# Alternating Direction Graph Matching

arXiv: https://arxiv.org/abs/1611.07583 · HTML: https://mlsanity.com/paper/1611.07583/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2016.

## Built on by (most cited first, 9 of 9)

- [A comprehensive survey on point cloud registration](https://mlsanity.com/paper/2103.02690/) (2021)
- [Q-Match: Iterative Shape Matching via Quantum Annealing](https://mlsanity.com/paper/2105.02878/) (2021)
- [A Scalable Combinatorial Solver for Elastic Geometrically Consistent 3D Shape Matching](https://mlsanity.com/paper/2204.12805/) (2022)
- [Regularized Frank-Wolfe for Dense CRFs: Generalizing Mean Field and Beyond](https://mlsanity.com/paper/2110.14759/) (2021)
- [Unsupervised Learning for Robust Fitting:A Reinforcement Learning Approach](https://mlsanity.com/paper/2103.03501/) (2021)
- [SIGMA: Scale-Invariant Global Sparse Shape Matching](https://mlsanity.com/paper/2308.08393/) (2023)
- [CURSOR: Scalable Mixed-Order Hypergraph Matching with CUR Decomposition](https://mlsanity.com/paper/2402.16594/) (2024)
- [Convex Joint Graph Matching and Clustering via Semidefinite Relaxations](https://mlsanity.com/paper/2110.11335/) (2021)
- [Permutation-Invariant Subgraph Discovery](https://mlsanity.com/paper/2104.01063/) (2021)

## Abstract (arXiv)

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a decomposition of the matching constraints. Graph matching is then reformulated as a non-convex non-separable optimization problem that can be split into smaller and much-easier-to-solve subproblems, by means of the alternating direction method of multipliers. The proposed framework is modular, scalable, and can be instantiated into different variants. Two instantiations are studied exploring pairwise and higher-order constraints. Experimental results on widely adopted benchmarks involving synthetic and real examples demonstrate that the proposed solutions outperform existing pairwise graph matching methods, and competitive with the state of the art in higher-order settings.