Many-to-Many Graph Matching: a Continuous Relaxation Approach

TL;DR

This paper introduces a continuous relaxation approach for many-to-many graph matching, enabling more flexible correspondences in computer vision applications, and demonstrates its effectiveness on benchmark datasets.

Contribution

It formulates many-to-many graph matching as a discrete optimization problem and proposes a novel approximate algorithm based on continuous relaxation.

Findings

The proposed method outperforms existing approaches on benchmark datasets.

Continuous relaxation enables efficient approximation of complex many-to-many matchings.

The approach is applicable to various computer vision tasks involving graph comparisons.

Abstract

Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a graph matching problem where one seeks a mapping between vertices of two graphs which optimally aligns their structure. In the classical formulation of graph matching, only one-to-one correspondences between vertices are considered. However, in many applications, graphs cannot be matched perfectly and it is more interesting to consider many-to-many correspondences where clusters of vertices in one graph are matched to clusters of vertices in the other graph. In this paper, we formulate the many-to-many graph matching problem as a discrete optimization problem and propose an approximate algorithm based on a continuous relaxation of the combinatorial problem. We compare our method with other existing methods on several benchmark computer vision datasets.