Relational Epipolar Graphs for Robust Relative Camera Pose Estimation

Introduction

Visual perception serves as a primary mechanism through which both biological and artificial systems perceive, navigate, and interact with their environments. For artificial systems, vision provides a rich source of information that enables complex tasks such as localization, mapping, and scene understanding to be performed. The objective of vision-based perception is 3-D reconstruction, with which spatial structure from 2-dimensional (2-D) image observations can be recovered. Frameworks such as SLAM and SfM address the objective of making accurate 3-D reconstruction by jointly estimating camera motion and reconstructing the surrounding environment from image sequences.

General Visual SLAM Pipeline

At the core of both SLAM and SfM lies the estimation of the camera’s 6 Degrees of Freedom (6-DoF) pose, which encodes its position and orientation relative to the world coordinate frame. Despite the advantages, vision-based localization remains challenging. Appearance variations, illumination changes, occlusions, texture-poor regions, dynamic objects, and camera motion instability all contribute to the difficulty of establishing reliable correspondences between images. Furthermore, practical systems must operate under computational and latency constraints, limiting the complexity of permissible algorithms.

Epipolar Graph Construction

The process of Epipolar Graph Construction is as follows:

Matched and Normalized Correspondences: For each image pair, LoFTR produces a set of $N\gg0$ matched normalized keypoints $\{(\mathbf{x}_i^{(1)}, \mathbf{x}_i^{(2)})\}_{i=1}^{N}$, where $\mathbf{x}_i^{(j)} \in \mathbb{R}^3$ denotes homogeneous normalized image coordinates. Each correspondence is stacked to form a feature vector.
Initial Graph Construction: A correspondence graph $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ is constructed where each node $v_i \in \mathcal{V}$ corresponds to a feature vector $\mathbf{f}_i$. Edges are formed using the $k$-nearest neighbor (k-NN) strategy based on Euclidean distance in the normalized coordinate space.
Initial Essential Matrix Estimation: To obtain an initial geometric model, a minimal random subset of correspondences is sampled. From this subset, an initial estimate of the essential matrix $\mathbf{E}$ is computed. This estimate serves as a reference for evaluating epipolar consistency.
Sampson Distance–Based Graph Pruning: For each node in the graph, the Sampson distance, $d_{\text{Sampson}}$, is computed to assess epipolar consistency with respect to $\mathbf{E}$. Given a threshold $\tau = 10^{-4}$, nodes whose correspondences violate $d_{\text{Sampson}} < \tau$ are identified as non-epipolar matches. Edges connected to such nodes are removed, resulting in a sparsified graph that preserves only geometrically consistent connections.

$$\mathbf{f}_i = \begin{bmatrix} \mathbf{x}_i^{(1)} & \mathbf{x}_i^{(2)} \end{bmatrix}^T \in \mathbb{R}^6$$

For a sequence of $M$ images, $M-1$ image pairs generate a tensor of size $(M-1, N, 6)$.

Epipolar Graph Construction

Graph Geometry Pose Regression

Final Graph Representation: The resulting graph consists of a reduced set of nodes corresponding to epipolar-consistent matched keypoints $\mathbf{F}' \in \mathbb{R}^{N' \times 6}$ and a sparsified edge set. This graph is subsequently passed to graph-based learning architectures for feature aggregation and selection of regions that satisfy epipolar geometry, enabling robust relative pose regression.

Epipolar Sparse Graph to Graph Based Pose Regression

When the matched and normalized keypoints, represented by patch region colors as shown in the plots, are passed through the GNN regression module, the layers of the GNN architecture cluster the keypoints before pooling them into a higher-dimensional feature vector that influences pose estimation.

Graph Relative Pose estimation

Regressed Pose and Trajectory Results

Comparative analysis of pose regression modules with the developed GNN module:

Tabular Results Testing on KiTTi

Trajectory Plot: CNN vs Graph

Citation

If you find this work useful for your research, please consider citing it once published:

@misc{rao2026relationalepipolargraphsrobust, title={Relational Epipolar Graphs for Robust Relative Camera Pose Estimation}, author={Prateeth Rao and Sachit Rao}, year={2026}, eprint={2604.04554}, archivePrefix={arXiv}, primaryClass={cs.CV}, url={https://arxiv.org/abs/2604.04554}, }