EpiDiffVO: Geometry-Aware Epipolar Diffusion for Robust Visual Odometry

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.

Relational Epipolar Graphs for Robust Relative Camera Pose Estimation

A key component of Visual Simultaneous Localization and Mapping (VSLAM) is estimating relative camera poses using matched keypoints. Accurate estimation is challenged by noisy correspondences. Classical methods rely on stochastic hypothesis sampling and iterative estimation, while learning-based methods often lack explicit geometric structure. In this work, we reformulate relative pose estimation as a relational inference problem over epipolar correspondence graphs, where matched keypoints are nodes and nearby ones are connected by edges. Graph operations such as pruning, message passing, and pooling estimate a quaternion rotation, translation vector, and the Essential Matrix (EM). Minimizing a loss comprising (i) $\mathcal{L}_2$ differences with ground truth (GT), (ii) Frobenius norm between estimated and GT EMs, (iii) singular value differences, (iv) heading angle differences, and (v) scale differences, yields the relative pose between image pairs. The dense detector-free method LoFTR is used for matching. Experiments on indoor and outdoor benchmarks show improved robustness to dense noise and large baseline variation compared to classical and learning-guided approaches, highlighting the effectiveness of global relational consensus.