Abstract
Graph matching is important in pattern recognition and computer vision which can solve the point correspondence problems. Graph matching is an NP-hard problem and approximate relaxation methods are used to solve this problem. But most of the existing relaxation methods solve graph matching problem in the continues domain without considering the discrete constraints. In this paper, we propose a fast normalized cut based graph matching method which takes the discrete constraints into consideration. Specifically, a regularization term which is related to the discrete form of the permutation matrix is added to the objective function. Then, the objective function is transformed to a form which is similar to the fast normalized cut framework. The fast normalized cut algorithm is generalized to get the permutation matrix iteratively. The comparisons with the state-of-the-art methods validate the effectiveness of the proposed method by the experiments on synthetic data and image sequences.
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References
Achuurmans, D., Li, W., Xu, L.: Fast normalized cut with linear constraints. In: 22th IEEE Conference on Computer Vision and Pattern Recognition, pp. 2866–2873. Miami (2009)
Bryan, K., Leise, T.: The 25,000,000,000 eigenvetor: the linear algebra behind google. Siam Rev. 48(3), 569–581 (2006)
Cetano, T.S., MeAuley, J.J., Cheng, L., Le, Q.V., Smola, A.J.: Learning graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 31(6), 1048–1058 (2009)
Cho, M., Lee, J., Lee, K.M.: Reweighted random walks for graph matching. In: 20th Conference and Workshop on Neural Information Processing Systems, pp. 313–320. Vancouver (2006)
Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. Int. J. Pattern Recognit. Artifical Intell. 18(3), 265–298 (2004)
Cour, M., Srinivasan, P., Shi, J.: Balanced graph matching. In: 20th Conference and Workshop on Neural Information Processing Systems, pp. 313–320. Vancouver (2006)
Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. Assoc. Comput. Mach. 24(6), 381–395 (1981)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 18(4), 377–388 (1996)
Hagen, L., Kahng, A.: New spectral methods for ratio cut partioning and clustering. IEEE Trans. Comput. Aided Des. Intergrated Circuits Syst. 11(9), 1074–1085 (1992)
James, M.: Algorithms for the assignment and transportation problems. SIAM J. Appl. Math. 5(1), 32–38 (1957)
Jiang, B., Tang, J., Ding, C., Luo, B.: Binary constraint preserving graph matching. In: 30th IEEE Conference on Computer Vision and Pattern Recognition, pp. 550–557. Hawaii (2017)
Jiang, H., Yu, X.S., Martin, D.R.: Linear scale and rotation invariant matching. IEEE Trans. Pattern Anal. Mach. Intell. 33(7), 1339–1355 (2011)
Leoedeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: 10th IEEE Conference on International Conference on Computer Vision, pp. 1482–1489. Beijing (2005)
Leoedeanu, M., Hebert, M., Sukthankar, R.: An integer projected fixed point method for graph matching and map inference. In: 23th Conference and Workshop on Neural Information Processing Systems, pp. 1114–1122. Vancouver (2009)
Michel, D., Oikonomidis, I., Argyros, A.A.: Scale invariant and deformation tolerant partial shape matching. Image Vis. Comput. 29(7), 459–469 (2011)
Shi, J.B., Jitendra, M.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)
Sullivan, J., Carlsson, S.: Recognizing and tracking human action. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 629–644. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-47969-4_42
Umeyama, S.: An eigendecomposition approach to weighted graph matching problems. IEEE Trans. Pattern Anal. Mach. Intell. 10(5), 695–703 (1988)
Zass, R., Shashua, A.: Probabilistic graph and hypergraph matching, In: 21th IEEE Conference on Computer Vision and Pattern Recognition, pp. 1-8. Anchorage(2008)
Zhang, Z.Y.: Iterative point matching for registration of free-form curves and surfaces. Int. J. Comput. Vis. 13(2), 119–152 (1994)
Zhou, F., De la Torre, F.: Factorized graph matching. In: 25th IEEE Conference on Computer Vision and Pattern Recognition, pp. 127–134. Providence (2012)
Acknowledgments
This work is supported partly by the National Natural Science Foundation (NSFC) of China (grants 61772479, 61662021, 61773047, 61503383, 61633009, U1613213, 61627808, 61502494, and U1713201), partly by the National Key Research and Development Plan of China (grant 2016YFC0300801 and 2017YFB1300202), and partly by the Development of Science and Technology of Guangdong Province Special Fund project (grant 2016B090910001).
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Yang, J., Yang, X., Zhou, ZB., Liu, ZY. (2018). Graph Matching Based on Fast Normalized Cut. In: Cheng, L., Leung, A., Ozawa, S. (eds) Neural Information Processing. ICONIP 2018. Lecture Notes in Computer Science(), vol 11306. Springer, Cham. https://doi.org/10.1007/978-3-030-04224-0_45
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