Differentiable Proximal Graph Matching

TL;DR

This paper introduces a differentiable graph matching algorithm that integrates with deep learning, improving accuracy and stability in matching tasks across various datasets.

Contribution

The paper proposes a novel differentiable proximal graph matching method that decomposes the quadratic assignment problem into convex steps, enabling end-to-end learning.

Findings

Outperforms existing algorithms on synthetic and real datasets

Achieves state-of-the-art performance on PASCAL VOC keypoints

Provides theoretical convergence guarantees

Abstract

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.