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.

翻译：本文研究了不完全多图匹配问题，该问题是NP难二次分配问题在匹配多个有限集合情况下的推广。多图匹配在计算机视觉领域（例如图像或形状匹配）具有核心作用，因此已有多种专用优化技术被提出。尽管运筹学界对密切相关的NP难多维分配问题已研究数十年，但其仅考虑完全匹配且具有不同的成本结构。我们通过将MDAP的经典近似算法迁移至不完全多图匹配来弥合这一差距。为此，我们重新审视相关算法，将其适配于不完全多图匹配，并提出扩展版本与并行化版本。实验验证表明，新方法在目标函数值与运行时间方面显著优于现有最优技术。例如，我们的算法可在两分钟内完成29幅图像（每幅含500多个关键点）的匹配，而所对比的最快竞品算法至少需要半小时且结果质量远逊。