Advertisement

Facial Shape Spaces from Surface Normals

  • Simone Ceolin
  • William A. P. Smith
  • Edwin Hancock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5112)

Abstract

In this paper, we draw on ideas from the field of statistical shape analysis to construct shape-spaces that span facial expressions and gender, and use the resulting shape-model to perform face recognition under varying expression and gender. Our novel contribution is to show how to construct shape-spaces over fields of surface normals rather than Cartesian landmark points. According to this model face needle-maps (or fields of surface normals) are points in a high-dimensional manifold referred to as a shape-space. We compute geodesic distances to compare the similarity between faces and gender difference.

Keywords

Shape-Space Surface Normals Geodesic distance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bookstein, F.L.: The measurement of biological shape and shape change. Lecture Notes in Biomathematics, vol. 24. Springer, Berlin (1978)MATHGoogle Scholar
  2. 2.
    Dryden, I.L., Mardia, K.V.: Statistical Shape Analysis. Wiley Series in Probability and Statistics (1998)Google Scholar
  3. 3.
    Fisher, N.I.: Spherical medians. J. R. Statist. Soc. B 47(2), 342–348 (1985)MATHGoogle Scholar
  4. 4.
    Kendall, D.G.: Shape manifolds, procrustean metrics, and complex projective spaces. Bulletin of the London Mathematical Society 16(2), 81–121 (1984)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Kendall, W.S.: The diffusion of shape. Advances in Applied Probability 3, 428–430 (1977)CrossRefGoogle Scholar
  6. 6.
    Le, H., Small, C.G.: Multidimensional scaling of simplex shapes. Pattern Recognition 32(9), 1601–1613 (1999)CrossRefGoogle Scholar
  7. 7.
    Mardia, K.V., Jupp, P.E.: Directional Statistics. John Wiley and Sons, Chichester (2000)MATHGoogle 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.
    Small, C.G., Le, H.: The statistical analysis of dynamic curves and sections. Pattern Recognition 25, 1597–1609 (2002)CrossRefGoogle Scholar
  10. 10.
    Small, C.G.: The Statistical Theory of Shape. Springer, Heidelberg (1996)MATHGoogle Scholar
  11. 11.
    Smith, W., Hancock, E.R.: Recovering facial shape using a statistical model of surface normal direction. IEEE Transactions on Pattern Analysis and Machine Intelligence 28, 1914–1930 (2006)CrossRefGoogle Scholar
  12. 12.
    Zhang, J., Zhang, X., Krim, H., Walter, G.G.: Object recognition and recognition in shape spaces. Pattern Recognition 36, 1143–1154 (2003)CrossRefGoogle Scholar
  13. 13.
    Ziezold, H.: On expected figures and a strong law of large numbers for random elements in quasi-metric spaces. In: Trans. 7th Praque Conf. Information Theory, Stat. Dec. Func, Random Processes, vol. A, pp. 491–510 (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Simone Ceolin
    • 1
  • William A. P. Smith
    • 1
  • Edwin Hancock
    • 1
  1. 1.Computer Vision and Pattern Recognition Group,Computer ScienceUniversity of York HeslingtonYorkUnited Kingdom

Personalised recommendations