Geometry at the Last Mile: Beyond Local Appearance-Only Correspondence Search in Feature Matching

Semi-dense matching has seen substantial progress, yet fine-stage localization remains predominantly driven by local appearance cues and lacks explicit pairwise geometry, leaving it vulnerable to ambiguous local evidence, especially under weak texture, repetitive patterns, and large viewpoint changes. We present GeMiL, an efficient local feature matcher that introduces shared image-pair geometry into the final stage of correspondence localization, moving beyond independent refinement driven solely by local appearance. At its core, a Structured Geometry Head, trained under direct supervision from camera pose, consolidates confident cross-view correspondences into a shared geometry prior. The resulting fundamental matrix acts as a gated and bounded geometric bias over fine candidates, suppressing inconsistent locations while reinforcing locally plausible ones. Since the quality of this geometry prior depends on the cross-view relation evidence from which it is inferred, we regularize the final cross-attention responses toward token-level correspondence targets through Correspondence-Grounded Cross-Attention. Sharp Relation Injection then propagates these correspondence-aware relation features across scales through content adaptive reassembly. Across diverse geometric tasks, GeMiL achieves consistently strong accuracy and leading efficiency among semi-dense matchers, running $1.8\times$ faster than ELoFTR with only 42% of its peak memory and 8.8% of its FLOPs.