MomentBA: Second-order Spatial Moments for Anisotropic Correspondence Uncertainty in Differentiable Bundle Adjustment

2026-09-11

AI Summary

本文提出MomentBA，通过使用局部相似响应的二阶空间矩来推导各向异性对应不确定性，改进了几何优化中的不确定度估计，从而提高单目视觉里程计精度。

Abstract

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.

Problem

• visual odometry
• correspondence uncertainty
• anisotropic

Innovation

• anisotropic correspondence uncertainty
• second-order spatial moments
• differentiable bundle adjustment
• geometry-aware