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CLAP: Concave Linear APproximation for Quadratic Graph Matching

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Advances in Visual Computing (ISVC 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15046))

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Abstract

Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem (QAP) with node-wise and edge-wise constraints. However, solving such a QAP can be both expensive and difficult due to numerous local extreme points. In this work, we introduce a novel linear model and solver designed to accelerate the computation of graph matching. Specifically, we employ a positive semi-definite matrix approximation to establish the structural attribute constraint. We then transform the original QAP into a linear model that is concave for maximization. This model can subsequently be solved using the Sinkhorn optimal transport algorithm, known for its enhanced efficiency and numerical stability compared to existing approaches. Experimental results on the widely used benchmark PascalVOC showcase that our algorithm achieves state-of-the-art performance with significantly improved efficiency. Source code: https://github.com/xmlyqing00/clap.

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References

  1. Cuturi, M.: Sinkhorn distances: lightspeed computation of optimal transport. In: Burges, C.J.C., Bottou, L., Welling, M., Ghahramani, Z., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems, vol. 26 (2013)

    Google Scholar 

  2. Ding, C., Zhou, D., He, X., Zha, H.: R 1-PCA: rotational invariant l 1-norm principal component analysis for robust subspace factorization. In: ICML (2006)

    Google Scholar 

  3. Everingham, M., Van Gool, L., Williams, C.K., Winn, J., Zisserman, A.: The pascal visual object classes (VOC) challenge. IJCV 88(2), 303–338 (2010)

    Article  Google Scholar 

  4. Gao, Q., Wang, F., Xue, N., Yu, J., Xia, G.: Deep graph matching under quadratic constraint. In: CVPR, pp. 5067–5074 (2021)

    Google Scholar 

  5. He, J., Huang, Z., Wang, N., Zhang, Z.: Learnable graph matching: incorporating graph partitioning with deep feature learning for multiple object tracking. In: CVPR, pp. 5299–5309 (2021)

    Google Scholar 

  6. Jaggi, M., Lacoste-Julien, S.: On the global linear convergence of Frank-Wolfe optimization variants. In: NeurIPS, vol. 28 (2015)

    Google Scholar 

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

  8. Johnson, D.S., Garey, M.R.: Computers and Intractability: A Guide to the Theory of NP-Completeness. WH Freeman, New York (1979)

    Google Scholar 

  9. Koopmans, T.C., Beckmann, M.: Assignment problems and the location of economic activities. Econometrica: J. Econometr. Soc. (1957)

    Google Scholar 

  10. Kwak, N.: Principal component analysis based on l1-norm maximization. IEEE T-PAMI 30(9), 1672–1680 (2008)

    Article  MATH  Google Scholar 

  11. Lawler, E.L.: The quadratic assignment problem. Manag. Sci. 9(4) (1963)

    Google Scholar 

  12. Liao, X., Xu, Y., Ling, H.: Hypergraph neural networks for hypergraph matching. In: ICCV, pp. 1266–1275 (2021)

    Google Scholar 

  13. Lin, Y., Yang, M., Yu, J., Hu, P., Zhang, C., Peng, X.: Graph matching with bi-level noisy correspondence. In: ICCV, pp. 23362–23371 (2023)

    Google Scholar 

  14. Loiola, E.M., de Abreu, N.M.M., Boaventura-Netto, P.O., Hahn, P., Querido, T.: A survey for the quadratic assignment problem. Eur. J. Oper. Res. 176(2), 657–690 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lu, Y., Huang, K., Liu, C.L.: A fast projected fixed-point algorithm for large graph matching. Pattern Recogn. 60, 971–982 (2016)

    Article  MATH  Google Scholar 

  16. Peyré, G., Cuturi, M., et al.: Computational optimal transport: with applications to data science. Found. Trends Mach. Learn. 11(5–6) (2019)

    Google Scholar 

  17. Puy, G., Boulch, A., Marlet, R.: FLOT: scene flow on point clouds guided by optimal transport. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, J.-M. (eds.) ECCV 2020. LNCS, vol. 12373, pp. 527–544. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58604-1_32

    Chapter  Google Scholar 

  18. Sarlin, P.E., DeTone, D., Malisiewicz, T., Rabinovich, A.: Superglue: learning feature matching with graph neural networks. In: CVPR, pp. 4938–4947 (2020)

    Google Scholar 

  19. Sun, J., Shen, Z., Wang, Y., Bao, H., Zhou, X.: Loftr: detector-free local feature matching with transformers. In: CVPR, pp. 8922–8931 (2021)

    Google Scholar 

  20. Umeyama, S.: An eigendecomposition approach to weighted graph matching problems. IEEE T-PAMI 10(5), 695–703 (1988)

    Article  MATH  Google Scholar 

  21. Varga, R.S.: Geršgorin and His Circles. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17798-9

    Book  MATH  Google Scholar 

  22. Wang, F.D., Xue, N., Zhang, Y., Xia, G.S., Pelillo, M.: A functional representation for graph matching. IEEE T-PAMI 42(11), 2737–2754 (2020)

    MATH  Google Scholar 

  23. Wang, R., Guo, Z., Jiang, S., Yang, X., Yan, J.: Deep learning of partial graph matching via differentiable top-k. In: CVPR, pp. 6272–6281 (2023)

    Google Scholar 

  24. Wang, R., Yan, J., Yang, X.: Learning combinatorial embedding networks for deep graph matching. In: ICCV, pp. 3056–3065 (2019)

    Google Scholar 

  25. Wang, R., Yan, J., Yang, X.: Combinatorial learning of robust deep graph matching: an embedding based approach. IEEE T-PAMI (2020)

    Google Scholar 

  26. Wang, R., Yan, J., Yang, X.: Neural graph matching network: learning Lawler’s quadratic assignment problem with extension to hypergraph and multiple-graph matching. IEEE T-PAMI (2021)

    Google Scholar 

  27. Wang, T., Liu, H., Li, Y., Jin, Y., Hou, X., Ling, H.: Learning combinatorial solver for graph matching. In: CVPR, pp. 7568–7577 (2020)

    Google Scholar 

  28. Yu, T., Wang, R., Yan, J., Li, B.: Learning deep graph matching with channel-independent embedding and Hungarian attention. In: ICLR (2019)

    Google Scholar 

  29. Zanfir, A., Sminchisescu, C.: Deep learning of graph matching. In: CVPR, pp. 2684–2693 (2018)

    Google Scholar 

  30. Zaslavskiy, M., Bach, F., Vert, J.P.: A path following algorithm for the graph matching problem. IEEE T-PAMI 31(12), 2227–2242 (2008)

    Article  MATH  Google Scholar 

  31. Zhang, Z., Xiang, Y., Wu, L., Xue, B., Nehorai, A.: KerGM: kernelized graph matching. In: NeurIPS, vol. 32, 3335–3346 (2019)

    Google Scholar 

  32. Zheng, W., Lin, Z., Wang, H.: L1-norm kernel discriminant analysis via Bayes error bound optimization for robust feature extraction. IEEE Trans. Neural Netw. Learn. Syst. 25(4), 793–805 (2013)

    Article  MATH  Google Scholar 

  33. Zhou, F., De la Torre, F.: Factorized graph matching. In: CVPR. IEEE (2012)

    Google Scholar 

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Acknowledgments

This research was partially supported by NSF CBET-2115405 and the Texas A&M University ASCEND Research Leadership Fellows Program. Part of the experiments were conducted using the computing resources provided by Texas A&M High Performance Research Computing.

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Authors and Affiliations

  1. Texas A&M University, College Station, TX, 77843, USA

    Yongqing Liang, Huijun Han & Xin Li

Authors
  1. Yongqing Liang
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  2. Huijun Han
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  3. Xin Li
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Corresponding author

Correspondence to Xin Li .

Editor information

Editors and Affiliations

  1. University of Nevada Reno, Reno, NV, USA

    George Bebis

  2. Johns Hopkins University, Baltimore, MD, USA

    Vishal Patel

  3. Chinese University of Hong Kong, Shatin, Hong Kong

    Jinwei Gu

  4. University of California, Davis, CA, USA

    Julian Panetta

  5. George Mason University, Fairfax, VA, USA

    Yotam Gingold

  6. University of Georgia, Athens, GA, USA

    Kyle Johnsen

  7. Colorado State University, Fort Collins, CO, USA

    Mohammed Safayet Arefin

  8. Indian Institute of Technology, Kanpur, Uttar Pradesh, India

    Soumya Dutta

  9. Los Alamos National Lab., Los Alamos, NM, USA

    Ayan Biswas

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Liang, Y., Han, H., Li, X. (2025). CLAP: Concave Linear APproximation for Quadratic Graph Matching. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2024. Lecture Notes in Computer Science, vol 15046. Springer, Cham. https://doi.org/10.1007/978-3-031-77392-1_22

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  • DOI: https://doi.org/10.1007/978-3-031-77392-1_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-77391-4

  • Online ISBN: 978-3-031-77392-1

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