  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.
