A General Multi-Graph Matching Approach via Graduated Consistency-regularized Boosting

TL;DR

This paper introduces a novel multi-graph matching method that combines affinity boosting with graduated consistency regularization, improving accuracy in identifying common node correspondences across multiple graphs.

Contribution

It proposes a unified approach that integrates affinity boosting and consistency regularization, along with a node-wise mechanism to handle outliers, advancing multi-graph matching techniques.

Findings

Outperforms existing methods on synthetic and image datasets.

Effectively identifies inlier nodes and improves matching accuracy.

Demonstrates robustness to noise and outliers.

Abstract

This paper addresses the problem of matching $N$ weighted graphs referring to an identical object or category. More specifically, matching the common node correspondences among graphs. This multi-graph matching problem involves two ingredients affecting the overall accuracy: i) the local pairwise matching affinity score among graphs; ii) the global matching consistency that measures the uniqueness of the pairwise matching results by different chaining orders. Previous studies typically either enforce the matching consistency constraints in the beginning of iterative optimization, which may propagate matching error both over iterations and across graph pairs; or separate affinity optimizing and consistency regularization in two steps. This paper is motivated by the observation that matching consistency can serve as a regularizer in the affinity objective function when the function is biased due to noises or inappropriate modeling. We propose multi-graph matching methods to incorporate the two aspects by boosting the affinity score, meanwhile gradually infusing the consistency as a regularizer. Furthermore, we propose a node-wise consistency/affinity-driven mechanism to elicit the common inlier nodes out of the irrelevant outliers. Extensive results on both synthetic and public image datasets demonstrate the competency of the proposed algorithms.