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Graduated Consistency-Regularized Optimization for Multi-graph Matching

  • Junchi Yan
  • Yin Li
  • Wei Liu
  • Hongyuan Zha
  • Xiaokang Yang
  • Stephen Mingyu Chu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8689)

Abstract

Graph matching has a wide spectrum of computer vision applications such as finding feature point correspondences across images. The problem of graph matching is generally NP-hard, so most existing work pursues suboptimal solutions between two graphs. This paper investigates a more general problem of matching N attributed graphs to each other, i.e. labeling their common node correspondences such that a certain compatibility/affinity objective is optimized. This multi-graph matching problem involves two key ingredients affecting the overall accuracy: a) the pairwise affinity matching score between two local graphs, and b) global matching consistency that measures the uniqueness and consistency of the pairwise matching results by different sequential matching orders. Previous work typically either enforces the matching consistency constraints in the beginning of iterative optimization, which may propagate matching error both over iterations and across different graph pairs; or separates score optimizing and consistency synchronization in two steps. This paper is motivated by the observation that affinity score and consistency are mutually affected and shall be tackled jointly to capture their correlation behavior. As such, we propose a novel multi-graph matching algorithm to incorporate the two aspects by iteratively approximating the global-optimal affinity score, meanwhile gradually infusing the consistency as a regularizer, which improves the performance of the initial solutions obtained by existing pairwise graph matching solvers. The proposed algorithm with a theoretically proven convergence shows notable efficacy on both synthetic and public image datasets.

Keywords

Permutation Matrix Graph Match Quadratic Assignment Problem Consistency Constraint Assignment Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Junchi Yan
    • 1
    • 2
  • Yin Li
    • 3
  • Wei Liu
    • 4
  • Hongyuan Zha
    • 3
    • 5
  • Xiaokang Yang
    • 1
  • Stephen Mingyu Chu
    • 2
  1. 1.Shanghai Jiao Tong UniversityShanghaiChina
  2. 2.IBM Research - ChinaShanghaiChina
  3. 3.Georgia Institute of TechnologyAtlantaUSA
  4. 4.IBM T.J. Watson Research CenterNew YorkUSA
  5. 5.East China Normal UniversityShanghaiChina

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