🤖 AI Summary
This work proposes a pixel-accurate epipolar-guided matching method to address the limitations of conventional approaches in challenging scenarios such as repetitive textures or large baselines, where coarse spatial binning introduces errors, necessitates post-processing, and often misses valid correspondences. By leveraging the fundamental matrix to enforce epipolar geometry, the method defines for each keypoint an angular interval derived from a tolerance circle in angle space, transforming the matching problem into a one-dimensional interval query. Efficient exact matching is achieved via a segment tree with logarithmic time complexity. The approach enables per-point tolerance control, eliminates approximation errors and redundant descriptor comparisons, and recovers a complete set of correspondences without post-processing. Evaluated on the ETH3D dataset, it significantly outperforms existing methods, achieving both higher completeness and notable speedup.
📝 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.