Using Subspace Multiple Linear Regression for 3D Face Shape Prediction from a Single Image

  • Mario Castelán
  • Gustavo A. Puerto-Souza
  • Johan Van Horebeek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5876)


In this paper, we compare four different Subspace Multiple Linear Regression methods for 3D face shape prediction from a single 2D intensity image. This problem is situated within the low observation-to-variable ratio context, where the sample covariance matrix is likely to be singular. Lately, efforts have been directed towards latent-variable based methods to estimate a regression operator while maximizing specific criteria between 2D and 3D face subspaces. Regularization methods, on the other hand, impose a regularizing term on the covariance matrix in order to ensure numerical stability and to improve the out-of-training error. We compare the performance of three latent-variable based and one regularization approach, namely, Principal Component Regression, Partial Least Squares, Canonical Correlation Analysis and Ridge Regression. We analyze the influence of the different latent variables as well as the regularizing parameters in the regression process. Similarly, we identify the strengths and weaknesses of both regularization and latent-variable approaches for the task of 3D face prediction.


Latent Variable Ground Truth Partial Little Square Local Binary Pattern Canonical Correlation 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.
    Ahmed, A., Farag, A.: A New Statistical Model Combining Shape and Spherical Harmonics Illumination for Face Reconstruction. In: Bebis, G., Boyle, R., Parvin, B., Koracin, D., Paragios, N., Tanveer, S.-M., Ju, T., Liu, Z., Coquillart, S., Cruz-Neira, C., Müller, T., Malzbender, T. (eds.) ISVC 2007, Part I. LNCS, vol. 4841, pp. 531–541. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Atick, J., Griffin, P., Redlich, N.: Statistical approach to shape from shading: Reconstruction of three-dimensional face surfaces from single two-dimensional images. Neural Computation 8, 1321–1340 (1996)CrossRefGoogle Scholar
  3. 3.
    Blanz, V., Vetter, T.: A morphable model for the synthesis of 3d faces. In: Proc. SIGGRAPH, pp. 187–194 (1999)Google Scholar
  4. 4.
    Blanz, V., Vetter, T.: Face recognition based on fitting a 3d morphable model. IEEE Trans. Pattern Anal. Mach. Intell. 25(9), 1063–1074 (2003)CrossRefGoogle Scholar
  5. 5.
    Castelán, M., Smith, W., Hancock, E.: A coupled statistical model for face shape recovery from brightness images. IEEE Transactions on Image Processing 16(4), 1139–1151 (2007)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Castelán, M., Van Horebeek, J.: 3D face shape approximation from intensities using Partial Least Squares. In: Proc. IEEE CVPRW, pp. 1–6 (2008)Google Scholar
  7. 7.
    Cootes, T., Edwards, G., Taylor, C.: Active appearance models. In: Burkhardt, H., Neumann, B. (eds.) ECCV 1998. LNCS, vol. 1407, pp. 484–498. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  8. 8.
    Frank, I., Friedman, J.: A statistical view of some chemometrics regression tools. Technometrics 25(2), 109–135 (1993)CrossRefGoogle Scholar
  9. 9.
    Geladi, P., Kowalski, B.: Partial least squares regression: a tutorial. Anal. Chim. Acta 185, 1–17 (1986)CrossRefGoogle Scholar
  10. 10.
    Hoegaerts, L., Suykens, J.A.K., Vandewalle, J., De Moor, B.: Kernel PLS variants for regression. In: Proc. of the 11th European Symposium on Artificial Neural Networks, pp. 203–208 (2003)Google Scholar
  11. 11.
    Hotelling, H.: Relations between two sets of variates. Biometrika 8, 321–377 (1936)Google Scholar
  12. 12.
    Horn, B., Brooks, M.: Shape from Shading. MIT Press, Cambridge (1989)Google Scholar
  13. 13.
    Kemelmacher, I., Basri, R.: Molding Face Shapes by Example. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, pp. 277–288. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Sirovich, L., Kirby, M.: Low-dimensional Procedure for the Characterization of Human Faces. Journal of the Optical Society of America 4, 519–524 (1987)CrossRefGoogle Scholar
  15. 15.
    Lei, Z., Bai, Q., He, R., Li, S.Z.: Face Shape Recovery from a Single Image Using CCA Mapping between Tensor Spaces. In: Proc. IEEE CVPR, pp. 1–7 (2008)Google Scholar
  16. 16.
    Li, A., Shan, S., Chen, X., Chai, X., Gao, W.: Recovering 3D facial shape via coupled 2D/3D space learning. In: Proc. IEEE International Conference on Automatic Face and Gesture Recognition, pp. 1–6 (2008)Google Scholar
  17. 17.
    Reiter, M., Donner, R., Langs, G., Bischof, H.: 3d and Infrared Face Reconstruction from RGB Data Using Canonical Correlation Analysis. In: Proc. IEEE ICPR (2006)Google Scholar
  18. 18.
    Smith, W.A.P., Hancock, E.R.: Recovering Facial Shape Using a Statistical Model of Surface Normal Direction. IEEE Trans. Pattern Anal. Mach. Intell. 28(12), 1914–1930 (2006)CrossRefGoogle Scholar
  19. 19.
    Smith, W.A.P., Hancock, E.R.: Facial shape-from-shading and recognition using principal geodesic analysis and robust statistics. International Journal of Computer Vision 76(1), 71–91 (2008)CrossRefGoogle Scholar
  20. 20.
    Worthington, P.L., Hancock, E.R.: New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE Trans. on Pattern Analysis and Machine Intelligence 21(12), 1250–1267 (1999)CrossRefGoogle Scholar
  21. 21.
    Zheng, Y., Wang, Z.: Robust depth estimation for efficient 3D face reconstruction. In: Proc. IEEE ICIP, pp. 1516–1519 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mario Castelán
    • 1
  • Gustavo A. Puerto-Souza
    • 2
  • Johan Van Horebeek
    • 2
  1. 1.Grupo de Robótica y Manufactura AvanzadaCentro de Investigación y de Estudios Avanzados del I.P.N.Ramos ArizpeMéxico
  2. 2.Centro de Investigación en MatemáticasGuanajuatoMéxico

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