MAGSAC: marginalizing sample consensus

A method called σ-consensus is proposed to eliminate the need for a user-defined inlier-outlier threshold in RANSAC. Instead of estimating σ, it is marginalized over a range of noise scales using a Bayesian estimator, i.e. the optimized model is obtained as the weighted average using the posterior probabilities as weights. Applying σ-consensus, two methods are proposed: (i) a postprocessing step which always improved the model quality on a wide range of vision problems without noticeable deterioration in processing time, i.e. at most 1-2 milliseconds; and (ii) a locally optimized RANSAC, called LO-MAGSAC, which includes σ-consensus to the local optimization of LO-RANSAC. The method is superior to the state-of-the-art in terms of geometric accuracy on publicly available real world datasets for epipolar geometry (F and E), homography and affine transformation estimation.