  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.
