Unlocking the Potential of Operations Research for Multi-Graph Matching

TL;DR

This paper adapts and extends approximation algorithms from operations research to solve the NP-hard incomplete multi-graph matching problem efficiently, significantly improving performance over previous methods in computer vision tasks.

Contribution

It bridges the gap between operations research algorithms and multi-graph matching, introducing adapted, extended, and parallelized algorithms for incomplete matchings.

Findings

Outperforms previous state-of-the-art in accuracy and runtime

Successfully matches 29 images with over 500 keypoints in under two minutes

Achieves substantial speedup compared to existing methods

Abstract

We consider the incomplete multi-graph matching problem, which is a generalization of the NP-hard quadratic assignment problem for matching multiple finite sets. Multi-graph matching plays a central role in computer vision, e.g., for matching images or shapes, so that a number of dedicated optimization techniques have been proposed. While the closely related NP-hard multi-dimensional assignment problem (MDAP) has been studied for decades in the operations research community, it only considers complete matchings and has a different cost structure. We bridge this gap and transfer well-known approximation algorithms for the MDAP to incomplete multi-graph matching. To this end, we revisit respective algorithms, adapt them to incomplete multi-graph matching, and propose their extended and parallelized versions. Our experimental validation shows that our new method substantially outperforms the previous state of the art in terms of objective and runtime. Our algorithm matches, for example, 29 images with more than 500 keypoints each in less than two minutes, whereas the fastest considered competitor requires at least half an hour while producing far worse results.