Learning the Face Prior for Bayesian Face Recognition

  • Chaochao Lu
  • Xiaoou Tang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8692)


For the traditional Bayesian face recognition methods, a simple prior on face representation cannot cover large variations in facial poses, illuminations, expressions, aging, and occlusions in the wild. In this paper, we propose a new approach to learn the face prior for Bayesian face recognition. First, we extend Manifold Relevance Determination to learn the identity subspace for each individual automatically. Based on the structure of the learned identity subspaces, we then propose to estimate Gaussian mixture densities in the observation space with Gaussian process regression. During the training of our approach, the leave-set-out algorithm is also developed for overfitting avoidance. On extensive experimental evaluations, the learned face prior can improve the performance of the traditional Bayesian face and other related methods significantly. It is also proved that the simple Bayesian face method with the learned face prior can handle the complex intra-personal variations such as large poses and large occlusions. Experiments on the challenging LFW benchmark shows that our algorithm outperforms most of the state-of-art methods.


Face Recognition Face Image Observation Space Fisher Vector Probabilistic Linear Discriminant Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Belhumeur, P.N., Hespanha, J.P., Kriegman, D.: Eigenfaces vs. fisherfaces: Recognition using class specific linear projection. TPAMI (1997)Google Scholar
  2. 2.
    Berg, T., Belhumeur, P.N.: Tom-vs-pete classifiers and identity-preserving alignment for face verification. In: BMVC (2012)Google Scholar
  3. 3.
    Bishop, C.M.: Pattern recognition and machine learning (2006)Google Scholar
  4. 4.
    Cao, X., Wipf, D., Wen, F., Duan, G., Sun, J.: A practical transfer learning algorithm for face verification. In: ICCV (2013)Google Scholar
  5. 5.
    Cao, Z., Yin, Q., Tang, X., Sun, J.: Face recognition with learning-based descriptor. In: CVPR (2010)Google Scholar
  6. 6.
    Chai, X., Shan, S., Chen, X., Gao, W.: Locally linear regression for pose-invariant face recognition. TIP (2007)Google Scholar
  7. 7.
    Chen, D., Cao, X., Wang, L., Wen, F., Sun, J.: Bayesian face revisited: A joint formulation. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part III. LNCS, vol. 7574, pp. 566–579. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Chen, D., Cao, X., Wen, F., Sun, J.: Blessing of dimensionality: High-dimensional feature and its efficient compression for face verification. In: CVPR (2013)Google Scholar
  9. 9.
    Damianou, A., Ek, C., Titsias, M.K., Lawrence, N.D.: Manifold relevance determination. In: ICML (2012)Google Scholar
  10. 10.
    Gross, R., Matthews, I., Baker, S.: Appearance-based face recognition and light-fields. TPAMI (2004)Google Scholar
  11. 11.
    Gross, R., Matthews, I., Cohn, J., Kanade, T., Baker, S.: Multipie. Image and Vision Computing (2010)Google Scholar
  12. 12.
    Huang, G.B., Ramesh, M., Berg, T., Learned-Miller, E.: Labeled faces in the wild: A database for studying face recognition in unconstrained environments. Tech. rep., University of Massachusetts, Amherst (2007)Google Scholar
  13. 13.
    Ioffe, S.: Probabilistic linear discriminant analysis. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006, Part IV. LNCS, vol. 3954, pp. 531–542. Springer, Heidelberg (2006)Google Scholar
  14. 14.
    Kan, M., Shan, S., Zhang, H., Lao, S., Chen, X.: Multi-view discriminant analysis. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part I. LNCS, vol. 7572, pp. 808–821. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  15. 15.
    Kumar, N., Berg, A.C., Belhumeur, P.N., Nayar, S.K.: Attribute and Simile Classifiers for Face Verification. In: ICCV (2009)Google Scholar
  16. 16.
    Lawrence, N.D.: Gaussian process latent variable models for visualisation of high dimensional data. In: NIPS (2003)Google Scholar
  17. 17.
    Li, A., Shan, S., Gao, W.: Coupled bias–variance tradeoff for cross-pose face recognition. TIP (2012)Google Scholar
  18. 18.
    Li, H., Hua, G., Lin, Z., Brandt, J., Yang, J.: Probabilistic elastic matching for pose variant face verification. In: CVPR (2013)Google Scholar
  19. 19.
    Li, P., Fu, Y., Mohammed, U., Elder, J.H., Prince, S.J.: Probabilistic models for inference about identity. TPAMI (2012)Google Scholar
  20. 20.
    Lu, C., Tang, X.: Surpassing human-level face verification performance on lfw with gaussianface. arXiv preprint arXiv:1404.3840 (2014)Google Scholar
  21. 21.
    Lu, C., Zhao, D., Tang, X.: Face recognition using face patch networks. In: ICCV (2013)Google Scholar
  22. 22.
    Martinez, A.M.: The ar face database. CVC Technical Report (1998)Google Scholar
  23. 23.
    Moghaddam, B., Jebara, T., Pentland, A.: Bayesian face recognition. Pattern Recognition (2000)Google Scholar
  24. 24.
    Nabney, I.: Netlab: algorithms for pattern recognition. Springer (2002)Google Scholar
  25. 25.
    Nickisch, H., Rasmussen, C.E.: Gaussian mixture modeling with gaussian process latent variable models. In: Goesele, M., Roth, S., Kuijper, A., Schiele, B., Schindler, K. (eds.) DAGM 2010. LNCS, vol. 6376, pp. 272–282. Springer, Heidelberg (2010)Google Scholar
  26. 26.
    Ojala, T., Pietikainen, M., Maenpaa, T.: Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. TPAMI (2002)Google Scholar
  27. 27.
    Prince, S.J., Elder, J.H.: Probabilistic linear discriminant analysis for inferences about identity. In: ICCV (2007)Google Scholar
  28. 28.
    Prince, S.J., Warrell, J., Elder, J.H., Felisberti, F.M.: Tied factor analysis for face recognition across large pose differences. TPAMI (2008)Google Scholar
  29. 29.
    Quinonero-Candela, J., Girard, A., Rasmussen, C.E.: Prediction at an Uncertain Input for Gaussian Processes and Relevance Vector Machines Application to Multiple-Step Ahead Time-Series Forecasting. IMM, Informatik og Matematisk Modelling, DTU (2003)Google Scholar
  30. 30.
    Rasmussen, C.E., Williams, C.K.: Gaussian processes for machine learning (2006)Google Scholar
  31. 31.
    Simonyan, K., Parkhi, O.M., Vedaldi, A., Zisserman, A.: Fisher vector faces in the wild. In: BMVC (2013)Google Scholar
  32. 32.
    Sun, Y., Wang, X., Tang, X.: Deep learning face representation by joint identification-verification. arXiv preprint arXiv:1406.4773 (2014)Google Scholar
  33. 33.
    Sun, Y., Wang, X., Tang, X.: Deep learning face representation from predicting 10,000 classes. In: CVPR (2014)Google Scholar
  34. 34.
    Taigman, Y., Yang, M., Ranzato, M., Wolf, L.: Deepface: Closing the gap to human-level performance in face verification. In: CVPR (2014)Google Scholar
  35. 35.
    Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology) (1999)Google Scholar
  36. 36.
    Turk, M., Pentland, A.: Eigenfaces for recognition. Journal of cognitive neuroscience (1991)Google Scholar
  37. 37.
    Wang, X., Tang, X.: Bayesian face recognition using gabor features. In: ACM SIGMM Workshop on Biometrics Methods and Applications (2003)Google Scholar
  38. 38.
    Wang, X., Tang, X.: A unified framework for subspace face recognition. TPAMI (2004)Google Scholar
  39. 39.
    Wang, X., Tang, X.: Subspace analysis using random mixture models. In: CVPR (2005)Google Scholar
  40. 40.
    Wasserman, L.: All of nonparametric statistics. Springer (2006)Google Scholar
  41. 41.
    Wright, J., Yang, A., Ganesh, A., Sastry, S., Ma, Y.: Robust face recognition via sparse representation. TPAMI (2009)Google Scholar
  42. 42.
    Yang, M., Zhang, L.: Gabor feature based sparse representation for face recognition with gabor occlusion dictionary. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part VI. LNCS, vol. 6316, pp. 448–461. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  43. 43.
    Zhou, Z., Wagner, A., Mobahi, H., Wright, J., Ma, Y.: Face recognition with contiguous occlusion using markov random fields. In: ICCV (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Chaochao Lu
    • 1
  • Xiaoou Tang
    • 1
  1. 1.Department of Information EngineeringThe Chinese University of Hong KongChina

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