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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))

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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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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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