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Synchronization Over the Birkhoff Polytope for Multi-graph Matching

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Graph-Based Representations in Pattern Recognition (GbRPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10310))

Abstract

In this paper we address the problem of simultaneously matching multiple graphs imposing cyclic or transitive consistency among the correspondences. This is obtained through a synchronization process that projects doubly-stochastic matrices onto a consistent set. We overcome the lack of group structure of the Birkhoff polytope, i.e., the space of doubly-stochastic matrices, by making use the Birkhoff-Von Neumann theorem stating that any doubly-stochastic matrix can be seen as the expectation of a distribution over the permutation matrices, and then cast the synchronization problem as one over the underlying permutations. This allows us to transform any graph-matching algorithm working on the Birkhoff polytope into a multi-graph matching algorithm. We evaluate the performance of two classic graph matching algorithms in their synchronized and un-synchronized versions with a state-of-the-art multi-graph matching approach, showing that synchronization can yield better and more robust matches.

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Authors and Affiliations

  1. Dipartimento di Scienze Ambientali, Informatica e Statistica, Universitá Ca’ Foscari Venezia, via Torino 155, 30172, Mestre, VE, Italy

    Michele Schiavinato & Andrea Torsello

Authors
  1. Michele Schiavinato
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  2. Andrea Torsello
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Corresponding author

Correspondence to Andrea Torsello .

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Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Pasquale Foggia

  2. Chinese Academy of Sciences, Beijing, China

    Cheng-Lin Liu

  3. Università degli Studi di Salerno, Fisciano, Italy

    Mario Vento

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Schiavinato, M., Torsello, A. (2017). Synchronization Over the Birkhoff Polytope for Multi-graph Matching. In: Foggia, P., Liu, CL., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2017. Lecture Notes in Computer Science(), vol 10310. Springer, Cham. https://doi.org/10.1007/978-3-319-58961-9_24

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  • DOI: https://doi.org/10.1007/978-3-319-58961-9_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58960-2

  • Online ISBN: 978-3-319-58961-9

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