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arXiv · 1004.4965

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

Mikhail Zaslavskiy·Francis Bach·Jean-Philippe Vert
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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.

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Mikhail Zaslavskiy, Francis Bach, Jean-Philippe Vert. 2010-04-28. Many-to-Many Graph Matching: a Continuous Relaxation Approach. https://arxiv.org/abs/1004.4965

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