# HARA: A Hierarchical Approach for Robust Rotation Averaging

arXiv: https://arxiv.org/abs/2111.08831 · HTML: https://mlsanity.com/paper/2111.08831/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 70 references that are in the map.
- First posted on arXiv 16 Nov 2021.

## Builds on (most cited first, 21 of 21)

- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Learning multiview 3D point cloud registration](https://mlsanity.com/paper/2001.05119/) (2020)
- [Shonan Rotation Averaging: Global Optimality by Surfing SO(p)n](https://mlsanity.com/paper/2008.02737/) (2020)
- [Robust Camera Location Estimation by Convex Programming](https://mlsanity.com/paper/1412.0165/) (2014)
- [NeuRoRA: Neural Robust Rotation Averaging](https://mlsanity.com/paper/1912.04485/) (2019)
- [Learning Transformation Synchronization](https://mlsanity.com/paper/1901.09458/) (2019)
- [Message Passing Least Squares Framework and its Application to Rotation Synchronization](https://mlsanity.com/paper/2007.13638/) (2020)
- [Hybrid Rotation Averaging: A Fast and Robust Rotation Averaging Approach](https://mlsanity.com/paper/2101.09116/) (2021)
- [Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions](https://mlsanity.com/paper/1506.00746/) (2015)
- [Rotation Coordinate Descent for Fast Globally Optimal Rotation Averaging](https://mlsanity.com/paper/2103.08292/) (2021)
- [Robust Single Rotation Averaging](https://mlsanity.com/paper/2004.00732/) (2020)
- [Rotation-Only Bundle Adjustment](https://mlsanity.com/paper/2011.11724/) (2020)
- [Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs](https://mlsanity.com/paper/2109.08046/) (2021)
- [Linear Global Translation Estimation with Feature Tracks](https://mlsanity.com/paper/1503.01832/) (2015)
- [Triangulation: Why Optimize?](https://mlsanity.com/paper/1907.11917/) (2019)
- [On the Distribution of Minima in Intrinsic-Metric Rotation Averaging](https://mlsanity.com/paper/2003.08310/) (2020)
- [Visual SLAM: Why Bundle Adjust?](https://mlsanity.com/paper/1902.03747/) (2019)
- [Efficient and Robust Registration on the 3D Special Euclidean Group](https://mlsanity.com/paper/1904.05519/) (2019)
- [Geometric Interpretations of the Normalized Epipolar Error](https://mlsanity.com/paper/2008.01254/) (2020)
- [Robust Uncertainty-Aware Multiview Triangulation](https://mlsanity.com/paper/2008.01258/) (2020)

## Built on by (most cited first, 23 of 23)

- [Robust Multiview Point Cloud Registration with Reliable Pose Graph Initialization and History Reweighting](https://mlsanity.com/paper/2304.00467/) (2023)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Robust Single Rotation Averaging Revisited](https://mlsanity.com/paper/2309.05388/) (2023)
- [What's Wrong with the Absolute Trajectory Error?](https://mlsanity.com/paper/2212.05376/) (2022)
- [From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation](https://mlsanity.com/paper/2312.05995/) (2023)
- [Alignment Scores: Robust Metrics for Multiview Pose Accuracy Evaluation](https://mlsanity.com/paper/2407.20391/) (2024)
- [FUSER: Feed-Forward MUltiview 3D Registration Transformer and SE(3)N Diffusion Refinement](https://mlsanity.com/paper/2512.09373/) (2025)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [A Taxonomy of Structure from Motion Methods](https://mlsanity.com/paper/2505.15814/) (2025)
- [Equivariant Flow Matching for Point Cloud Assembly](https://mlsanity.com/paper/2505.21539/) (2025)
- [Recovering Simultaneously Structured Data via Non-Convex Iteratively Reweighted Least Squares](https://mlsanity.com/paper/2306.04961/) (2023)
- [Incremental Rotation Averaging Revisited](https://mlsanity.com/paper/2309.16924/) (2023)
- [Rotation Averaging: A Primal-Dual Method and Closed-Forms in Cycle Graphs](https://mlsanity.com/paper/2406.18564/) (2024)
- [Robustness of Generalized Median Computation for Consensus Learning in Arbitrary Spaces](https://mlsanity.com/paper/2503.05215/) (2025)
- [Matching Distance and Geometric Distribution Aided Learning Multiview Point Cloud Registration](https://mlsanity.com/paper/2505.03692/) (2025)
- [EAR-Net: Pursuing End-to-End Absolute Rotations from Multi-View Images](https://mlsanity.com/paper/2310.10051/) (2023)
- [PRAGO: Differentiable Multi-View Pose Optimization From Objectness Detections](https://mlsanity.com/paper/2403.08586/) (2024)
- [Mitigating Heterogeneity among Factor Tensors via Lie Group Manifolds for Tensor Decomposition Based Temporal Knowledge Graph Embedding](https://mlsanity.com/paper/2404.09155/) (2024)
- [Multiple Rotation Averaging with Constrained Reweighting Deep Matrix Factorization](https://mlsanity.com/paper/2409.09790/) (2024)
- [Making Rotation Averaging Fast and Robust with Anisotropic Coordinate Descent](https://mlsanity.com/paper/2506.01940/) (2025)
- [HETA++: Global Structure-from-Motion with Hybrid Explicit Translation Averaging](https://mlsanity.com/paper/2607.15912/) (2026)
- [Spectral Consistency-Guided Multiview Point Cloud Registration for Low-Overlap Scenes](https://mlsanity.com/paper/2609.12417/) (2026)
- [MemReg: Streaming Outdoor LiDAR Point Cloud Registration with Hybrid Memory Buffers](https://mlsanity.com/paper/2610.12624/) (2026)

## Abstract (arXiv)

We propose a novel hierarchical approach for multiple rotation averaging, dubbed HARA. Our method incrementally initializes the rotation graph based on a hierarchy of triplet support. The key idea is to build a spanning tree by prioritizing the edges with many strong triplet supports and gradually adding those with weaker and fewer supports. This reduces the risk of adding outliers in the spanning tree. As a result, we obtain a robust initial solution that enables us to filter outliers prior to nonlinear optimization. With minimal modification, our approach can also integrate the knowledge of the number of valid 2D-2D correspondences. We perform extensive evaluations on both synthetic and real datasets, demonstrating state-of-the-art results.