frames, ViBA enforces stable and accurate feature representations. We evaluate ViBA on EuRoC and UMA datasets. Compared with state-of-the-art methods such as SuperPoint+SuperGlue, ALIKED, and LightGlue, ViBA reduces mean absolute translation error (ATE) by 12-18% and absolute rotation error (ARE) by 5-10% across sequences, while maintaining real-time inference speeds (FPS 36-91). When evaluated on unseen sequences, it retains over 90% localization accuracy, demonstrating robust generalization. These results show that ViBA supports continuous online learning with geometric and temporal consistency, consistently improving navigation and localization in real-world scenarios.
Xiaoji Niu, Yuqing Wang, Yan Wang +2
GNSS Research Center, Wuhan University, Wuhan 430079, China · Electronic Information School, Wuhan University, Wuhan 430079, China · Hubei Technology Innovation Center for Spatiotemporal Information and Positioning Navigation +1
Visual odometry is essential for autonomous navigation in GPS-denied environments, yet RGB-based methods remain vulnerable to motion blur, challenging illumination, and dropped frames. Event cameras complement conventional cameras with high temporal resolution and dynamic range, but their asynchronous measurements complicate reliable correspondence estimation. We present DAPEVO, a learned visual odometry system that estimates image and event correspondences independently at shared patch locations and fuses their correlation evidence before motion refinement. Each tracked patch maintains image and event descriptors, and a learned scalar gate combines modality-specific correlation embeddings for each patch--frame edge before a shared recurrent refinement and bundle-adjustment update. DAPEVO also supports event-only observations, enabling continued tracking when RGB frames are sparse or unavailable, while modality-aware keyframe culling preserves scarce frame constraints. On UZH-FPV, when retaining only one in six RGB frames, DAPEVO's mean absolute trajectory error (ATE) increases by only 36%, from 1.00 to 1.36m, whereas the ATE of DPVO and RAMP-VO rises by factors of 3.7× and 3.1×, respectively. On TartanEvent, DAPEVO similarly remains below 1m ATE at 3Hz RGB input, while DPVO and RAMP-VO exceed 9m. Under degraded RGB input on TartanEvent, DAPEVO achieves an ATE of 0.60m, compared with more than 4m for both DPVO and RAMP-VO, while also outperforming event-only DEVO at 0.87m.
Estimating relative pose from image pairs fundamentally requires only a minimal subset of geometrically consistent correspondences. However, most learning-based approaches rely on dense matching or direct regression, leading to redundancy and reduced geometric interpretability. In this work, we propose a sparse epipolar matching framework that predicts a compact set of correspondences optimized for geometric consistency across varying temporal baselines. To address residual noise and misalignment, we introduce an epipolar diffusion process that models correspondence uncertainty and refines keypoints toward epipolar consistency. The refined correspondences, along with depth cues, are lifted into a graph representation forming a Steiner graph that encodes relational structure between points. A graph neural network learns a compact subset of informative correspondences, which are passed to a differentiable singular value decomposition solver for end-to-end geometric estimation. Relative pose is recovered from the resulting essential matrix and evaluated in a visual odometry setting on the TartanAir and KITTI SLAM datasets. Experimental results demonstrate that combining sparse matching, diffusion-based refinement, and graph-based subset selection reduces correspondence redundancy while maintaining robust pose estimation across challenging baselines.
Prateeth Rao
International Institute of Information Technology Bangalore, Bengaluru, India