Skip to main content
SpringerLink
Log in

Robust face recognition using sparse representation in LDA space

  • Short Paper
  • Published:
Machine Vision and Applications Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Notes

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

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

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

  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.

References

  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. 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. 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)

    Google Scholar 

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

    Article  Google Scholar 

  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)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  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. 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)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

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

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

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

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

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

    Google Scholar 

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

  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. 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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics “Federigo Enriques”, University of Milan, Via Saldini 50, 20133, Milan, Italy

    Alessandro Adamo

  2. Department of Computer Science, University of Milan, Via Comelico 39, 20135, Milan, Italy

    Giuliano Grossi, Raffaella Lanzarotti & Jianyi Lin

Authors
  1. Alessandro Adamo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giuliano Grossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raffaella Lanzarotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jianyi Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raffaella Lanzarotti.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00138-015-0694-x

Keywords

Search

Navigation