Abstract
We focus on the problem of graph matching that is fundamental in computer vision and machine learning. Many state-of-the-arts frequently formulate it as integer quadratic programming, which incorporates both unary and second-order terms. This formulation is in general NP-hard thus obtaining an exact solution is computationally intractable. Therefore most algorithms seek the approximate optimum by relaxing techniques. This paper commences with the finding of the “circular” character of solution chain obtained by the iterative Gradient Assignment (via Hungarian method) in the discrete domain, and proposes a method for guiding the solver converging to a fixed point, resulting a convergent algorithm for graph matching in discrete domain. Furthermore, we extend the algorithms to their counterparts in continuous domain, proving the classical graduated assignment algorithm will converge to a double-circular solution chain, and the proposed Soft Constrained Graduated Assignment (SCGA) method will converge to a fixed (discrete) point, both under wild conditions. Competitive performances are reported in both synthetic and real experiments.
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. IJPRAI (2004)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. PAMI (1996)
Leordeanu, M., Hebert, M.: A Spectral Technique for Correspondence Problems using Pairwise Constraints. In: ICCV (2005)
Cho, M., Lee, J., Lee, K.M.: Reweighted Random Walks for Graph Matching. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part V. LNCS, vol. 6315, pp. 492–505. Springer, Heidelberg (2010)
Leordeanu, M., Herbert, M.: An integer projected fixed point method for graph matching and map inference. In: NIPS (2009)
Gold, S., Rangarajan, A.: Softmax to softassign: neural network algorithms for combinatorial optimization. J. Artif. Neural Netw., 3810–399 (1995)
Rangarajan, A., Yuille, A.: Convergence properties of the softassign quadratic assignment algorithm. Neural Computation (1999)
Kuhn, H.W.: The Hungarian method for the assignment problem. Naval Research Logistics Quarterly 2(1-2), 83–97 (1955)
Christmas, W., Kittler, J., Petrou, M.: Structural matching in computer vision using probabilistic relaxation. PAMI 19(6), 634–648 (1997)
Wilson, R., Hancock, E.: Structural matching by discrete relaxation. IEEE Trans. Pattern Anal. Mach. Intell. 17(8), 749–764 (1995)
Cour, T., Srinivasan, P., Shi, J.: Balanced Graph Matching. In: NIPS (2006)
Lee, J., Cho, M., Lee, K.M.: Hyper-graph Matching via Reweighted RandomWalks. In: CVPR (2011)
Kosowsky, J.J., Yuille, A.L.: The Invisible Hand Algorithm: Solving the Assignment Problem With Statistical Physics. Neural Networks 7(3) (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tian, Y., Yan, J., Zhang, H., Zhang, Y., Yang, X., Zha, H. (2012). On the Convergence of Graph Matching: Graduated Assignment Revisited. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds) Computer Vision – ECCV 2012. ECCV 2012. Lecture Notes in Computer Science, vol 7574. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33712-3_59
Download citation
DOI: https://doi.org/10.1007/978-3-642-33712-3_59
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33711-6
Online ISBN: 978-3-642-33712-3
eBook Packages: Computer ScienceComputer Science (R0)