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# Reweighted random walks for graph matching

ECCV (5), (2010): 492-505

EI

Abstract

Graph matching is an essential problem in computer vision and machine learning. In this paper, we introduce a random walk view on the problem and propose a robust graph matching algorithm against outliers and deformation. Matching between two graphs is formulated as node selection on an association graph whose nodes represent candidate co...More

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Introduction

- Graph matching is an essential problem in theoretical computer science; it is related to various research areas in computer vision, pattern recognition, and machine learning [1].
- The problem of graph matching is to determine a mapping between the nodes of the two graphs that preserves the relationships between the nodes as much as possible.
- Many graph matching algorithms proposed in the 1980s and 1990s focused on exploiting relatively weak unary and pair-wise attributes and did not aim at optimizing a well-defined objective function [1].
- IQP explicitly takes into consideration both unary and pair-wise terms reflecting the compatibilities in local appearance as well as the pair-wise geometric relationships between the matching features.
- Since IQP is known to be NP-hard, approximate solutions

Highlights

- Graph matching is an essential problem in theoretical computer science; it is related to various research areas in computer vision, pattern recognition, and machine learning [1]
- Recent resurgence of combinatorial optimization approaches to feature matching [2,3,4,5,6,7,8] has changed the situation and firmly settled graph matching formulations based on Integer Quadratic Programming (IQP), which is a generalization of the classical graph matching problems
- Our work provides a novel interpretation of graph matching in a random walk view and relates it to the Integer Quadratic Programming formulation
- Introducing an association graph constructed with nodes as candidate correspondences and edges as pair-wise compatibilities between candidate correspondences, we show that the search for correspondences between the given two graphs can be cast as a node ranking [9,10] and selection problem in the association graph
- We introduced a graph matching framework based on random walks and proposed a novel graph matching algorithm inspired by the personalized random walks [10,11] and the Sinkhorn method [18]
- The comparison reveals that the matching accuracy in the challenging situations largely depends on the effective exploitation of the matching constraints

Conclusion

- The authors introduced a graph matching framework based on random walks and proposed a novel graph matching algorithm inspired by the personalized random walks [10,11] and the Sinkhorn method [18].
- The experiments demonstrated that it outperforms the state-of-the-art methods [3,4,6,8,13,14] in the presence of outliers and deformation.
- The authors will improve the framework and method for this direction

- Table1: Matching performance on the real image dataset (30 pairs)

Funding

- This work was supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD) (KRF-2008-314-D00377). 8 http://research.microsoft.com/en-us/projects/objectclassrecognition/

Reference

- Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. In: IJPRAI (2004)
- Berg, A.C., Berg, T.L., Malik, J.: Shape matching and object recognition using low distortion correspondences. In: CVPR (2005)
- Leordeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: ICCV (2005)
- Cour, T., Srinivasan, P., Shi, J.: Balanced graph matching. In: NIPS (2006)
- Torresani, L., Kolmogorov, V., Rother, C.: Feature correspondence via graph matching: Models and global optimization. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part II. LNCS, vol. 5303, pp. 596–609. Springer, Heidelberg (2008)
- Zass, R., Shashua, A.: Probabilistic graph and hypergraph matching. In: CVPR (2008)
- Duchenne, O., Bach, F., Kweon, I., Ponce, J.: A tensor-based algorithm for highorder graph matching. In: CVPR (2009)
- Leordeanu, M., Herbert, M.: An integer projected fixed point method for graph matching and map inference. In: NIPS (2009)
- Kleinberg, J.: Authoritative sources in a hyperlinked environment. Journal of the ACM (1999)
- Page, L., Brin, S., Motwani, R., Winograd, T.: The pagerank citation ranking: Bringing order to the web. Technical Report, Stanford University (1998)
- Haveliwala, T.H.: Topic-sensitive pagerank. In: WWW (2002)
- Maciel, J., Costeira, J.P.: A global solution to sparse correspondence problems. PAMI (2003)
- Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. PAMI (1996) 14. van Wyk, B.J., van Wyk, M.A.: A pocs-based graph matching algorithm. PAMI (2004)
- 15. Lee, J., Cho, M., Lee, K.M.: Graph matching algorithm using data-driven markov chain monte carlo sampling. In: ICPR (2010)
- 16. Gori, M., Maggini, M., Sarti, L.: Exact and approximate graph matching using random walks. PAMI (2005) 17. Robles-Kelly, A., Hancock, E.R.: String edit distance, random walks and graph matching. In: IJPRAI (2004)
- 18. Sinkhorn, R.: A relationship between arbitrary positive matrices and doubly stochastic matrices. Ann. Math. Statistics (1964)
- 19. Langville, A.N., Meyer, C.D.: Deeper inside pagerank. Internet Mathematics (2003)
- 20. Seneta, E.: Non negative matrices and markov chains. Springer, Heidelberg (2006)
- 21. Munkres, J.: Algorithms for the assignment and transportation problems. SIAM, Philadelphia (1957)
- 22. Matas, J., Chum, O., Urban, M., Pajdla, T.: Robust wide baseline stereo from maximally stable extremal regions. In: BMVC (2002)
- 23. Lowe, D.G.: Object recognition from local scale-invariant features. In: ICCV, pp. 1150–1157 (1999)
- 24. Cho, M., Lee, J., Lee, K.M.: Feature correspondence and deformable object matching via agglomerative correspondence clustering. In: ICCV (2009)

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