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Nuclear-\(L_1\) Norm Joint Regression for Face Reconstruction and Recognition

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Book cover Computer Vision -- ACCV 2014 (ACCV 2014)

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Abstract

Recognizing a face with significant lighting, disguise and occlusion variations is an interesting and challenging problem in pattern recognition. To address this problem, many regression based methods, represented by sparse representation classifier (SRC), are presented recently. SRC uses the \(L_1\)-norm to characterize the pixel-level sparse noise but ignore the spatial information of noise. In this paper, we find that nuclear-norm is good for characterizing image-wise structural noise, and thus we use the nuclear norm and \(L_1\)-norm to jointly characterize the error image in regression model. Our experimental results demonstrate that the proposed method is more effective than state-of-the-art regression methods for face reconstruction and recognition.

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References

  1. Wright, J., Yang, A., Ganesh, A., Sastry, S.S., Ma, Y.: Robust face recognition via sparse representation. IEEE PAMI 31, 210–227 (2009)

    Article  Google Scholar 

  2. Cover, T., Hart, P.: Nearest neighbor pattern classification. IEEE Trans. Inf. Theory 13, 21–27 (1967)

    Article  MATH  Google Scholar 

  3. Li, S., Lu, J.: Face recognition using the nearest feature line method. IEEE Trans. Neural Networks 10, 439–443 (1999)

    Article  Google Scholar 

  4. Lu, C.Y., Min, H., Gui, J., Zhu, L., Lei, Y.K.: Face recognition via weighted sparse representation. J. Vis. Commun. Image Represent 24, 111–116 (2003)

    Article  Google Scholar 

  5. Daubechies, I., Devore, R., Fornasier, M., Gunturk, C.: Iteratively re-weighted least squares minimization for sparse recovery. arXiv: 0807.0575 (2008)

  6. Cands, E., Wakin, M., Boydg, S.: Enhancing sparsity by reweighted l1 minimization. J. Fourier Anal. Appl. 14, 877–905 (2008)

    Article  MathSciNet  Google Scholar 

  7. Zhang, L., Yang, M., Feng, X.: Sparse representation or collaborative representation: which helps face recognition? In: ICCV (2011)

    Google Scholar 

  8. Yang, J., Zhang, L., Xu, Y., Yang, J.Y.: Beyond sparsity: the role of l1-optimizer in pattern classification. Pattern Recognit. 45, 1104–1118 (2012)

    Article  MATH  Google Scholar 

  9. Yang, J., Chu, D., Zhang, L., Xu, Y.: Sparse representation classifier steered discriminative projection with applications to face recognition. IEEE Trans. Neural Networks. Learn. Syst. 24, 1023–1035 (2013)

    Article  Google Scholar 

  10. Zheng, Z., Zhang, H., Jia, J., Zhao, J., Guo, L., Fu, F., Yu, M.: Low-rank matrix recovery with discriminant regularization. In: Pei, J., Tseng, V.S., Cao, L., Motoda, H., Xu, G. (eds.) PAKDD 2013, Part II. LNCS, vol. 7819, pp. 437–448. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Naseem, I., Togneri, R., Bennamoun, M.: Linear regression for face recognition. IEEE PAMI 32, 2106–2112 (2010)

    Article  Google Scholar 

  12. Yang, M., Zhang, L., Yang, J., Zhang, D.: Robust sparse coding for face recognition. In: CVPR (2011)

    Google Scholar 

  13. He, R., Zheng, W.S., Hu, B.G.: Maximum correntropy criterion for robust face recognition. IEEE PAMI 22, 1753–1766 (2011)

    Google Scholar 

  14. Li, X.X., Dai, D.Q., Zhang, X.F., Ren, C.X.: Structured sparse error coding for face recognition with occlusion. IEEE Trans. Image Process. 22, 1889–1990 (2013)

    Article  MathSciNet  Google Scholar 

  15. Jia, K., Chan, T.-H., Ma, Y.: Robust and practical face recognition via structured sparsity. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part IV. LNCS, vol. 7575, pp. 331–344. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  16. Yang, J., Qian, J.J., Luo, L., Zhang, F.L., Gao, Y.C.: Nuclear norm based matrix regression with applications to face recognition with occlusion and illumination changes. arXiv:1405.1207 (2014)

  17. Gabay, D., Mercier, B.: A dual algorithm for the solution of nonlinear variational problems via finite element approximations. IEEE Trans. Image Process. 22, 17–140 (1976)

    Google Scholar 

  18. Gabay, D.: Applications of the method of multipliers to variational inequalities. In: Fortin, M., Glowinski, R. (eds.) Augmented Lagrangian Methods: Applications to the Numerical Solution of Boundary-Value Problems, pp. 299–331. North-Holland, Amsterdam (1983)

    Chapter  Google Scholar 

  19. Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statisticallearning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3, 1–112 (2011)

    Article  Google Scholar 

  20. Hansson, A., Liu, Z., Vandenberghe, L.: Subspace system identification via weighted nuclear norm optimization. In: CDC, pp. 3439–3444 (2012)

    Google Scholar 

  21. Lin, Z., Chen, M., Ma, Y.: Multiplier method for exact recovery of corrupted low-rank matrices. UIUC Technical Report UILU-ENG-09-2215 (2009)

    Google Scholar 

  22. Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Trans. Patt. Anal. Mach. Intell. 35, 171–184 (2013)

    Article  Google Scholar 

  23. He, B., Tao, M., Yuan, X.: Alternating direction method with gaussian back substitution for separable convex programming. SIAM J. Optim. 22, 313–340 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  24. Luan, X., Liu, B., Yang, L., Qian, J.: Extracting sparse error of robust pca for face recognition in the presence of varying illumination and occlusion. Pattern Recognit. 47, 495–508 (2014)

    Article  Google Scholar 

  25. Li, J., Lu, C.Y.: A new decision rule for sparse representation based classification for face recognition. Neurocomputing 116, 265–271 (2013)

    Article  Google Scholar 

  26. Gu, Z.H., Shao, M., Li, L.Y.: Discriminative metric: schatten norm vs. vector norm. In: ICPR 2012, Tsukuba, Japan

    Google Scholar 

  27. Martinez, A., benavente, R.: The ar face database. Tech-nical Report 24, CVC (1998)

    Google Scholar 

  28. Lee, K., Ho, J., Kriegman, D.: Acquiring linear subspaces for face recognition under variable lighting. IEEE PAMI 27, 684–698 (2005)

    Article  Google Scholar 

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Correspondence to Jian Yang .

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Luo, L., Yang, J., Qian, J., Tai, Y. (2015). Nuclear-\(L_1\) Norm Joint Regression for Face Reconstruction and Recognition. In: Cremers, D., Reid, I., Saito, H., Yang, MH. (eds) Computer Vision -- ACCV 2014. ACCV 2014. Lecture Notes in Computer Science(), vol 9004. Springer, Cham. https://doi.org/10.1007/978-3-319-16808-1_44

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  • DOI: https://doi.org/10.1007/978-3-319-16808-1_44

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