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

Mikhail Zaslavskiy 1, 2 Francis Bach 3, 4 Jean-Philippe Vert 1, 2
3 WILLOW - Models of visual object recognition and scene understanding
DI-ENS - Département d'informatique de l'École normale supérieure, ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
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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Contributeur : Mikhail Zaslavskiy <>
Soumis le : lundi 22 mars 2010 - 11:50:25
Dernière modification le : jeudi 29 septembre 2016 - 01:22:19
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  • HAL Id : hal-00465916, version 1
  • ARXIV : 1004.4965

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Mikhail Zaslavskiy, Francis Bach, Jean-Philippe Vert. Many-to-Many Graph Matching: a Continuous Relaxation Approach. 19. 2009. <hal-00465916>

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