# GlobalPointer: Large-Scale Plane Adjustment with Bi-Convex Relaxation

arXiv: https://arxiv.org/abs/2407.13537 · HTML: https://mlsanity.com/paper/2407.13537/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 18 Jul 2024.

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

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Shonan Rotation Averaging: Global Optimality by Surfing SO(p)n](https://mlsanity.com/paper/2008.02737/) (2020)
- [BALM: Bundle Adjustment for Lidar Mapping](https://mlsanity.com/paper/2010.08215/) (2020)
- [Hybrid Rotation Averaging: A Fast and Robust Rotation Averaging Approach](https://mlsanity.com/paper/2101.09116/) (2021)
- [The Hilti SLAM Challenge Dataset](https://mlsanity.com/paper/2109.11316/) (2021)
- [Revisiting Rotation Averaging: Uncertainties and Robust Losses](https://mlsanity.com/paper/2303.05195/) (2023)
- [An Efficient Solution to Non-Minimal Case Essential Matrix Estimation](https://mlsanity.com/paper/1903.09067/) (2019)
- [Rotation Coordinate Descent for Fast Globally Optimal Rotation Averaging](https://mlsanity.com/paper/2103.08292/) (2021)
- [Efficient and Consistent Bundle Adjustment on Lidar Point Clouds](https://mlsanity.com/paper/2209.08854/) (2022)
- [On the local stability of semidefinite relaxations](https://mlsanity.com/paper/1710.04287/) (2017)
- [An Efficient Planar Bundle Adjustment Algorithm](https://mlsanity.com/paper/2006.00187/) (2020)
- [Efficient Second-Order Plane Adjustment](https://mlsanity.com/paper/2211.11542/) (2022)
- [Semidefinite Relaxations for Robust Multiview Triangulation](https://mlsanity.com/paper/2301.11431/) (2023)
- [Eigen-Factors a Bilevel Optimization for Plane SLAM of 3D Point Clouds](https://mlsanity.com/paper/2304.01055/) (2023)

## Built on by (most cited first, 11 of 11)

- [ReTrack: Evidence-Driven Dual-Stream Directional Anchor Calibration Network for Composed Video Retrieval](https://mlsanity.com/paper/2604.17898/) (2026)
- [INTENT: Invariance and Discrimination-aware Noise Mitigation for Robust Composed Image Retrieval](https://mlsanity.com/paper/2604.18051/) (2026)
- [HABIT: Chrono-Synergia Robust Progressive Learning Framework for Composed Image Retrieval](https://mlsanity.com/paper/2604.18037/) (2026)
- [FedAdamW: A Communication-Efficient Optimizer with Convergence and Generalization Guarantees for Federated Large Models](https://mlsanity.com/paper/2510.27486/) (2025)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [EEO-TFV: Escape-Explore Optimizer for Web-Scale Time-Series Forecasting and Vision Analysis](https://mlsanity.com/paper/2602.02551/) (2026)
- [CATCH: A Modular Cross-domain Adaptive Template with Hook](https://mlsanity.com/paper/2510.26582/) (2025)
- [Neural Predictor-Corrector: Solving Homotopy Problems with Reinforcement Learning](https://mlsanity.com/paper/2602.03086/) (2026)
- [Coarse-to-Fine Personalized LLM Impressions for Streamlined Radiology Reports](https://mlsanity.com/paper/2508.15845/) (2025)
- [BlackMirror: Black-Box Backdoor Detection for Text-to-Image Models via Instruction-Response Deviation](https://mlsanity.com/paper/2603.05921/) (2026)
- [Deep Image Clustering Based on Curriculum Learning and Density Information](https://mlsanity.com/paper/2604.03306/) (2026)

## Abstract (arXiv)

Plane adjustment (PA) is crucial for many 3D applications, involving simultaneous pose estimation and plane recovery. Despite recent advancements, it remains a challenging problem in the realm of multi-view point cloud registration. Current state-of-the-art methods can achieve globally optimal convergence only with good initialization. Furthermore, their high time complexity renders them impractical for large-scale problems. To address these challenges, we first exploit a novel optimization strategy termed textitBi-Convex Relaxation, which decouples the original problem into two simpler sub-problems, reformulates each sub-problem using a convex relaxation technique, and alternately solves each one until the original problem converges. Building on this strategy, we propose two algorithmic variants for solving the plane adjustment problem, namely textitGlobalPointer and textitGlobalPointer++, based on point-to-plane and plane-to-plane errors, respectively. Extensive experiments on both synthetic and real datasets demonstrate that our method can perform large-scale plane adjustment with linear time complexity, larger convergence region, and robustness to poor initialization, while achieving similar accuracy as prior methods. The code is available at https://github.com/wu-cvgl/GlobalPointer.