Probable and Improbable Faces

Chapter
Part of the Mathematics for Industry book series (MFI, volume 4)

Abstract

The multivariate normal is widely used as the expected distribution of face shape. It has been used for face detection and tracking in computer vision, as a prior for facial animation editing in computer graphics, and as a model in psychological theory. In this contribution we consider the character of the multivariate normal in high dimensions, and show that these applications are not justified. While we provide limited evidence that facial proportions are not Gaussian, this is tangential to our conclusion: even if faces are truly “Gaussian”, maximum a posteriori and other applications and conclusions that assume that typical faces lie near the mean are not valid.

Keywords

Principal component analysis (PCA) Multivariate Gaussian (distribution) Blendshapes Mahalanobis distance Curse of dimensionality Active appearance model (AAM) Maximum a posteriori (MAP) 

Notes

Acknowledgments

This research is partially supported by the Japan Science and Technology Agency, CREST project. JPL acknowledges a helpful discussion with Marcus Frean.

References

  1. 1.
    Anjyo K, Todo H, Lewis J (2012) A practical approach to direct manipulation blendshapes. J Graph Tools 16(3):160–176Google Scholar
  2. 2.
    Blanz T, Vetter T (1999) A morphable model for the synthesis of 3d faces. In: Proceedings of ACM SIGGRAPH, pp 187–194Google Scholar
  3. 3.
    Cootes TF, Edwards GJ, Taylor CJ (1998) Active appearance models. In: Burkhardt H, Neumann B (eds) ECCV’98: computer vision. Proceedings of the 5th European conference on computer vision, Volume II. Lecture notes in computer science vol 1407, Springer, BerlinGoogle Scholar
  4. 4.
    Lewis J, Anjyo K (2010) Direct manipulation blendshapes. Comput Graph Appl (special issue: Digital Human Faces) 30(4):42–50CrossRefGoogle Scholar
  5. 5.
    Li H, Yu J, Ye Y, Bregler C (2013) Realtime facial animation with on-the-fly correctives. ACM Trans Graph 42:1–10Google Scholar
  6. 6.
    MacKay DJ (1996) Hyperparameters: Optimize, or integrate out? In: Heidbreder G (ed) Maximum entropy and Bayesian methods. Springer, New York, pp 43–59Google Scholar
  7. 7.
    Matthews I, Xiao J, Baker S (2006) On the dimensionality of deformable face models. CMU-RI-TR-06-12Google Scholar
  8. 8.
    Meytlis M, Sirovich L (2007) On the dimensionality of face space. IEEE Trans Pattern Anal Mach Intell 29(7):1262–1267CrossRefGoogle Scholar
  9. 9.
    Mo Z, Lewis J, Neumann U (2004) Face inpainting with local linear representations. In: BMVC, BMVA, pp 347–356Google Scholar
  10. 10.
    Patel A, Smith W (2009) 3D morphable face models revisited. In: Computer vision and pattern recognition (CVPR), IEEE Computer Society, Los Alamitos, CA, USA, pp 1327–1334Google Scholar
  11. 11.
    Penev PS, Sirovich L (2000) The global dimensionality of face space. In: Proceedings of 4th international conference automatic face and gesture recognition, pp 264–270Google Scholar
  12. 12.
    Phillips PJ, Wechsler H, Huang J, Rauss P (1998) The feret database and evaluation procedure for face recognition algorithms. Image Vis Comput J 16(5):295–306CrossRefGoogle Scholar
  13. 13.
    Seo J, Irving G, Lewis JP, Noh J (2011) Compression and direct manipulation of complex blendshape models. ACM Trans Graph 30(6):164:1–164:10CrossRefGoogle Scholar
  14. 14.
    Valentine T (2012) Face-space models of face recognition. In: Wenger M, Townsend J (eds) Computational, geometric, and process perspectives on facial cognition: contexts and challenges, Scientific Psychology Series. Taylor & Francis, OxfordGoogle Scholar
  15. 15.
    Vlasic D, Brand M, Pfister H, Popovic J (2005) Face transfer with multilinear models. ACM Trans Graph 24(3):426–433CrossRefGoogle Scholar
  16. 16.
    Wang J (2011) Geometric structure of high-dimensional data and dimensionality reduction. Springer-Verlag, Berlin, HeidelbergGoogle Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  • J. P. Lewis
    • 1
  • Zhenyao Mo
    • 2
  • Ken Anjyo
    • 3
  • Taehyun Rhee
    • 4
  1. 1.School of Engineering and Computer ScienceVictoria University of Wellington/JST CRESTWellingtonNew Zealand
  2. 2.Google Inc.Mountain ViewUSA
  3. 3.OLM Digital, Inc./JST CRESTSetagaya-kuJapan
  4. 4.School of Engineering and Computer ScienceVictoria University of WellingtonWellingtonNew Zealand

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