# Multi-Image Matching via Fast Alternating Minimization

arXiv: https://arxiv.org/abs/1505.04845 · HTML: https://mlsanity.com/paper/1505.04845/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2015.

## Built on by (most cited first, 30 of 33)

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- [A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts](https://mlsanity.com/paper/2410.14770/) (2024)
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- [Cycle Consistency Driven Object Discovery](https://mlsanity.com/paper/2306.02204/) (2023)
- [Sparse Quadratic Optimisation over the Stiefel Manifold with Application to Permutation Synchronisation](https://mlsanity.com/paper/2110.00053/) (2021)
- [Scalable Cluster-Consistency Statistics for Robust Multi-Object Matching](https://mlsanity.com/paper/2201.04797/) (2022)
- [A-ACT: Action Anticipation through Cycle Transformations](https://mlsanity.com/paper/2204.00942/) (2022)
- [Temporal Consistency-Aware Text-to-Motion Generation](https://mlsanity.com/paper/2602.18057/) (2026)
- [Low-rank Matrix Recovery With Unknown Correspondence](https://mlsanity.com/paper/2110.07959/) (2021)
- [Structured Prediction Problem Archive](https://mlsanity.com/paper/2202.03574/) (2022)
- [Joint Deep Multi-Graph Matching and 3D Geometry Learning from Inhomogeneous 2D Image Collections](https://mlsanity.com/paper/2103.17229/) (2021)
- [Kernelized multi-graph matching](https://mlsanity.com/paper/2210.05206/) (2022)
- [Learning Universe Model for Partial Matching Networks over Multiple Graphs](https://mlsanity.com/paper/2210.10374/) (2022)
- [Optimizing Incomplete, Large-Scale and Sparse Multi-Graph Matching in Bioimaging](https://mlsanity.com/paper/2406.18215/) (2024)
- [MIXER: Multiattribute, Multiway Fusion of Uncertain Pairwise Affinities](https://mlsanity.com/paper/2210.08360/) (2022)
- [Population-wise Labeling of Sulcal Graphs using Multi-graph Matching](https://mlsanity.com/paper/2301.13532/) (2023)
- [A Novel and Optimal Spectral Method for Permutation Synchronization](https://mlsanity.com/paper/2303.12051/) (2023)
- [Non-Negative Spherical Relaxations for Universe-Free Multi-Matching and Clustering](https://mlsanity.com/paper/2310.13311/) (2023)
- [PathFusion: Path-consistent Lidar-Camera Deep Feature Fusion](https://mlsanity.com/paper/2212.06244/) (2022)
- [AlignGraph: A Group of Generative Models for Graphs](https://mlsanity.com/paper/2301.11273/) (2023)
- [M3C: A Framework towards Convergent, Flexible, and Unsupervised Learning of Mixture Graph Matching and Clustering](https://mlsanity.com/paper/2310.18444/) (2023)

## Abstract (arXiv)

In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike previous convex methods relying on semidefinite programming, we formulate the problem as a low-rank matrix recovery problem and show that the desired semidefiniteness of a solution can be spontaneously fulfilled. The low-rank formulation enables us to derive a fast alternating minimization algorithm in order to handle practical problems with thousands of features. Both simulation and real experiments demonstrate that the proposed algorithm can achieve a competitive performance with an order of magnitude speedup compared to the state-of-the-art algorithm. In the end, we demonstrate the applicability of the proposed method to match the images of different object instances and as a result the potential to reconstruct category-specific object models from those images.