MAGSAC: marginalizing sample consensus.

A method called, sigma-consensus, is proposed to eliminate the need for a user-defined inlier-outlier threshold in RANSAC. Instead of estimating the noise sigma, it is marginalized over a range of noise scales. The optimized model is obtained by weighted least-squares fitting where the weights come from the marginalization over sigma of the point likelihoods of being inliers. A new quality function is proposed not requiring sigma and, thus, a set of inliers to determine the model quality. Also, a new termination criterion for RANSAC is built on the proposed marginalization approach. Applying sigma-consensus, MAGSAC is proposed with no need for a user-defined sigma and improving the accuracy of robust estimation significantly. It 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) and homography estimation. In addition, applying sigma-consensus only once as a post-processing step to the RANSAC output always improved the model quality on a wide range of vision problems without noticeable deterioration in processing time, adding a few milliseconds.