Graph matching is a fundamental tool in computer vision and pattern
recognition. In this paper, we introduce an algorithm for graph matching based
on the proximal operator, referred to as differentiable proximal graph matching
(DPGM). Specifically, we relax and decompose the quadratic assignment problem
for the graph matching into a sequence of convex optimization problems. The
whole algorithm can be considered as a differentiable map from the graph
affinity matrix to the prediction of node correspondence. Therefore, the
proposed method can be organically integrated into an end-to-end deep learning
framework to jointly learn both the deep feature representation and the graph
affinity matrix. In addition, we provide a theoretical guarantee to ensure the
proposed method converges to a stable point with a reasonable number of
iterations. Numerical experiments show that PGM outperforms existing graph
matching algorithms on diverse datasets such as synthetic data, and CMU House.
Meanwhile, PGM can fully harness the capability of deep feature extractors and
achieve state-of-art performance on PASCAL VOC keypoints.

本文介绍了一种基于邻近算子的图匹配算法 (DPGM)，通过将图匹配问题转化为一系列凸优化问题，实现了从图亲和矩阵到节点对应预测的可微分映射，该方法能够与深度学习框架有机地集成在一起，同时在合理的迭代次数内收敛于稳定点，并在多样数据集和 PASCAL VOC 关键点上取得了良好性能，超过了现有的图匹配算法。