Combining Probabilistic Shape-from-Shading and Statistical Facial Shape Models

  • Touqeer Ahmad
  • Richard C. Wilson
  • William A. P. Smith
  • Tom S. F. Haines
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6978)


Shape-from-shading is an interesting approach to the problem of finding the shape of a face because it only requires one image and no subject participation. However, SfS is not accurate enough to produce good shape models. Previously, SfS has been combined with shape models to produce realistic face reconstructions. In this work, we aim to improve the quality of such models by exploiting a probabilistic SfS model based on Fisher-Bingham 8-parameter distributions (FB8). The benefits are two-fold; firstly we can correctly weight the contributions of the data and model where the surface normals are uncertain, and secondly we can locate areas of shadow and facial hair using inconsistencies between the data and model. We sample the FB8 distributions using a Gibbs sampling algorithm. These are then modelled as Gaussian distributions on the surface tangent plane defined by the model. The shape model provides a second Gaussian distribution describing the likely configurations of the model; these distributions are combined on the tangent plane of the directional sphere to give the most probable surface normal directions for all pixels. The Fisher criterion is used to locate inconsistencies between the two distributions and smoothing is used to deal with outliers originating in the shadowed and specular regions. A surface height model is then used to recover surface heights from surface normals. The combined approach shows improved results over the case when only surface normals from shape-from-shading are used.


Tangent Space Surface Normal Tangent Plane Shape Model Facial Hair 
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.


  1. 1.
    Haines, T.S.F., Wilson, R.C.: Belief propagation with directional statistics for solving the shape-from-shading problem. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 780–791. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Lee, K.M., Kuo, C.J.: Shape from shading with perspective projection. CVGIP: Image Understanding 59(2), 202–212 (1994)CrossRefGoogle Scholar
  3. 3.
    Worthington, P.L., Hancock, E.R.: New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE Trans. Pattern Anal. Intell. 21(12), 1250–1267 (1999)CrossRefGoogle Scholar
  4. 4.
    Smith, W.A.P.: Statistical Methods For Facial Shape-from-Shading and Recognition. PhD thesis, University of York (2007)Google Scholar
  5. 5.
    USF HumanID 3D Face Database, Courtesy of Sundeep. Sarkar, University of South Florida, Tampa, FLGoogle Scholar
  6. 6.
    Blanz, V., Vetter, T.: Face Recognition based on fitting a 3D morphabale model. IEEE Trans. Pattern Anal. Intell. 25(9), 1063–1074 (2003)CrossRefGoogle Scholar
  7. 7.
    Fletcher, P.T., Joshi, S., Lu, C., Pizer, S.M.: Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Trans. Med. Imaging. 23(8), 995–1005 (2004)CrossRefGoogle Scholar
  8. 8.
    Pennec, X.: Probabilities and statistics on Riemannian manifolds: basic tools for geometric measurements. In: Proc. IEEE Workshop on Nonlinear Signal and Image Processing (1999)Google Scholar
  9. 9.
    Kume, A., Walker, S.G.: On the Fisher-Bingham distribution. Stat. and Comput. 19, 167–172 (2009)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Mardia, K.V., Jupp, P.E.: Directional Statistics. John Wiley and Sons Ltd., Chichester (2000)zbMATHGoogle Scholar
  11. 11.
    Felzenszwalb, P.F., Huttenlocher, D.P.: Efficient belief propagation for early vision. In: Computer Vision and Pattern Recognition, vol. 1, pp. 261–268 (2004)Google Scholar
  12. 12.
    Phillips, J.M., Liu, R., Tomasi, C.: Outlier Robust ICP for Minimizing Fractional RMSD. In: 6th International Conference on 3-D Digital Imaging and Modeling, pp. 427–434 (2007)Google Scholar
  13. 13.
    Luebke, K., Weihs, C.: Improving Feature Extraction by Replacing the Fisher Criterion by an Upper Error Bound. Pattern Recognition 38(2005), 2220–2223 (2005)CrossRefGoogle Scholar
  14. 14.
    Maciej, S., Witold, M.: Versatile Pattern Recognition System Based on Fisher Criterion. In: Proceedings of the KOSYR, pp. 343–348 (2003)Google Scholar
  15. 15.
    William, A.P.: Smith and Edwin R. Hancock. Facial Shape-from-shading and Recognition Using Principal Geodesic Analysis and Robust Statistics. International Journal of Computer Vision 76(1), 71–91 (2008)Google Scholar
  16. 16.
    Prados, E., Faugeras, O.: Unifying approaches and removing unrealistic assumptions in shape from shading: Mathematics can help. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 141–154. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Zhao, W.Y., Chellappa, R.: Symmetric shape-from-shading using self-ratio image. International Journal of Computer Vision 45, 55–75 (2001)CrossRefzbMATHGoogle Scholar
  18. 18.
    Samaras, D., Metaxas, D.: Illumination constraints in deformable models for shape and light direction estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(2), 247–264 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Touqeer Ahmad
    • 1
    • 2
  • Richard C. Wilson
    • 1
  • William A. P. Smith
    • 1
  • Tom S. F. Haines
    • 3
  1. 1.Department of Computer ScienceThe University of YorkUK
  2. 2.School of Science and EngineeringLUMSPakistan
  3. 3.Queen Mary University of LondonUK

Personalised recommendations