Abstract
Attributed relational graph (ARG) matching problem can usually be formulated as an Integer Quadratic Programming (IQP) problem. Since it is NP-hard, relaxation methods are required. In this paper, we propose a new relaxation method, called Bistochastic Preserving Sparse Relaxation Matching (BPSRM), for ARG matching problem. The main benefit of BPSRM is that the mapping constraints involving both discrete and bistochastic constraint can be well incorporated in BPSRM optimization. Thus, it can generate an approximate binary solution with one-to-one mapping constraint for ARG matching problem. Experimental results show the effectiveness of the proposed method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. IJPRAI 18(3), 265–298 (2004)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE Trans. on PAMI 18(4), 377–388 (1996)
Leordeanu, M., Hebert, M.: A spectral technique for correspondence problem using pairwise constraints. In: ICCV, pp. 1482–1489 (2005)
Cour, M., Srinivasan, P., Shi, J.: Balanced graph matching. In: NIPS, pp. 313–320 (2006)
Leordeanu, M., Hebert, M., Sukthankar, R.: An integer projected fixed point method for graph macthing and map inference. In: NIPS, pp. 1114–1122 (2009)
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)
Zhou, F., la Torre, F.D.: Factorized graph matching. In: CVPR, pp. 127–134 (2012)
van Wyk, B.J., van Wyk, M.A.: A pocs-based graph matching algorithm. IEEE Trans. on PAMI 16(11), 1526–1530 (2004)
Albarelli, A., Bulo, S.R., Torsello, A., Pelillo, M.: Matching as a non-coorperative game. In: ICCV, pp. 1319–1326 (2009)
Albarelli, A., Rodolà , E., Torsello, A.: Imposing semi-local geometric constraints for accurate correspondences selection in structure from motion: a game-theoretic perspective. International Journal of Computer Vision 97(1), 36–53 (2012)
Liu, H., Yan, S.: Common visual pattern discovery via spatially coherent correspondences. In: CVPR, pp. 1609–1616 (2010)
Rodolà , E., Bronstein, A.M., Albarelli, A., Bergamasco, F., Torsello, A.: A game-theoretic approach to deformable shape matching. In: CVPR, pp. 182–189 (2012)
Donoho, D.: Compressed sensing. In: Technical Report, Stanford University (2006)
Rodolà , E., Torsello, A., Harada, T., Kuniyoshi, Y., Cremers, D.: Elastic net constraints for shape matching. In: ICCV, pp. 1169–1176 (2013)
Jiang, B., Zhao, H.F., Tang, J., Luo, B.: A sparse nonnegative matrix factorization technique for graph matching problem. Pattern Recognition 47(1), 736–747 (2014)
Sinkhorn, R.: A relationship between arbitray positive matrices and doubly stochastic matrices. Ann. Mach. Statistics 35(2), 876–879 (1964)
Ding, C., Li, T., Jordan, M.I.: Nonnegative matrix factorization for combinatorial optimization: Spectral clustering, graph matching and clique finding. In: ICDM, pp. 183–192 (2008)
Caetano, T.S., McAuley, J.J., Cheng, L., Le, Q.V., Smola, A.J.: Learning graph matching. IEEE Trans. on PAMI 31(6), 1048–1058 (2009)
Ng, E.S., Kingsbury, N.G.: Matching of interest point groups with pairwise spatial constraints. In: ICIP, pp. 2693–2696 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Jiang, B., Tang, J., Luo, B. (2015). Attributed Relational Graph Matching with Sparse Relaxation and Bistochastic Normalization. In: Liu, CL., Luo, B., Kropatsch, W., Cheng, J. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2015. Lecture Notes in Computer Science(), vol 9069. Springer, Cham. https://doi.org/10.1007/978-3-319-18224-7_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-18224-7_22
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18223-0
Online ISBN: 978-3-319-18224-7
eBook Packages: Computer ScienceComputer Science (R0)