RANSAC Scoring Done Right

arXiv:2606.27385v2 Announce Type: replace-cross Abstract: The most widely used RANSAC variants score a candidate model by summing per-point scores that fall to zero beyond a threshold. These scores derive from the negative log-likelihood of a Gaussian-uniform mixture. The threshold separates inliers, which follow the noise model, from outliers, and it is a function of the observation noise level, also known as the inlier scale. We remove this dependence on the threshold by reversing the usual order of RANSAC inference: rather than estimating the scale and then scoring against it, we marginalize the scale in closed form for a fixed inlier partition and then optimize over partitions. The resulting score is maximized by a single sort followed by a linear sweep. A single closed-form expression spans informative and non-informative priors, so the same score adapts to datasets with extensive or limited ground-truth annotation. The proposed score has a single hyperparameter, the half-width of the uniform outlier distribution. We show that this half-width is far less sensitive to miscalibration than the inlier threshold and is easier to cross-validate. The proposed score is the first likelihood-based RANSAC score in which the inlier scale is absent from the formula. Project page: https://ransacscoringdoneright.github.io