MAGSAC++, a Fast, Reliable and Accurate Robust Estimator

We propose MAGSAC++ and Progressive NAPSAC sampler, P-NAPSAC in short. In MAGSAC++, we replace the model quality and polishing functions of the original method by an iteratively re-weighted least-squares fitting with weights determined via marginalizing over the noise scale. MAGSAC++ is fast -- often an order of magnitude faster -- and more geometrically accurate than MAGSAC. P-NAPSAC merges the advantages of local and global sampling by drawing samples from gradually growing neighborhoods. Exploiting 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. The methods are tested on homography and fundamental matrix fitting on six publicly available datasets. MAGSAC combined with P-NAPSAC sampler is superior to state-of-the-art robust estimators in terms of speed, accuracy and failure rate.