Pixel-Accurate Epipolar Guided Matching
This work addresses a domain-specific problem in computer vision for tasks like Structure from Motion (SfM), offering an incremental improvement over existing epipolar-guided matching methods.
The paper tackles the problem of keypoint matching being slow and unreliable in challenging conditions like repetitive textures or wide-baseline views by introducing an exact formulation that performs candidate selection directly in angular space, resulting in noticeable speedups and recovery of exact correspondence sets on ETH3D.
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.