Pixel-Accurate Epipolar Guided Matching

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.