# MAGSAC: marginalizing sample consensus

arXiv: https://arxiv.org/abs/1803.07469 · HTML: https://mlsanity.com/paper/1803.07469/

## Key facts

- Cited by 123 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2018.

## Built on by (most cited first, 30 of 123)

- [LightGlue: Local Feature Matching at Light Speed](https://mlsanity.com/paper/2306.13643/) (2023)
- [Back to the Feature: Learning Robust Camera Localization from Pixels to Pose](https://mlsanity.com/paper/2103.09213/) (2021)
- [COTR: Correspondence Transformer for Matching Across Images](https://mlsanity.com/paper/2103.14167/) (2021)
- [Map-free Visual Relocalization: Metric Pose Relative to a Single Image](https://mlsanity.com/paper/2210.05494/) (2022)
- [Reloc3r: Large-Scale Training of Relative Camera Pose Regression for Generalizable, Fast, and Accurate Visual Localization](https://mlsanity.com/paper/2412.08376/) (2024)
- [OSOP: A Multi-Stage One Shot Object Pose Estimation Framework](https://mlsanity.com/paper/2203.15533/) (2022)
- [PDC-Net+: Enhanced Probabilistic Dense Correspondence Network](https://mlsanity.com/paper/2109.13912/) (2021)
- [GIM: Learning Generalizable Image Matcher From Internet Videos](https://mlsanity.com/paper/2402.11095/) (2024)
- [SC^2-PCR: A Second Order Spatial Compatibility for Efficient and Robust Point Cloud Registration](https://mlsanity.com/paper/2203.14453/) (2022)
- [PF3plat: Pose-Free Feed-Forward 3D Gaussian Splatting](https://mlsanity.com/paper/2410.22128/) (2024)
- [SiLK -- Simple Learned Keypoints](https://mlsanity.com/paper/2304.06194/) (2023)
- [GLACE: Global Local Accelerated Coordinate Encoding](https://mlsanity.com/paper/2406.04340/) (2024)
- [Progressive Correspondence Pruning by Consensus Learning](https://mlsanity.com/paper/2101.00591/) (2021)
- [Iterative Deep Homography Estimation](https://mlsanity.com/paper/2203.15982/) (2022)
- [Unifying Correspondence, Pose and NeRF for Pose-Free Novel View Synthesis from Stereo Pairs](https://mlsanity.com/paper/2312.07246/) (2023)
- [Generalized Differentiable RANSAC](https://mlsanity.com/paper/2212.13185/) (2022)
- [Motion Basis Learning for Unsupervised Deep Homography Estimation with Subspace Projection](https://mlsanity.com/paper/2103.15346/) (2021)
- [LocalTrans: A Multiscale Local Transformer Network for Cross-Resolution Homography Estimation](https://mlsanity.com/paper/2106.04067/) (2021)
- [Depth-Aware Multi-Grid Deep Homography Estimation with Contextual Correlation](https://mlsanity.com/paper/2107.02524/) (2021)
- [Emergent Outlier View Rejection in Visual Geometry Grounded Transformers](https://mlsanity.com/paper/2512.04012/) (2025)
- [Visual Localization using Imperfect 3D Models from the Internet](https://mlsanity.com/paper/2304.05947/) (2023)
- [End2End Multi-View Feature Matching with Differentiable Pose Optimization](https://mlsanity.com/paper/2205.01694/) (2022)
- [Unsupervised Homography Estimation with Coplanarity-Aware GAN](https://mlsanity.com/paper/2205.03821/) (2022)
- [DeepMatcher: A Deep Transformer-based Network for Robust and Accurate Local Feature Matching](https://mlsanity.com/paper/2301.02993/) (2023)
- [MADiff: Motion-Aware Mamba Diffusion Models for Hand Trajectory Prediction on Egocentric Videos](https://mlsanity.com/paper/2409.02638/) (2024)
- [Neural Reprojection Error: Merging Feature Learning and Camera Pose Estimation](https://mlsanity.com/paper/2103.07153/) (2021)
- [VSAC: Efficient and Accurate Estimator for H and F](https://mlsanity.com/paper/2106.10240/) (2021)
- [Scalable 3D Registration via Truncated Entry-wise Absolute Residuals](https://mlsanity.com/paper/2404.00915/) (2024)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [Convex Relaxation for Robust Vanishing Point Estimation in Manhattan World](https://mlsanity.com/paper/2505.04788/) (2025)

## Abstract (arXiv)

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. The source code is at https://github.com/danini/magsac.