A novel method for robust estimation, called Graph-Cut RANSAC 1 , GC-RANSAC in short, is introduced. To separate inliers and outliers, it runs the graph-cut algorithm in the local optimization (LO) step which is applied when a sofar-the-best model is found. The proposed LO step is conceptually simple, easy to implement, globally optimal and efficient. GC-RANSAC is shown experimentally, both on synthesized tests and real image pairs, to be more geometrically accurate than state-of-the-art methods on a range of problems, e.g. line fitting, homography, affine transformation, fundamental and essential matrix estimation. It runs in real-time for many problems at a speed approximately equal to that of the less accurate alternatives (in milliseconds on standard CPU).

We present a new method for estimating the 6D pose of rigid objects with available 3D models from a single RGB input image. The method is applicable to a broad range of objects, including challenging ones with global or partial symmetries. An object is represented by compact surface fragments which allow handling symmetries in a systematic manner. Correspondences between densely sampled pixels and the fragments are predicted using an encoder-decoder network. At each pixel, the network predicts: (i) the probability of each object's presence, (ii) the probability of the fragments given the object's presence, and (iii) the precise 3D location on each fragment. A data-dependent number of corresponding 3D locations is selected per pixel, and poses of possibly multiple object instances are estimated using a robust and efficient variant of the PnP-RANSAC algorithm. In the BOP Challenge 2019, the method outperforms all RGB and most RGB-D and D methods on the T-LESS and LM-O datasets.

A method called, σ-consensus, is proposed to eliminate the need for a user-defined inlier-outlier threshold in RANSAC. Instead of estimating the noise σ, 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 σ of the point likelihoods of being inliers. A new quality function is proposed not requiring σ 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 σ-consensus, MAGSAC is proposed with no need for a user-defined σ and improving the accuracy of robust estimation significantly. It is superior to the state-ofthe-art in terms of geometric accuracy on publicly available real-world datasets for epipolar geometry (F and E) and homography estimation. In addition, applying σ-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. 1

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.