New RANSAC Scoring Method Improves Model Accuracy Without Scale Parameter

Traditional RANSAC (Random Sample Consensus) variants, widely used for robust model fitting, rely on scoring candidate models by counting inliers or summing point scores. A critical drawback is the requirement for a user-supplied inlier scale parameter, which itself must be estimated from potentially noisy data. This research proposes a new RANSAC scoring approach that removes this dependency. The core innovation involves reversing the inference order: instead of estimating the scale and then scoring, the inlier scale is analytically marginalized in closed form under a conjugate Inverse-Gamma prior. This results in a single, closed-form expression that adapts across data-rich and data-scarce scenarios without algorithm changes. The proposed score is the first to genuinely exclude the inlier scale from its formula and can be computed efficiently in O(N log N) time. Benchmarking across nearly 70,000 image pairs and various two-view estimation problems shows that this new score outperforms state-of-the-art methods like MSAC and MAGSAC, maintaining accuracy even with threshold miscalibration and achieving near-optimal results with significantly less validation data.