# Scalable 3D Registration via Truncated Entry-wise Absolute Residuals

arXiv: https://arxiv.org/abs/2404.00915 · HTML: https://mlsanity.com/paper/2404.00915/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 77 references that are in the map.
- First posted on arXiv 1 Apr 2024.

## Builds on (most cited first, 27 of 27)

- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [PointDSC: Robust Point Cloud Registration using Deep Spatial Consistency](https://mlsanity.com/paper/2103.05465/) (2021)
- [Graph-Cut RANSAC](https://mlsanity.com/paper/1706.00984/) (2017)
- [MAGSAC: marginalizing sample consensus](https://mlsanity.com/paper/1803.07469/) (2018)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection](https://mlsanity.com/paper/1909.08605/) (2019)
- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [Rotation-Invariant Transformer for Point Cloud Matching](https://mlsanity.com/paper/2303.08231/) (2023)
- [Guaranteed Outlier Removal for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/1711.10209/) (2017)
- [Deep Hough Voting for Robust Global Registration](https://mlsanity.com/paper/2109.04310/) (2021)
- [Robust Outlier Rejection for 3D Registration with Variational Bayes](https://mlsanity.com/paper/2304.01514/) (2023)
- [A Quaternion-based Certifiably Optimal Solution to the Wahba Problem with Outliers](https://mlsanity.com/paper/1905.12536/) (2019)
- [CLIPPER: A Graph-Theoretic Framework for Robust Data Association](https://mlsanity.com/paper/2011.10202/) (2020)
- [Practical optimal registration of terrestrial LiDAR scan pairs](https://mlsanity.com/paper/1811.09962/) (2018)
- [Block Coordinate Descent on Smooth Manifolds: Convergence Theory and Twenty-One Examples](https://mlsanity.com/paper/2305.14744/) (2023)
- [ARCS: Accurate Rotation and Correspondence Search](https://mlsanity.com/paper/2203.14493/) (2022)
- [Deep Graph-based Spatial Consistency for Robust Non-rigid Point Cloud Registration](https://mlsanity.com/paper/2303.09950/) (2023)
- [Accelerating Globally Optimal Consensus Maximization in Geometric Vision](https://mlsanity.com/paper/2304.05156/) (2023)
- [TriVoC: Efficient Voting-based Consensus Maximization for Robust Point Cloud Registration with Extreme Outlier Ratios](https://mlsanity.com/paper/2111.00657/) (2021)
- [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)
- [A New Outlier Removal Strategy Based on Reliability of Correspondence Graph for Fast Point Cloud Registration](https://mlsanity.com/paper/2205.07404/) (2022)
- [Global Linear and Local Superlinear Convergence of IRLS for Non-Smooth Robust Regression](https://mlsanity.com/paper/2208.11846/) (2022)
- [Efficient and Deterministic Search Strategy Based on Residual Projections for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/2305.11716/) (2023)

## Built on by (most cited first, 16 of 16)

- [TurboReg: TurboClique for Robust and Efficient Point Cloud Registration](https://mlsanity.com/paper/2507.01439/) (2025)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [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)
- [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)
- [Fast globally optimal Truncated Least Squares point cloud registration with fixed rotation axis](https://mlsanity.com/paper/2508.15613/) (2025)
- [Toward Zero-Shot Point Cloud Registration Across Diverse Scales, Scenes, and Sensor Setups](https://mlsanity.com/paper/2601.02759/) (2026)
- [Decomposed Global Optimization for Robust Point Matching with Low-Dimensional Branching](https://mlsanity.com/paper/2405.08589/) (2024)
- [Linearly Solving Robust Rotation Estimation](https://mlsanity.com/paper/2506.11547/) (2025)
- [GMOR: A Lightweight Robust Point Cloud Registration Framework via Geometric Maximum Overlapping](https://mlsanity.com/paper/2508.17427/) (2025)
- [ViGG: Robust RGB-D Point Cloud Registration using Visual-Geometric Mutual Guidance](https://mlsanity.com/paper/2511.22908/) (2025)
- [Global Truncated Loss Minimization for Robust and Threshold-Resilient Geometric Estimation](https://mlsanity.com/paper/2603.14796/) (2026)
- [Non-Minimal Sampling and Consensus for Prohibitively Large Datasets](https://mlsanity.com/paper/2604.22518/) (2026)
- [Point Cloud Registration via Probabilistic Self-Update Local Correspondence and Line Vector Sets](https://mlsanity.com/paper/2604.26318/) (2026)
- [AutoCompass: Accurate Visual Localization on Public Maps by Learning from Weak Labels](https://mlsanity.com/paper/2609.02798/) (2026)

## Abstract (arXiv)

Given an input set of 3D point pairs, the goal of outlier-robust 3D registration is to compute some rotation and translation that align as many point pairs as possible. This is an important problem in computer vision, for which many highly accurate approaches have been recently proposed. Despite their impressive performance, these approaches lack scalability, often overflowing the 16GB of memory of a standard laptop to handle roughly 30,000 point pairs. In this paper, we propose a 3D registration approach that can process more than ten million (107) point pairs with over 99% random outliers. Moreover, our method is efficient, entails low memory costs, and maintains high accuracy at the same time. We call our method TEAR, as it involves minimizing an outlier-robust loss that computes Truncated Entry-wise Absolute Residuals. To minimize this loss, we decompose the original 6-dimensional problem into two subproblems of dimensions 3 and 2, respectively, solved in succession to global optimality via a customized branch-and-bound method. While branch-and-bound is often slow and unscalable, this does not apply to TEAR as we propose novel bounding functions that are tight and computationally efficient. Experiments on various datasets are conducted to validate the scalability and efficiency of our method.