RANSAC Scoring Done Right

The most widely used RANSAC variants score candidate models by counting inliers or summing truncated likelihoods; every such score requires a user-supplied parameter that is a function of the inlier scale, which must itself be estimated from contaminated data. We remove this dependence by reversing the usual order of inference: for a fixed inlier partition we marginalize $\sigma$ analytically in closed form under a conjugate Inverse-Gamma prior, then optimize over partitions. A single closed-form expression spans the non-informative Jeffreys limit (which requires no validation data to fit the prior) and informative empirical-Bayes priors fit from a small validation set, so the same score adapts across data-rich and data-scarce regimes without any change to the algorithm. To our knowledge this is the first RANSAC score in which the inlier scale is genuinely absent from the score formula. The score admits $O(N \log N)$ computation via sort-and-sweep. On a benchmark of nearly $70\,000$ image pairs spanning different two-view estimation problems and both engineered and learned feature pipelines, the proposed score matches or exceeds the state of the art (RANSAC, MSAC, GaU, MAGSAC++), excelling in robustness to hyperparameter miscalibration, sample efficiency at small validation budgets, and adaptive regularization across data-rich and data-scarce regimes.