# Accelerating Globally Optimal Consensus Maximization in Geometric Vision

arXiv: https://arxiv.org/abs/2304.05156 · HTML: https://mlsanity.com/paper/2304.05156/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 55 references that are in the map.
- First posted on arXiv 11 Apr 2023.

## Builds on (most cited first, 17 of 17)

- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [A Polynomial-time Solution for Robust Registration with Extreme Outlier Rates](https://mlsanity.com/paper/1903.08588/) (2019)
- [Globally-Optimal Contrast Maximisation for Event Cameras](https://mlsanity.com/paper/2206.05127/) (2022)
- [Robust Fitting in Computer Vision: Easy or Hard?](https://mlsanity.com/paper/1802.06464/) (2018)
- [The Alignment of the Spheres: Globally-Optimal Spherical Mixture Alignment for Camera Pose Estimation](https://mlsanity.com/paper/1812.01232/) (2018)
- [Practical optimal registration of terrestrial LiDAR scan pairs](https://mlsanity.com/paper/1811.09962/) (2018)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [Globally-Optimal Inlier Set Maximisation for Simultaneous Camera Pose and Feature Correspondence](https://mlsanity.com/paper/1709.09384/) (2017)
- [Consensus Maximization Tree Search Revisited](https://mlsanity.com/paper/1908.02021/) (2019)
- [Globally-Optimal Event Camera Motion Estimation](https://mlsanity.com/paper/2203.03914/) (2022)
- [Deterministic consensus maximization with biconvex programming](https://mlsanity.com/paper/1807.09436/) (2018)
- [Efficient Globally-Optimal Correspondence-Less Visual Odometry for Planar Ground Vehicles](https://mlsanity.com/paper/2203.00291/) (2022)
- [Globally optimal point set registration by joint symmetry plane fitting](https://mlsanity.com/paper/2002.07988/) (2020)
- [Globally optimal consensus maximization for robust visual inertial localization in point and line map](https://mlsanity.com/paper/2002.11905/) (2020)

## Built on by (most cited first, 14 of 14)

- [Scalable 3D Registration via Truncated Entry-wise Absolute Residuals](https://mlsanity.com/paper/2404.00915/) (2024)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [RePoseD: Efficient Relative Pose Estimation With Known Depth Information](https://mlsanity.com/paper/2501.07742/) (2025)
- [Efficient and Robust Point Cloud Registration via Heuristics-guided Parameter Search](https://mlsanity.com/paper/2404.06155/) (2024)
- [BUFFER-X: Towards Zero-Shot Point Cloud Registration in Diverse Scenes](https://mlsanity.com/paper/2503.07940/) (2025)
- [Robust Fitting on a Gate Quantum Computer](https://mlsanity.com/paper/2409.02006/) (2024)
- [Transformation Decoupling Strategy based on Screw Theory for Deterministic Point Cloud Registration with Gravity Prior](https://mlsanity.com/paper/2311.01432/) (2023)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [A Comprehensive Survey for Real-World Industrial Defect Detection: Challenges, Approaches, and Prospects](https://mlsanity.com/paper/2507.13378/) (2025)
- [fCOP: Focal Length Estimation from Category-level Object Priors](https://mlsanity.com/paper/2409.19641/) (2024)
- [Toward Zero-Shot Point Cloud Registration Across Diverse Scales, Scenes, and Sensor Setups](https://mlsanity.com/paper/2601.02759/) (2026)
- [Inteval Analysis for two spherical functions arising from robust Perspective-n-Lines problem](https://mlsanity.com/paper/2503.00400/) (2025)
- [GMOR: A Lightweight Robust Point Cloud Registration Framework via Geometric Maximum Overlapping](https://mlsanity.com/paper/2508.17427/) (2025)
- [Global Truncated Loss Minimization for Robust and Threshold-Resilient Geometric Estimation](https://mlsanity.com/paper/2603.14796/) (2026)

## Abstract (arXiv)

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an n-1 dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to four fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, point set registration, and rotation and focal length estimation. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios.