Boosting Correspondence Learning with Structure-Aware Estimator

Correspondence learning aims to estimate accurate geomet-ric model parameters from the data with severe outliers and is crucial formany computer vision tasks. While recent deep correspondence learningmethods have substantially improved inlier-outlier identification, most ofthem still rely on a differentiable weighted least squares (WLS) estima-tor to recover the final model parameters. This strategy typically treatscorrespondences as conditionally independent observations and there-fore ignores the structured dependencies among inliers. In real-worldscenarios, inliers are often sampled from geometric manifolds and tendto appear in spatially dense clusters, especially in texture-rich regions.As a result, WLS may be dominated by dense inlier groups, leadingto a poorly-conditioned estimation problem that is vulnerable to noiseor degenerate configurations. To address this bottleneck, we propose astructure-aware estimator, which explicitly models inlier correlations viaa graph Laplacian matrix and integrates this prior into a maximum-likelihood framework. Our proposed estimator is fully differentiable, ar-chitecturally lightweight, and can seamlessly replace the standard WLSestimator in existing correspondence learning pipelines. Extensive exper-iments on multiple benchmarks demonstrate consistent improvementswhile introducing a modest increase in computational cost. The code ispublicly available at: https://github.com/Tianyu-Yan/SAE