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 Mestimation 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 stateof-the-art robust methods. It is faster, more geometrically accurate and fails less often.

We propose Progressive NAPSAC, P-NAPSAC in short, which merges the advantages of local and global sampling by drawing samples from gradually growing neighborhoods. Exploiting the fact that nearby points are more likely to originate from the same geometric model, P-NAPSAC finds local structures earlier than global samplers. We show that the progressive spatial sampling in P-NAPSAC can be integrated with PROSAC sampling, which is applied to the first, location-defining, point. P-NAPSAC is embedded in USAC [21], a state-of-the-art robust estimation pipeline, which we further improve by implementing its local optimization as in Graph-Cut RANSAC [1]. We call the resulting estimator USAC * .The method is tested on homography and fundamental matrix fitting on a total of 10 691 models from seven publicly available datasets. USAC * with P-NAPSAC outperforms reference methods in terms of speed on all problems.

We present VSAC, a RANSAC-type robust estimator with a number of novelties. It benefits from the introduction of the concept of independent inliers that improves significantly the efficacy of the dominant plane handling and, also, allows near error-free rejection of incorrect models, without false positives. The local optimization process and its application is improved so that it is run on average only once. Further technical improvements include adaptive sequential hypothesis verification and efficient model estimation via Gaussian elimination. Experiments on four standard datasets show that VSAC is significantly faster than all its predecessors and runs on average in 1-2 ms, on a CPU. It is two orders of magnitude faster and yet as precise as MAGSAC++, the currently most accurate estimator of twoview geometry. In the repeated runs on EVD, HPatches, PhotoTourism, and Kusvod2 datasets, it never failed.

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