Graph matching (GM) has been a building block in various areas including computer vision and pattern recognition. Despite recent impressive progress, existing deep GM methods often have obvious difficulty in handling outliers, which are ubiquitous in practice. We propose a deep reinforcement learning based approach RGM, whose sequential node matching scheme naturally fits the strategy for selective inlier matching against outliers. A revocable action framework is devised to improve the agent's flexibility against the complex constrained GM. Moreover, we propose a quadratic approximation technique to regularize the affinity score, in the presence of outliers. As such, the agent can finish inlier matching timely when the affinity score stops growing, for which otherwise an additional parameter i.e. the number of inliers is needed to avoid matching outliers. In this paper, we focus on learning the back-end solver under the most general form of GM: the Lawler's QAP, whose input is the affinity matrix. Especially, our approach can also boost existing GM methods that use such input. Experiments on multiple real-world datasets demonstrate its performance regarding both accuracy and robustness.

翻译：图匹配（GM）在计算机视觉和模式识别等多个领域一直是基础性技术。尽管近期取得了令人瞩目的进展，但现有的深度图匹配方法在处理实践中普遍存在的离群点时往往存在明显困难。我们提出了一种基于深度强化学习的方法RGM，其顺序节点匹配策略天然适合在离群点干扰下选择性匹配内点。为了提升智能体应对复杂约束图匹配的灵活性，我们设计了一种可撤销动作框架。此外，针对存在离群点的情况，我们提出了一种二次近似技术对亲和度分数进行正则化。当亲和度分数停止增长时，智能体可以及时完成内点匹配，而传统方法需要额外参数（即内点数量）来避免匹配离群点。本文专注于在最一般的图匹配形式——Lawler二次分配问题（其输入为亲和度矩阵）下学习后端求解器。特别地，我们的方法还能增强使用此类输入的现有图匹配方法。在多个真实数据集上的实验证明了该方法在准确性和鲁棒性方面的性能。