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

• URL: http://arxiv.org/abs/2609.13691v1
• Date: Sat, 12 Sep 2026 03:58:09 GMT
• Title: MomentBA: Second-order Spatial Moments for Anisotropic Correspondence Uncertainty in Differentiable Bundle Adjustment
• Abstract summary: We propose MomentBA, a geometry-aware bundle adjustment framework that derives anisotropic correspondence uncertainty from second-order spatial moments of local similarity responses.<n> 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.
• Score: 25.614583001276767
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates [3.5829219417440368]
  We introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation.<n>The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation.
  arXiv  Detail & Related papers  (2026-08-11T21:02:31Z)
• Sensor-Informed Per-Point Covariance for Structured-Light 3D Imaging [0.0]
  Per-point uncertainty models are important in structured-light 3D reconstruction for probabilistic registration, fusion, and quality assessment.<n>This paper presents a sensor-informed first-order method for constructing a per-point 3 x 3 covariance field from experimentally measured phase precision and calibrated mappings.
  arXiv  Detail & Related papers  (2026-08-11T13:05:22Z)
• Rethinking Structural Anomaly Detection: From Decision Boundaries to Projection Operators [51.771100367755544]
  We introduce a geometric perspective to address the mismatch between the inductive bias of existing methods and the structure of the data.<n>Specifically, we learn a projection operator onto the manifold of normal samples and define a sample as anomalous if it is altered by this projection.<n> Notably, it provides a unifying interpretation of reconstruction-based methods by explaining their success and failure in terms of projection quality.
  arXiv  Detail & Related papers  (2026-06-13T12:37:20Z)
• EpiDiffVO: Geometry-Aware Epipolar Diffusion for Robust Visual Odometry [0.0]
  Estimating relative pose from image pairs requires only a minimal subset of geometrically consistent correspondences.<n>We propose a sparse epipolar matching framework that predicts a compact set of correspondences optimized for geometric consistency.
  arXiv  Detail & Related papers  (2026-05-19T08:53:26Z)
• Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration [71.51826063983434]
  Image restoration is an inherently ill posed inverse problem.<n>We use non strict symmetry as a constraint to formulate the restoration inverse problem.<n>We show that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size.
  arXiv  Detail & Related papers  (2026-05-13T16:22:19Z)
• An Isotropic Approach to Efficient Uncertainty Quantification with Gradient Norms [7.439615448864818]
  We propose a lightweight method for quantifying predictive uncertainty in neural networks.<n>We use two approximations: a first-order Taylor expansion that expresses uncertainty in terms of the gradient of the prediction, and an isotropy assumption on the parameter covariance.<n>We then use the estimates to investigate when each uncertainty type carries useful signal for predicting answer correctness in question answering with large language models.
  arXiv  Detail & Related papers  (2026-03-31T09:13:09Z)
• Revisiting Zeroth-Order Optimization: Minimum-Variance Two-Point Estimators and Directionally Aligned Perturbations [57.179679246370114]
  We identify the distribution of random perturbations that minimizes the estimator's variance as the perturbation stepsize tends to zero.<n>Our findings reveal that such desired perturbations can align directionally with the true gradient, instead of maintaining a fixed length.
  arXiv  Detail & Related papers  (2025-10-22T19:06:39Z)
• Adaptive Dual Uncertainty Optimization: Boosting Monocular 3D Object Detection under Test-Time Shifts [80.32933059529135]
  Test-Time Adaptation (TTA) methods have emerged to adapt to target distributions during inference.<n>We propose Dual Uncertainty Optimization (DUO), the first TTA framework designed to jointly minimize both uncertainties for robust M3OD.<n>In parallel, we design a semantic-aware normal field constraint that preserves geometric coherence in regions with clear semantic cues.
  arXiv  Detail & Related papers  (2025-08-28T07:09:21Z)
• On Equivariant Model Selection through the Lens of Uncertainty [49.137341292207]
  Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead.<n>We compare frequentist (via Conformal Prediction), Bayesian (via the marginal likelihood), and calibration-based measures to naive error-based evaluation.<n>We find that uncertainty metrics generally align with predictive performance, but Bayesian model evidence does so inconsistently.
  arXiv  Detail & Related papers  (2025-06-23T13:35:06Z)
• AirIMU: Learning Uncertainty Propagation for Inertial Odometry [29.093168179953185]
  Inertial odometry (IO) using strap-down inertial measurement units (IMUs) is critical in many robotic applications. We present AirIMU, a hybrid approach to estimate the uncertainty, especially the non-deterministic errors, by data-driven methods. We demonstrate its effectiveness on various platforms, including hand-held devices, vehicles, and a helicopter that covers a trajectory of 262 kilometers.
  arXiv  Detail & Related papers  (2023-10-07T17:08:22Z)
• Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction [40.73187749820041]
  Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. A prevalent approach in current deep learning is the set-based approach which measures the discrepancy between two surfaces by comparing two randomly sampled point-clouds from the two meshes with Chamfer pseudo-distance. We propose a novel metric for learning mesh deformation, defined by sliced Wasserstein distance on meshes represented as probability measures that generalize the set-based approach.
  arXiv  Detail & Related papers  (2023-05-27T19:10:19Z)
• A Model for Multi-View Residual Covariances based on Perspective Deformation [88.21738020902411]
  We derive a model for the covariance of the visual residuals in multi-view SfM, odometry and SLAM setups. We validate our model with synthetic and real data and integrate it into photometric and feature-based Bundle Adjustment.
  arXiv  Detail & Related papers  (2022-02-01T21:21:56Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.