Graph Matching with Anchor Nodes: A Learning Approach

TL;DR

This paper introduces a learning-based method for weighted graph matching that leverages anchor nodes and graph Laplacian signatures to improve matching accuracy, demonstrated through experiments on synthetic and real image data.

Contribution

It proposes a novel optimization framework using node signatures and anchor nodes, avoiding explicit parametric forms, to enhance graph matching performance.

Findings

Superior accuracy on synthetic graphs

Effective on real image sequences

Outperforms existing signature-based methods

Abstract

In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the Laplacian family signature (LFS) on the nodes, and the pairwise heat kernel map on the edges. In this paper, without assuming an explicit form of parametric dependence nor a distance metric between node signatures, we formulate an optimization problem which incorporates the knowledge of anchor nodes. Solving this problem gives us an optimized proximity measure specific to the graphs under consideration. Using this as a first order compatibility term, we then set up an integer quadratic program (IQP) to solve for a near optimal graph matching. Our experiments demonstrate the superior performance of our approach on randomly generated graphs and on two widely-used image sequences, when compared with other existing signature and adjacency matrix based graph matching methods.