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Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers

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Computer Vision – ECCV 2020 (ECCV 2020)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12373))

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Abstract

Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial solvers. Using the presence of heavily optimized combinatorial solvers together with some improvements in architecture design, we advance state-of-the-art on deep graph matching benchmarks for keypoint correspondence. In addition, we highlight the conceptual advantages of incorporating solvers into deep learning architectures, such as the possibility of post-processing with a strong multi-graph matching solver or the indifference to changes in the training setting. Finally, we propose two new challenging experimental setups.

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References

  1. Adams, R.P., Zemel, R.S.: Ranking via sinkhorn propagation (2011)

    Google Scholar 

  2. Abu Alhaija, H., Sellent, A., Kondermann, D., Rother, C.: GraphFlow – 6D large displacement scene flow via graph matching. In: Gall, J., Gehler, P., Leibe, B. (eds.) GCPR 2015. LNCS, vol. 9358, pp. 285–296. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24947-6_23

    Chapter  Google Scholar 

  3. Amos, B., Kolter, J.Z.: OptNet: differentiable optimization as a layer in neural networks. In: International Conference on Machine Learning. ICML 2017, pp. 136–145 (2017)

    Google Scholar 

  4. Baker, S., Scharstein, D., Lewis, J.P., Roth, S., Black, M.J., Szeliski, R.: A database and evaluation methodology for optical flow. Int. J. Comput. Vision 92(1), 1–31 (2011). https://doi.org/10.1007/s11263-010-0390-2

    Article  Google Scholar 

  5. Balcan, M., Dick, T., Sandholm, T., Vitercik, E.: Learning to branch. In: International Conference on Machine Learning. ICML 2018, pp. 353–362 (2018)

    Google Scholar 

  6. Battaglia, P., et al.: Relational inductive biases, deep learning, and graph networks. arXiv preprint arXiv:1806.01261 (2018)

  7. Bello, I., Pham, H., Le, Q.V., Norouzi, M., Bengio, S.: Neural combinatorial optimization with reinforcement learning. In: International Conference on Learning Representations, Workshop Track. ICLR 2017 (2017)

    Google Scholar 

  8. Bourdev, L., Malik, J.: Poselets: Body part detectors trained using 3D human pose annotations. In: IEEE International Conference on Computer Vision. ICCV 2009, pp. 1365–1372 (2009)

    Google Scholar 

  9. Burkard, R., Dell’Amico, M., Martello, S.: Assignment Problems. Society for Industrial and Applied Mathematics, Philadelphia (2009)

    Book  Google Scholar 

  10. Burkard, R.E., Karisch, S.E., Rendl, F.: QAPLIB-a quadratic assignment problem library. J. Global Optim. 10(4), 391–403 (1997). https://doi.org/10.1023/A:1008293323270

    Article  MathSciNet  MATH  Google Scholar 

  11. Cao, Z., Simon, T., Wei, S.E., Sheikh, Y.: Realtime multi-person 2D pose estimation using part affinity fields. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2017 (2017)

    Google Scholar 

  12. Chang, J.R., Chen, Y.S.: Pyramid stereo matching network. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2018, pp. 5410–5418 (2018)

    Google Scholar 

  13. Chen, H.T., Lin, H.H., Liu, T.L.: Multi-object tracking using dynamical graph matching. In: Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, vol. 2, pp. II-II. IEEE (2001)

    Google Scholar 

  14. Cho, M., Alahari, K., Ponce, J.: Learning graphs to match. In: IEEE International Conference on Computer Vision. ICCV 2013 (2013)

    Google Scholar 

  15. Delaunay, B.: Sur la sphere vide. Izv. Akad. Nauk SSSR Otdelenie Matematicheskii i Estestvennyka Nauk 7, 793–800 (1934)

    MATH  Google Scholar 

  16. Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., Fei-Fei, L.: ImageNet: a large-scale hierarchical image database. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2009, pp. 248–255 (2009)

    Google Scholar 

  17. Deudon, M., Cournut, P., Lacoste, A., Adulyasak, Y., Rousseau, L.-M.: Learning heuristics for the TSP by policy gradient. In: van Hoeve, W.-J. (ed.) CPAIOR 2018. LNCS, vol. 10848, pp. 170–181. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93031-2_12

    Chapter  Google Scholar 

  18. Duchenne, O., Joulin, A., Ponce, J.: A graph-matching kernel for object categorization. In: 2011 International Conference on Computer Vision, pp. 1792–1799. IEEE (2011)

    Google Scholar 

  19. Elmsallati, A., Clark, C., Kalita, J.: Global alignment of protein-protein interaction networks: a survey. IEEE/ACM Trans. Comput. Biol. Bioinform. 13(4), 689–705 (2016)

    Article  Google Scholar 

  20. Everingham, M., Van Gool, L., Williams, C., Winn, J., Zisserman, A.: The pascal visual object classes (VOC) challenge. Int. J. Comput. Vision 88(2), 303–338 (2010). https://doi.org/10.1007/s11263-009-0275-4

    Article  Google Scholar 

  21. Ferber, A., Wilder, B., Dilkina, B., Tambe, M.: Mipaal: Mixed integer program as a layer. arXiv preprint arXiv:1907.05912 (2019)

  22. Fey, M., Eric Lenssen, J., Weichert, F., Müller, H.: SplineCNN: fast geometric deep learning with continuous b-spline kernels. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2018, pp. 869–877 (2018)

    Google Scholar 

  23. Fey, M., Lenssen, J.E., Morris, C., Masci, J., Kriege, N.M.: Deep graph matching consensus. In: International Conference on Learning Representations. ICLR 2020 (2020)

    Google Scholar 

  24. Fey, M., Lenssen, J.E., Morris, C., Masci, J., Kriege, N.M.: Deep graph matching consensus. https://github.com/rusty1s/deep-graph-matching-consensus (2020). Commit: be1c4c

  25. Gasse, M., Chételat, D., Ferroni, N., Charlin, L., Lodi, A.: Exact combinatorial optimization with graph convolutional neural networks. In: Advances in Neural Information Processing Systems. NIPS 2019, pp. 15554–15566 (2019)

    Google Scholar 

  26. Grohe, M., Rattan, G., Woeginger, G.J.: Graph similarity and approximate isomorphism. In: 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), vol. 117, pp. 20:1–20:16 (2018)

    Google Scholar 

  27. Jiang, B., Sun, P., Tang, J., Luo, B.: GLMNet: graph learning-matching networks for feature matching. arXiv preprint arXiv:1911.07681 (2019)

  28. Kainmueller, D., Jug, F., Rother, C., Myers, G.: Active graph matching for automatic joint segmentation and annotation of C. elegans. In: Golland, P., Hata, N., Barillot, C., Hornegger, J., Howe, R. (eds.) MICCAI 2014. LNCS, vol. 8673, pp. 81–88. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10404-1_11

    Chapter  Google Scholar 

  29. Khalil, E., Dai, H., Zhang, Y., Dilkina, B., Song, L.: Learning combinatorial optimization algorithms over graphs. In: Advances in Neural Information Processing Systems. NIPS 2017, pp. 6348–6358 (2017)

    Google Scholar 

  30. Khalil, E.B., Bodic, P.L., Song, L., Nemhauser, G., Dilkina, B.: Learning to branch in mixed integer programming. In: AAAI Conference on Artificial Intelligence. AAAI 2016, pp. 724–731 (2016)

    Google Scholar 

  31. Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: International Conference on Learning Representations. ICLR 2014 (2014)

    Google Scholar 

  32. Kool, W., van Hoof, H., Welling, M.: Attention, learn to solve routing problems! In: International Conference on Learning Representations. ICLR 2019 (2019)

    Google Scholar 

  33. Lawler, E.L.: The quadratic assignment problem. Manag. Sci. 9(4), 586–599 (1963)

    Article  MathSciNet  Google Scholar 

  34. Li, Y., Zemel, R., Brockschmidt, M., Tarlow, D.: Gated graph sequence neural networks. In: International Conference on Learning Representations. ICLR 2016 (2016)

    Google Scholar 

  35. Liu, L., Cheung, W.K., Li, X., Liao, L.: Aligning users across social networks using network embedding. In: International Joint Conference on Artificial Intelligence. IJCAI 2016, pp. 1774–1780 (2016)

    Google Scholar 

  36. Luo, W., Schwing, A.G., Urtasun, R.: Efficient deep learning for stereo matching. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2016, pp. 5695–5703 (2016)

    Google Scholar 

  37. Mandi, J., Demirovic, E., Stuckey, P.J., Guns, T.: Smart predict-and-optimize for hard combinatorial optimization problems. arXiv preprint arXiv:1911.10092 (2019)

  38. Min, J., Lee, J., Ponce, J., Cho, M.: SPair-71k: a large-scale benchmark for semantic correspondance. arXiv preprint arXiv:1908.10543 (2019)

  39. Nam, H., Han, B.: Learning multi-domain convolutional neural networks for visual tracking. arXiv preprint arXiv:1510.07945 (2015)

  40. Niculae, V., Martins, A., Blondel, M., Cardie, C.: SparseMAP: differentiable sparse structured inference. In: International Conference on Machine Learning. ICML 2018, pp. 3799–3808 (2018)

    Google Scholar 

  41. Pachauri, D., Kondor, R., Singh, V.: Solving the multi-way matching problem by permutation synchronization. In: Advances in Neural Information Processing Systems. NIPS 2013, pp. 1860–1868 (2013)

    Google Scholar 

  42. Rolínek, M., Musil, V., Paulus, A., Vlastelica, M., Michaelis, C., Martius, G.: Optimizing ranking-based metrics with blackbox differentiation. In: Conference on Computer Vision and Pattern Recognition. CVPR 2020, pp. 7620–7630 (2020)

    Google Scholar 

  43. Sahillioğlu, Y.: Recent advances in shape correspondence. Vis. Comput. 36(8), 1705–1721 (2019). https://doi.org/10.1007/s00371-019-01760-0

    Article  Google Scholar 

  44. Scarselli, F., Gori, M., Tsoi, A.C., Hagenbuchner, M., Monfardini, G.: The graph neural network model. Trans. Neur. Netw. 20(1), 61–80 (2009)

    Article  Google Scholar 

  45. Schroff, F., Kalenichenko, D., Philbin, J.: FaceNet: a unified embedding for face recognition and clustering. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2015, pp. 815–823 (2015)

    Google Scholar 

  46. Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556 (2014)

  47. Sinkhorn, R., Knopp, P.: Concerning nonnegative matrices and doubly stochastic matrices. Pac. J. Math. 21, 343–348 (1967)

    Article  MathSciNet  Google Scholar 

  48. Storvik, G., Dahl, G.: Lagrangian-based methods for finding MAP solutions for MRF models. IEEE Trans. Image Process. 9(3), 469–479 (2000)

    Article  Google Scholar 

  49. Sun, D., Roth, S., Black, M.J.: A quantitative analysis of current practices in optical flow estimation and the principles behind them. Int. J. Comput. Vis. 106(2), 115–137 (2014). https://doi.org/10.1007/s11263-013-0644-x

    Article  Google Scholar 

  50. Sun, D., Yang, X., Liu, M.Y., Kautz, J.: PWC-Net: CNNs for optical flow using pyramid, warping, and cost volume. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2018, June 2018

    Google Scholar 

  51. Swoboda, P., Kuske, J., Savchynskyy, B.: A dual ascent framework for Lagrangean decomposition of combinatorial problems. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2017, pp. 1596–1606 (2017)

    Google Scholar 

  52. Swoboda, P., Mokarian, A., Theobalt, C., Bernard, F., et al.: A convex relaxation for multi-graph matching. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2019, pp. 11156–11165 (2019)

    Google Scholar 

  53. Swoboda, P., Rother, C., Alhaija, H.A., Kainmüller, D., Savchynskyy, B.: A study of Lagrangean decompositions and dual ascent solvers for graph matching. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2016, pp. 7062–7071 (2016)

    Google Scholar 

  54. Torresani, L., Kolmogorov, V., Rother, C.: A dual decomposition approach to feature correspondence. IEEE Trans. Pattern Anal. Mach. Intell. 35(2), 259–271 (2013)

    Article  Google Scholar 

  55. Ufer, N., Ommer, B.: Deep semantic feature matching. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2017, pp. 6914–6923 (2017)

    Google Scholar 

  56. Vlastelica, M., Paulus, A., Musil, V., Martius, G., Rolínek, M.: Differentiation of blackbox combinatorial solvers. In: International Conference on Learning Representations. ICLR 2020 (2020)

    Google Scholar 

  57. Wang, L., Ouyang, W., Wang, X., Lu, H.: Visual tracking with fully convolutional networks. In: IEEE International Conference on Computer Vision. ICCV 2015, pp. 3119–3127 (2015)

    Google Scholar 

  58. Wang, P.W., Donti, P., Wilder, B., Kolter, Z.: SATNet: bridging deep learning and logical reasoning using a differentiable satisfiability solver. In: International Conference on Machine Learning, pp. 6545–6554 (2019)

    Google Scholar 

  59. Wang, R., Yan, J., Yang, X.: Learning combinatorial embedding networks for deep graph matching. In: IEEE International Conference on Computer Vision. ICCV 2019, pp. 3056–3065 (2019)

    Google Scholar 

  60. Wang, R., Yan, J., Yang, X.: Neural graph matching network: learning Lawler’s quadratic assignment problem with extension to hypergraph and multiple-graph matching. arXiv preprint arXiv:1911.11308 (2019)

  61. Yu, T., Wang, R., Yan, J., Li, B.: Learning deep graph matching with channel-independent embedding and Hungarian attention. In: International Conference on Learning Representations. ICLR 2020 (2020)

    Google Scholar 

  62. Zanfir, A., Sminchisescu, C.: Deep learning of graph matching. In: Conference on Computer Vision and Pattern Recognition. CVPR 2018, pp. 2684–2693 (2018)

    Google Scholar 

  63. Zhang, Y., Hare, J., Prügel-Bennett, A.: Learning representations of sets through optimized permutations. arXiv preprint arXiv:1812.03928 (2018)

  64. Zhang, Z., Lee, W.S.: Deep graphical feature learning for the feature matching problem. In: IEEE International Conference on Computer Vision. ICCV 2019 (2019)

    Google Scholar 

  65. Zhang, Z., Shi, Q., McAuley, J., Wei, W., Zhang, Y., van den Hengel, A.: Pairwise matching through max-weight bipartite belief propagation. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2016 (2016)

    Google Scholar 

  66. Zhou, F., la Torre, F.D.: Factorized graph matching. In: IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2012, pp. 127–134 (2012)

    Google Scholar 

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Rolínek, M., Swoboda, P., Zietlow, D., Paulus, A., Musil, V., Martius, G. (2020). Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12373. Springer, Cham. https://doi.org/10.1007/978-3-030-58604-1_25

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