Pixel-Accurate Epipolar Guided Matching

TL;DR

This paper introduces an exact epipolar-guided keypoint matching method that operates in angular space, achieving pixel-level accuracy, increased robustness, and faster performance compared to previous approaches.

Contribution

It presents a novel formulation for epipolar-guided matching that performs candidate selection directly in angular space using segment trees, eliminating approximation errors and reducing computation.

Findings

Achieves significant speedups over existing methods.

Recovers exact correspondence sets in challenging conditions.

Supports per-keypoint control and pixel-level tolerance.

Abstract

Keypoint matching can be slow and unreliable in challenging conditions such as repetitive textures or wide-baseline views. In such cases, known geometric relations (e.g., the fundamental matrix) can be used to restrict potential correspondences to a narrow epipolar envelope, thereby reducing the search space and improving robustness. These epipolar-guided matching approaches have proved effective in tasks such as SfM; however, most rely on coarse spatial binning, which introduces approximation errors, requires costly post-processing, and may miss valid correspondences. We address these limitations with an exact formulation that performs candidate selection directly in angular space. In our approach, each keypoint is assigned a tolerance circle which, when viewed from the epipole, defines an angular interval. Matching then becomes a 1D angular interval query, solved efficiently in logarithmic time with a segment tree. This guarantees pixel-level tolerance, supports per-keypoint control, and removes unnecessary descriptor comparisons. Extensive evaluation on ETH3D demonstrates noticeable speedups over existing approaches while recovering exact correspondence sets.