# Scalable Cluster-Consistency Statistics for Robust Multi-Object Matching

arXiv: https://arxiv.org/abs/2201.04797 · HTML: https://mlsanity.com/paper/2201.04797/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 13 Jan 2022.

## Builds on (most cited first, 13 of 13)

- [A Survey of Structure from Motion](https://mlsanity.com/paper/1701.08493/) (2017)
- [Robust Camera Location Estimation by Convex Programming](https://mlsanity.com/paper/1412.0165/) (2014)
- [Multi-Image Matching via Fast Alternating Minimization](https://mlsanity.com/paper/1505.04845/) (2015)
- [Higher-order Projected Power Iterations for Scalable Multi-Matching](https://mlsanity.com/paper/1811.10541/) (2018)
- [Robust Group Synchronization via Cycle-Edge Message Passing](https://mlsanity.com/paper/1912.11347/) (2019)
- [Message-passing algorithms for synchronization problems over compact groups](https://mlsanity.com/paper/1610.04583/) (2016)
- [Near-Optimal Joint Object Matching via Convex Relaxation](https://mlsanity.com/paper/1402.1473/) (2014)
- [The Projected Power Method: An Efficient Algorithm for Joint Alignment from Pairwise Differences](https://mlsanity.com/paper/1609.05820/) (2016)
- [Synchronisation of Partial Multi-Matchings via Non-negative Factorisations](https://mlsanity.com/paper/1803.06320/) (2018)
- [Multi-Image Semantic Matching by Mining Consistent Features](https://mlsanity.com/paper/1711.07641/) (2017)
- [A New Rank Constraint on Multi-view Fundamental Matrices, and its Application to Camera Location Recovery](https://mlsanity.com/paper/1702.03023/) (2017)
- [Robust Multi-object Matching via Iterative Reweighting of the Graph Connection Laplacian](https://mlsanity.com/paper/2006.06658/) (2020)
- [Distributed and Consistent Multi-Image Feature Matching via QuickMatch](https://mlsanity.com/paper/1910.13317/) (2019)

## Built on by (most cited first, 6 of 6)

- [Fast, Accurate and Memory-Efficient Partial Permutation Synchronization](https://mlsanity.com/paper/2203.16505/) (2022)
- [A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion](https://mlsanity.com/paper/2404.11590/) (2024)
- [Tensor-Based Synchronization and the Low-Rankness of the Block Trifocal Tensor](https://mlsanity.com/paper/2409.09313/) (2024)
- [MIXER: Multiattribute, Multiway Fusion of Uncertain Pairwise Affinities](https://mlsanity.com/paper/2210.08360/) (2022)
- [Higher-Order Group Synchronization](https://mlsanity.com/paper/2505.21932/) (2025)
- [Recovery Theory for Projected Power Iterations in Permutation Synchronization](https://mlsanity.com/paper/2609.09502/) (2026)

## Abstract (arXiv)

We develop new statistics for robustly filtering corrupted keypoint matches in the structure from motion pipeline. The statistics are based on consistency constraints that arise within the clustered structure of the graph of keypoint matches. The statistics are designed to give smaller values to corrupted matches and than uncorrupted matches. These new statistics are combined with an iterative reweighting scheme to filter keypoints, which can then be fed into any standard structure from motion pipeline. This filtering method can be efficiently implemented and scaled to massive datasets as it only requires sparse matrix multiplication. We demonstrate the efficacy of this method on synthetic and real structure from motion datasets and show that it achieves state-of-the-art accuracy and speed in these tasks.