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International Journal of Computer Vision

, Volume 109, Issue 3, pp 169–186 | Cite as

Graph Matching by Simplified Convex-Concave Relaxation Procedure

  • Zhi-Yong Liu
  • Hong Qiao
  • Xu Yang
  • Steven C. H. Hoi
Article

Abstract

The convex and concave relaxation procedure (CCRP) was recently proposed and exhibited state-of-the-art performance on the graph matching problem. However, CCRP involves explicitly both convex and concave relaxations which typically are difficult to find, and thus greatly limit its practical applications. In this paper we propose a simplified CCRP scheme, which can be proved to realize exactly CCRP, but with a much simpler formulation without needing the concave relaxation in an explicit way, thus significantly simplifying the process of developing CCRP algorithms. The simplified CCRP can be generally applied to any optimizations over the partial permutation matrix, as long as the convex relaxation can be found. Based on two convex relaxations, we obtain two graph matching algorithms defined on adjacency matrix and affinity matrix, respectively. Extensive experimental results witness the simplicity as well as state-of-the-art performance of the two simplified CCRP graph matching algorithms.

Keywords

Graph matching Combinatorial optimization Deterministic annealing Graduated optimization Feature correspondence 

Notes

Acknowledgments

The authors thank Dr. Feng Zhou at Carnegie Mellon University for some helpful discussions on his factorized graph matching algorithm Zhou and De la Torre (2012). Many thanks also go to the anonymous reviewers and associate editor whose comments and suggestions greatly improved the manuscripts. This work was supported by the National Science Foundation of China (NSFC) (grants 61375005, 61033011, 61210009), and by Singapore MOE tier 1 research grant (RG33/11).

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Zhi-Yong Liu
    • 1
  • Hong Qiao
    • 1
  • Xu Yang
    • 1
  • Steven C. H. Hoi
    • 2
  1. 1.The State Key Laboratory of Management and Control for Complex SystemsInstitute of Automation, Chinese Academy of SciencesBeijingChina
  2. 2.School of Computer EngineeringNanyang Technological UniversitySingaporeSingapore

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