Advertisement

Branching Path Following for Graph Matching

  • Tao Wang
  • Haibin Ling
  • Congyan Lang
  • Jun Wu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9906)

Abstract

Recently, graph matching algorithms utilizing the path following strategy have exhibited state-of-the-art performances. However, the paths computed in these algorithms often contain singular points, which usually hurt the matching performance. To deal with this issue, in this paper we propose a novel path following strategy, named branching path following (BPF), which consequently improves graph matching performance. In particular, we first propose a singular point detector by solving an KKT system, and then design a branch switching method to seek for better paths at singular points. Using BPF, a new graph matching algorithm named BPF-G is developed by applying BPF to a recently proposed path following algorithm named GNCCP (Liu&Qiao 2014). For evaluation, we compare BPF-G with several recently proposed graph matching algorithms on a synthetic dataset and four public benchmark datasets. Experimental results show that our approach achieves remarkable improvement in matching accuracy and outperforms other algorithms.

Keywords

Graph matching Path following Numerical continuation Singular point Branch switching 

Notes

Acknowledgments

This work is supported by the National Nature Science Foundation of China (nos. 61300071, 61272352, 61472028, and 61301185), the National Key Research and Development Plan under Grant(No.2016YFB1001200), Beijing Natural Science Foundation (nos. 4142045 and 4162048), the Fundamental Research Funds for the Central Universities (no. 2015JBM029), and in part by the US National Science Foundation under Grants 1407156 and 1350521.

References

  1. 1.
    Serradell, E., Pinheiro, M.A., Sznitman, R., Kybic, J., Moreno-Noguer, F., Fua, P.: Non-rigid graph registration using active testing search. PAMI 37(3), 625–638 (2015)CrossRefGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Wang, J., Li, S.: Query-driven iterated neighborhood graph search for large scale indexing. In: ACM MM, pp. 179–188 (2012)Google Scholar
  4. 4.
    Bai, X., Yang, X., Latecki, L.J., Liu, W., Tu, Z.: Learning context-sensitive shape similarity by graph transduction. PAMI 32(5), 861–874 (2010)CrossRefGoogle Scholar
  5. 5.
    Michel, D., Oikonomidis, I., Argyros, A.A.: Scale invariant and deformation tolerant partial shape matching. Image Vis. Comput. 29(7), 459–469 (2011)CrossRefGoogle Scholar
  6. 6.
    Wang, T., Ling, H., Lang, C., Feng, S.: Symmetry-aware graph matching. Pattern Recogn. 60, 657–668 (2016)CrossRefGoogle Scholar
  7. 7.
    Duchenne, O., Joulin, A., Ponce, J.: A graph-matching kernel for object categorization. In: ICCV, pp. 1792–1799 (2011)Google Scholar
  8. 8.
    Wu, J., Shen, H., Li, Y., Xiao, Z., Lu, M., Wang, C.: Learning a hybrid similarity measure for image retrieval. Pattern Recogn. 46(11), 2927–2939 (2013)CrossRefzbMATHGoogle Scholar
  9. 9.
    Cai, Z., Wen, L., Lei, Z., Vasconcelos, N., Li, S.Z.: Robust deformable and occluded object tracking with dynamic graph. TIP 23(12), 5497–5509 (2014)MathSciNetGoogle Scholar
  10. 10.
    Chen, C.Y., Grauman, K.: Efficient activity detection with max-subgraph search. In: CVPR, pp. 1274–1281 (2012)Google Scholar
  11. 11.
    Leordeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: ICCV, pp. 1482–1489 (2005)Google Scholar
  12. 12.
    Cour, T., Srinivasan, P., Shi, J.: Balanced graph matching. NIPS 19, 313–320 (2007)Google Scholar
  13. 13.
    Cho, M., Lee, J., Lee, K.M.: Reweighted random walk for graph matching. In: ECCV, pp. 492–505 (2010)Google Scholar
  14. 14.
    Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. PAMI 18(4), 377–388 (1996)CrossRefGoogle Scholar
  15. 15.
    Zaslavskiy, M., Bach, F., Vert, J.P.: A path following algorithm for the graph matching problem. PAMI 31(12), 2227–2242 (2009)CrossRefGoogle Scholar
  16. 16.
    Zhou, F., De la Torre, F.: Factorized graph matching. In: CVPR, pp. 127–134 (2012)Google Scholar
  17. 17.
    Liu, Z., Qiao, H.: GNCCP - graduated nonconvexity and concavity procedure. PAMI 36(6), 1258–1267 (2014)CrossRefGoogle Scholar
  18. 18.
    Liu, Z., Qiao, H., Yang, X., Hoi, S.C.H.: Graph matching by simplified convex-concave relaxation procedure. IJCV 109(3), 169–186 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Zass, R., Shashua, A.: Probabilistic graph and hypergraph matching. In: CVPR, pp. 1–8 (2008)Google Scholar
  20. 20.
    Egozi, A., Keller, Y., Guterman, H.: A probabilistic approach to spectral graph matching. PAMI 35(1), 18–27 (2013)CrossRefGoogle Scholar
  21. 21.
    Allgower, E.L., Georg, K.: Numerical Continuation Methods. Springer, Heidelberg (1990)CrossRefzbMATHGoogle Scholar
  22. 22.
    Keller, H.B.: Lectures on Numerical Methods in Bifurcation Theory. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 79. Springer, Berlin (1987)Google Scholar
  23. 23.
    Dickson, K.I., Kelley, C.T., Ipsen, I.C.F., Kevrekidis, I.G.: Condition estimates for pseudo-arclength continuation. SIAM J. Numer. Anal. 45(1), 263–276 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. Int. J. Pattern Recogn. Artif. Intell. 18(3), 265–298 (2004)CrossRefGoogle Scholar
  25. 25.
    Foggia, P., Percannella, G., Vento, M.: Graph matching and learning in pattern recognition in the last 10 years. Int. J. Pattern Recogn. Artif. Intell. 28(1), 1–40 (2014)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Yan, J., Zhang, C., Zha, H., Liu, W., Yang, X., Chu, S.M.: Discrete hyper-graph matching. In: CVPR, pp. 1520–1528 (2015)Google Scholar
  27. 27.
    Adamczewski, K., Suh, Y., Lee, K.M.: Discrete tabu search for graph matching. In: ICCV, pp. 109–117 (2015)Google Scholar
  28. 28.
    Leordeanu, M., Hebert, M.: An integer projected fixed point method for graph matching and map inference. In: NIPS (2009)Google Scholar
  29. 29.
    Wang, T., Ling, H.: Path following with adaptive path estimation for graph matching. In: AAAI, pp. 3625–3631 (2016)Google Scholar
  30. 30.
    Frank, M., Wolfe, P.: An algorithm for quadratic programming. Nav. Res. Logistics Q. 3, 95–100 (1956)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Proceedings of 2nd Berkeley Symposium, pp. 481–492 (1951)Google Scholar
  32. 32.
    Shacham, M.: Numerical solution of constrained nonlinear algebraic equations. Int. J. Numer. Methods Eng. 23, 1455–1481 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Dankowicz, H., Schilder, F.: An extended continuation problem for bifurcation analysis in the presence of constraints. J. Comput. Nonlinear Dyn. 6(3), 1–14 (2010)Google Scholar
  34. 34.
    Crisfield, M.A.: Non-linear Finite Element Analysis Solids and Structure. Wiley, Hoboken (1996)Google Scholar
  35. 35.
    Kudryavtsev, L.: Implicit Function. Encyclopedia of Mathematics. Springer, Heidelberg (2001)Google Scholar
  36. 36.
    Deuflhard, P.: Newton Methods for Nonlinear Problems - Affine Invariance and Adaptive Algorithms. Series Computational Mathematics, vol. 35. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  37. 37.
    Branch, M.A., Coleman, T.F., Li, Y.: A subspace, interior and conjugate gradient method for large-scale bound-constrained minimization problems. SIAM J. Sci. Comput. 21(1), 1–23 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Caetano, T.S., Caelli, T., Schuurmans, D., Barone, D.A.: Graphical models and point pattern matching. PAMI 28(10), 1646–1663 (2006)CrossRefGoogle Scholar
  39. 39.
    Lee, D.T., Schachter, B.J.: Two algorithms for constructing a delaunay triangulation. Int. J. Comput. Inf. Sci. 9, 219–242 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Leordeanu, M., Sukthankar, R., Hebert, M.: Unsupervised learning for graph matching. IJCV 96(1), 28–45 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Cho, M., Alahari, K., Ponce, J.: Learning graphs to match. In: ICCV, pp. 25–32 (2013)Google Scholar
  42. 42.
    Mikolajczyk, K., Schmid, C.: An affine invariant interest point detector. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002, Part I. LNCS, vol. 2350, pp. 128–142. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  43. 43.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. IJCV 60(2), 91–110 (2004)CrossRefGoogle Scholar
  44. 44.
    Donoser, M., Bischof, H.: Efficient maximally stable extremal region (MSER) tracking. In: CVPR, pp. 553–560 (2006)Google Scholar
  45. 45.
    Cho, M., Lee, J., Lee, K.M.: Feature correspondence and deformable object matching via agglomerative correspondence clustering. In: ICCV, pp. 1280–1287 (2009)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Meitu HiScene LabHiScene Information TechnologiesShanghaiChina
  2. 2.School of Computer and Information TechnologyBeijing Jiaotong UniversityBeijingChina
  3. 3.Computer and Information Sciences DepartmentTemple UniversityPhiladelphiaUSA

Personalised recommendations