# Practical optimal registration of terrestrial LiDAR scan pairs

arXiv: https://arxiv.org/abs/1811.09962 · HTML: https://mlsanity.com/paper/1811.09962/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2018.

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

- [MULLS: Versatile LiDAR SLAM via Multi-metric Linear Least Square](https://mlsanity.com/paper/2102.03771/) (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)
- [Accelerating Globally Optimal Consensus Maximization in Geometric Vision](https://mlsanity.com/paper/2304.05156/) (2023)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [A New Outlier Removal Strategy Based on Reliability of Correspondence Graph for Fast Point Cloud Registration](https://mlsanity.com/paper/2205.07404/) (2022)
- [Efficient and Robust Point Cloud Registration via Heuristics-guided Parameter Search](https://mlsanity.com/paper/2404.06155/) (2024)
- [Point Cloud Registration for LiDAR and Photogrammetric Data: a Critical Synthesis and Performance Analysis on Classic and Deep Learning Algorithms](https://mlsanity.com/paper/2302.07184/) (2023)
- [Efficient and Deterministic Search Strategy Based on Residual Projections for Point Cloud Registration with Correspondences](https://mlsanity.com/paper/2305.11716/) (2023)
- [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)
- [GlobalMatch: Registration of Forest Terrestrial Point Clouds by Global Matching of Relative Stem Positions](https://mlsanity.com/paper/2112.11121/) (2021)
- [Micro-Structures Graph-Based Point Cloud Registration for Balancing Efficiency and Accuracy](https://mlsanity.com/paper/2410.21857/) (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)
- [Point Cloud Registration via Probabilistic Self-Update Local Correspondence and Line Vector Sets](https://mlsanity.com/paper/2604.26318/) (2026)

## Abstract (arXiv)

Point cloud registration is a fundamental problem in 3D scanning. In this paper, we address the frequent special case of registering terrestrial LiDAR scans (or, more generally, levelled point clouds). Many current solutions still rely on the Iterative Closest Point (ICP) method or other heuristic procedures, which require good initializations to succeed and/or provide no guarantees of success. On the other hand, exact or optimal registration algorithms can compute the best possible solution without requiring initializations; however, they are currently too slow to be practical in realistic applications. Existing optimal approaches ignore the fact that in routine use the relative rotations between scans are constrained to the azimuth, via the built-in level compensation in LiDAR scanners. We propose a novel, optimal and computationally efficient registration method for this 4DOF scenario. Our approach operates on candidate 3D keypoint correspondences, and contains two main steps: (1) a deterministic selection scheme that significantly reduces the candidate correspondence set in a way that is guaranteed to preserve the optimal solution; and (2) a fast branch-and-bound (BnB) algorithm with a novel polynomial-time subroutine for 1D rotation search, that quickly finds the optimal alignment for the reduced set. We demonstrate the practicality of our method on realistic point clouds from multiple LiDAR surveys.