# Global Truncated Loss Minimization for Robust and Threshold-Resilient Geometric Estimation

arXiv: https://arxiv.org/abs/2603.14796 · HTML: https://mlsanity.com/paper/2603.14796/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 79 references that are in the map.
- First posted on arXiv 16 Mar 2026.

## Builds on (most cited first, 24 of 24)

- [ORB-SLAM2: an Open-Source SLAM System for Monocular, Stereo and RGB-D Cameras](https://mlsanity.com/paper/1610.06475/) (2016)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [FAST-LIO2: Fast Direct LiDAR-inertial Odometry](https://mlsanity.com/paper/2107.06829/) (2021)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [Map-free Visual Relocalization: Metric Pose Relative to a Single Image](https://mlsanity.com/paper/2210.05494/) (2022)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [An Alternative Probabilistic Interpretation of the Huber Loss](https://mlsanity.com/paper/1911.02088/) (2019)
- [Globally-Optimal Contrast Maximisation for Event Cameras](https://mlsanity.com/paper/2206.05127/) (2022)
- [Outlier-Robust Estimation: Hardness, Minimally Tuned Algorithms, and Applications](https://mlsanity.com/paper/2007.15109/) (2020)
- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [The Alignment of the Spheres: Globally-Optimal Spherical Mixture Alignment for Camera Pose Estimation](https://mlsanity.com/paper/1812.01232/) (2018)
- [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)
- [Accelerating Globally Optimal Consensus Maximization in Geometric Vision](https://mlsanity.com/paper/2304.05156/) (2023)
- [Globally-Optimal Inlier Set Maximisation for Simultaneous Camera Pose and Feature Correspondence](https://mlsanity.com/paper/1709.09384/) (2017)
- [Estimation Contracts for Outlier-Robust Geometric Perception](https://mlsanity.com/paper/2208.10521/) (2022)
- [An Inexact Projected Gradient Method with Rounding and Lifting by Nonlinear Programming for Solving Rank-One Semidefinite Relaxation of Polynomial Optimization](https://mlsanity.com/paper/2105.14033/) (2021)
- [Efficient and Robust Point Cloud Registration via Heuristics-guided Parameter Search](https://mlsanity.com/paper/2404.06155/) (2024)
- [Certifiably Optimal Rotation and Pose Estimation Based on the Cayley Map](https://mlsanity.com/paper/2308.12418/) (2023)
- [Less Biased Noise Scale Estimation for Threshold-Robust RANSAC](https://mlsanity.com/paper/2503.13433/) (2025)
- [FracGM: A Fast Fractional Programming Technique for Geman-McClure Robust Estimator](https://mlsanity.com/paper/2409.13978/) (2024)

## Abstract (arXiv)

To achieve outlier-robust geometric estimation, robust objective functions are generally employed to mitigate the influence of outliers. The widely used consensus maximization(CM) is highly robust when paired with global branch-and-bound(BnB) search. However, CM relies solely on inlier counts and is sensitive to the inlier threshold. Besides, the discrete nature of CM leads to loose bounds, necessitating extensive BnB iterations and computation cost. Truncated losses(TL), another continuous alternative, leverage residual information more effectively and could potentially overcome these issues. But to our knowledge, no prior work has systematically explored globally minimizing TL with BnB and its potential for enhanced threshold resilience or search efficiency. In this work, we propose GTM, the first unified BnB-based framework for globally-optimal TL loss minimization across diverse geometric problems. GTM involves a hybrid solving design: given an n-dimensional problem, it performs BnB search over an (n-1)-dimensional subspace while the remaining 1D variable is solved by bounding the objective function. Our hybrid design not only reduces the search space, but also enables us to derive Lipschitz-continuous bounding functions that are general, tight, and can be efficiently solved by a classic global Lipschitz solver named DIRECT, which brings further acceleration. We conduct a systematic evaluation on various BnB-based methods for CM and TL on the robust linear regression problem, showing that GTM enjoys remarkable threshold resilience and the highest efficiency compared to baseline methods. Furthermore, we apply GTM on different geometric estimation problems with diverse residual forms. Extensive experiments demonstrate that GTM achieves state-of-the-art outlier-robustness and threshold-resilience while maintaining high efficiency across these estimation tasks.