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Robust face recognition using sparse representation in LDA space

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In this article, we address the problem of face recognition under uncontrolled conditions. The proposed solution is a numerical robust algorithm dealing with face images automatically registered and projected via the linear discriminant analysis (LDA) into a holistic low-dimensional feature space. At the heart of this discriminative system, there are suitable nonconvex parametric mappings based on which a fixed-point technique finds the sparse representation of test images allowing their classification. We theoretically argue that the success achieved in sparsity promoting is due to the sequence of values imposed on a characteristic parameter of the used mapping family. Experiments carried out on several databases (ORL, YaleB, BANCA, FRGC v2.0) show the robustness and the ability of the system for classification purpose. In particular, within the area of sparsity promotion, our recognition system shows very good performance with respect to those achieved by the state-of-the-art \(\ell _1\) norm-based sparse representation classifier (SRC), the recently proposed \(\ell _2\) norm-based collaborative representation classifier (CRC), the LASSO-based sparse decomposition technique, and the weighted sparse representation method (WSRC), which integrates sparsity and data locality structure.

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  1. 1.

    By construction, the method cannot work directly with \(k=1\). To this end, virtual samples should be created [34].

  2. 2.

    MATLAB code of \(k\) -LiMapS_HFR and all tests done are available on the website http://dalab.di.unimi.it/klimaps.html.

  3. 3.

    The standard deviation is always very low (varying between 0.013 and 0.019), indicating a good stability of the system.

  4. 4.

    Given the high computational costs of this method, an exhaustive search of the optimal feature dimensionality would be very time consuming and beyond the scope of this work.


  1. 1.

    Adamo A, Grossi G (2011) A fixed-point iterative schema for error minimization in \(k\)-sparse decomposition. In: Proceedings of the IEEE International Symposium on Signal Processing and Information Technology (ISSPIT’11), pp. 167–172

  2. 2.

    Adamo A, Grossi G, Lanzarotti R (2012) Sparse representation based classification for face recognition by k-limaps algorithm. In: Image and Signal Processing 5th International Conference, ICISP 2012, Springer, Lecture Notes in Computer Science, vol. 7340, pp. 245–252

  3. 3.

    Ayarpadi, K., Kannan, E., Nair, R.R., Anitha, T., Srinivasan, R., Scholar, P.: Face recognition under expressions and lighting variations using masking and synthesizing. Int. J. Eng. Res. Appl. (IJERA). 2(1), 758–763 (2012)

  4. 4.

    Belhumeur P, Hespanha J, Kriegman D (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. Pattern. Anal. Mach. Intell. IEEE. Trans. 19(7):711–720

  5. 5.

    Campadelli, P., Lanzarotti, R., Lipori, G.: Precise eye and mouth localization. Int. J. Pattern. Recognit. Artif. Intell. 23(3), 359–377 (2009)

  6. 6.

    Campadelli, P., Lanzarotti, R., Lipori, G.: Automatic facial feature extraction for face recognition. In: Delac, K., Grgic, M. (eds.) Face recognition, pp. 31–58. I-Tech Education and Publishing, Vienna (2007)

  7. 7.

    Candes, E., Romberg, J., Tao, T.: Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure. Appl. Math. 59(8), 1207–1223 (2005)

  8. 8.

    Chan C, Kittler J (2010) Sparse representation of ( multiscale ) histograms for face recognition robust to registration and illumination problems. In: Proceedings of the International Conference on Image Processing, pp. 2441–4

  9. 9.

    Dong, W., Zhang, L., Shi, G., Wu, X.: Image deblurring and supper-resolution by adaptive sparse domain selection and adaptive regularization. IEEE. Trans. Image. Process. 20(7), 1838–1857 (2011)

  10. 10.

    Gao, S., Tsang, I., Chia, L.: Sparse representation with kernels. IEEE. Trans. Image Process. 22(2), 423–434 (2013)

  11. 11.

    He, R., Zheng, W., Hu, B.: Maximum correntropy criterion for robust face recognition. IEEE. Trans. Pattern. Anal. Mach. Intell. 33(8), 1561–1576 (2011)

  12. 12.

    He, X., Yan, S., Hu, Y., Niyogi, P., Zhang, H.J.: Face recognition using Laplacianfaces. IEEE. Trans. Pattern. Anal. Mach. Intell. 27(3), 328–340 (2005)

  13. 13.

    Hui, K., Li, C., Zhang, L.: Sparse neighbor representation for classification. Pattern Recognit. Lett. 33(5), 661–669 (2012)

  14. 14.

    Huo C, Zhang R, Yin D, Wu Q, Xu D (2012) Hyperspectral data compression using sparse representation. In: Hyperspectral Image and Signal Processing: evolution in Remote Sensing (WHISPERS)

  15. 15.

    Jesorsky, O., Kirchberg, K., Frischholz, R.: Robust face detection using the Hausdorff distance. Lecture Notes Comput. Sci. 2091, 212–227 (2001)

  16. 16.

    Jiang Z, Zhang G, Davis L (2012) Submodular dictionary learning for sparse coding. Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, pp. 3418–3425

  17. 17.

    Kang C, Liao S, Xiang S, Pan C (2011) Kernel sparse representation with local patterns for face recognition. Proceedings of IEEE Conference on Image Processing, pp. 3009–3012

  18. 18.

    Koç, N., Barkana, A.: A new solution to one sample problem in face recognition using FLDA. Appl. Math. Comput. 217(24), 10368–10376 (2011)

  19. 19.

    Kyperountas M, Tefas A, Pitas I (2008) Face recognition via adaptive discriminant clustering. In: Interntional Conference on Image Processing, IEEE, pp. 2744–47

  20. 20.

    Li C, Guo J, Zhang H (2010) Local sparse representation based classification. In: ICPR, pp. 649–652

  21. 21.

    Liu H, Sun F (2010) Visual tracking using sparsity induced similarity. In: ICPR, IEEE, pp. 1702–1705

  22. 22.

    Lu, C.Y., Min, H., Gui, J., Zhu, L., Lei, Y.K.: Face recognition via weighted sparse representation. J. Vis. Commun. Image Represent. 24(2), 111–116 (2013)

  23. 23.

    Nabatchian, A., Abdel-Raheem, E., Ahmadi, M.: Illumination invariant feature extraction and mutual-information-based local matching for face recognition under illumination variation and occlusion. Pattern Recognit. 44(10–11), 2576–2587 (2011)

  24. 24.

    Nagesh P, Li B (2009) A compressive sensing approach for expression-invariant face recognition. Proceedings International Conference on Computer Vision and Pattern Recognition, pp. 1518–1525

  25. 25.

    Ortiz, E., Becker, B.: Face recognition for web-scale datasets. Comput. Vision Image Underst. 118, 153–170 (2014)

  26. 26.

    Patel, V., Wu, T., Biswas, S., Phillips, P., Chellappa, R.: Dictionary-based face recognition under variable lighting and pose. IEEE Trans. Inform. Forensics Secur. 7(3), 954–965 (2012)

  27. 27.

    Pothos, V., Theoharatos, C., Economou, G.: A local spectral distribution approach to face recognition. Comput. Vision Image Underst. 116(6), 663–675 (2012)

  28. 28.

    Qiao, L., Chen, S., Tan, X.: Sparsity preserving discriminant analysis for single training image face recognition. Pattern Recognit. Lett. 31(5), 422–429 (2010)

  29. 29.

    Rabia, J., Hamid, R.: A survey of face recognition techniques. J. Inform. Process. Syst. 5, 41–68 (2009)

  30. 30.

    Schwartz, W., Guo, H., Choi, J., Davis, L.: Face identification using large feature sets. IEEE. Trans. Image Process. 21(4), 2245–2255 (2012)

  31. 31.

    Shashua, A., Riklin-Raviv, T.: The quotient image: class-based re- rendering and recognition with varying illuminations. IEEE. Trans. Pattern. Anal. Mach. Intell. 23, 129–139 (2001)

  32. 32.

    Shi Q, Shen C, Li H (2010) Rapid face recognition using hashing. In: CVPR, pp. 2753–60

  33. 33.

    Shit Q, Erikssont A, van den Hengelt A, Shen C (2011) Is face recognition really a compressive sensing problem? Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 553–560

  34. 34.

    Tan X, Chen S, Zhou ZH, Zhang F (2006) Face recognition from a single image per person: a survey. Pattern Recognit. pp. 1725–1745

  35. 35.

    Tibshirani R (1996) Regression shrinkage and selection via the lasso. J. Royal Stat. Soc. Series. B. 58

  36. 36.

    Tolba, A., El-Baz, A., El-Harby, A.: Face recognition: a literature review. Int. J. Signal. Process. 2, 88–103 (2006)

  37. 37.

    Turker, M., Pentland, A.: Face recognition using eigenfaces. J. Cognitive Neurosci. 3(1), (1991)

  38. 38.

    Viola, P., Jones, M.: Rapid object detection using a boosted cascade of simple features. Proceedings IEEE Conference Computer Vision and Pattern Recognition 1, 511–518 (2001)

  39. 39.

    Wagner, A., Wright, J.: Toward a practical face recognition system: robust alignment and illumination by sparse representation. IEEE. Trans. Pattern. Anal. Mach. Intell. 34(2), 372–386 (2012)

  40. 40.

    Wright, J., Yang, A.Y., Ganesh, A., Sastry, S.S., Ma, Y.: Robust face recognition via sparse representation. IEEE. Trans. Pattern. Anal. Mach. Intell. 31(2), 210–227 (2008)

  41. 41.

    Xu, J., Yang, G., Yin, Y., Man, H., He, H.: Sparse-representation-based classification with structure-preserving dimension reduction. Cognitive Comput. 6(3), 608–621 (2014)

  42. 42.

    Xu, Y., Zhang, D., Yang, J., Yang, J.: A two-phase test sample sparse representation method for use with face recognition. IEEE. Trans. Circuits Syst. Video Technol. 21(9), 1255–1262 (2011)

  43. 43.

    Yan, S., Wang, H., Liu, J., Tang, X., Huang, T.: Misalignment-robust face recognition. IEEE. Trans. Image Process. 19(4), 1087–1096 (2010)

  44. 44.

    Yang J, Yu K, Huang T (2010) Efficient highly over-complete sparse coding using a mixture model. In: Proceedings of ECCV

  45. 45.

    Yang, J., Chu, D., Zhang, L., Xu, Y., Yang, J.: Sparse representation classifier steered discriminative projection with applications to face recognition. IEEE. Trans. Neural Netw. Learn. Syst. 24(7), 1023–1035 (2013)

  46. 46.

    Yang M, Zhang L (2010) Gabor feature based sparse representation for face recognition with gabor occlusion dictionary. In: Proceedings of ECCV, p. 448–461

  47. 47.

    Zhang L, Yang M, Feng X (2011) Sparse representation or collaborative representation: Which helps face recognition? Proceedings IEEE International Conference on Computer Vision, pp. 471–478

  48. 48.

    Zhang, S., Yao, H., Zhou, H., Sun, X., Liu, S.: Robust visual tracking based on online learning sparse representation. Neurocomputing 100, 31–40 (2013)

  49. 49.

    Zhao, W., Chellappa, R., Phillips, P., Rosenfeld, A.: Face recognition: a literature survey. ACM. Comput. Surveys 35(4), 399–458 (2003)

  50. 50.

    Zini, L., Noceti, N., Fusco, G., Odone, F.: Structured multi-class feature selection with an application to face recognition. Pattern Recognit. Lett. 55, 35–41 (2015)

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Correspondence to Raffaella Lanzarotti.

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Adamo, A., Grossi, G., Lanzarotti, R. et al. Robust face recognition using sparse representation in LDA space. Machine Vision and Applications 26, 837–847 (2015). https://doi.org/10.1007/s00138-015-0694-x

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  • Sparsity recovery
  • Face recognition
  • Fixed-point iteration schema
  • Nonlinear nonconvex mappings
  • SRC, CRC, LASSO, WSRC algorithms