A new method for robust estimation, MAGSAC++, is proposed. It introduces a new model quality (scoring) function that does not make inlier-outlier decisions, and a novel marginalization procedure formulated as an M-estimation with a novel class of M-estimators (a robust kernel) solved by an iteratively re-weighted least squares procedure. Instead of the inlier-outlier threshold, it requires only its loose upper bound which can be chosen from a significantly wider range. Also, we propose a new termination criterion and a technique for selecting a set of inliers in a data-driven manner as a post-processing step after the robust estimation finishes. On a number of publicly available real-world datasets for homography, fundamental matrix fitting and relative pose, MAGSAC++ produces results superior to the state-of-the-art robust methods. It is more geometrically accurate, fails fewer times, and it is often faster. It is shown that MAGSAC++ is significantly less sensitive to the setting of the threshold upper bound than the other state-of-the-art algorithms to the inlier-outlier threshold. Therefore, it is easier to be applied to unseen problems and scenes without acquiring information by hand about the setting of the inlier-outlier threshold. The source code and examples both in C++ and Python are available at https://github.com/danini/magsac.

A new method for robust estimation, MAGSAC++1, is proposed. It introduces a new model quality (scoring) function that does not require the inlier-outlier decision, and a novel marginalization procedure formulated as an M-estimation with a novel class of M-estimators (a robust kernel) solved by an iteratively re-weighted least squares procedure. We also propose a new sampler, Progressive NAPSAC, for RANSAC-like robust estimators. Exploiting the fact that nearby points often originate from the same model in real-world data, it finds local structures earlier than global samplers. The progressive transition from local to global sampling does not suffer from the weaknesses of purely localized samplers. On six publicly available realworld datasets for homography and fundamental matrix fitting, MAGSAC++ produces results superior to the state-of-the-art robust methods. It is faster, more geometrically accurate and fails less often.

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.