Probable and Improbable Faces

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


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.


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



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


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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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