Skip to main content
SpringerLink
Log in

The Perspective Face Shape Ambiguity

  • Conference paper
  • First Online:
Perspectives in Shape Analysis

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

When a face is viewed under perspective projection, its shape (i.e. the 2D position of features) changes dramatically as the distance between face and camera varies. This causes substantial variation in appearance which is significant enough to disrupt human recognition of unfamiliar faces. However, a face viewed at any distance is still perceived as natural and humans are bad at interpreting the subject-camera distance given only a face image. We show that perspective viewing of faces leads to an ambiguity. Namely, that observed configurational information (position of projected vertices) and shading can be explained by a continuous class of possible faces. To demonstrate the ambiguity, we propose a novel method for efficiently fitting a 3D morphable model to 2D vertex positions when the subject-camera distance is known. By varying this distance, we obtain a subspace of faces, all of which are consistent with the observed data. We additionally show that faces within this subspace can all produce approximately the same shading pattern via a spherical harmonic lighting model.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Albrecht, T., Knothe, R., Vetter, T.: Modeling the remaining flexibility of partially fixed statistical shape models. In: Proceedings of the Workshop on the Mathematical Foundations of Computational Anatomy (2008)

    Google Scholar 

  2. Aldrian, O., Smith, W.A.P.: Inverse rendering of faces with a 3D morphable model. IEEE Trans. Pattern Anal. Mach. Intell. 35 (5), 1080–1093 (2013)

    Article  Google Scholar 

  3. Amberg, B., Blake, A., Fitzgibbon, A., Romdhani, S., Vetter, T.: Reconstructing high quality face-surfaces using model based stereo. In: Proceedings of the ICCV, Rio de Janeiro (2007)

    Book  Google Scholar 

  4. Basri, R., Jacobs, D.W.: Lambertian reflectance and linear subspaces. IEEE Trans. Pattern Anal. Mach. Intell. 25 (2), 218–233 (2003)

    Article  Google Scholar 

  5. Belhumeur, P.N., Kriegman, D.J., Yuille, A.L.: The bas–relief ambiguity. Int. J. Comput. Vis. 35 (1), 33–44 (1999)

    Article  Google Scholar 

  6. Blanz, V., Mehl, A., Vetter, T., Seidel, H.P.: A statistical method for robust 3D surface reconstruction from sparse data. In: Proceedings of the 3DPVT, Thessaloniki, pp. 293–300 (2004)

    Google Scholar 

  7. Blanz, V., Vetter, T.: Face recognition based on fitting a 3D morphable model. IEEE Trans. Pattern Anal. Mach. Intell. 25 (9), 1063–1074 (2003)

    Article  Google Scholar 

  8. Brunton, A., Salazar, A., Bolkart, T., Wuhrer, S.: Review of statistical shape spaces for 3D data with comparative analysis for human faces. Comput. Vis. Image Underst. 128, 1–17 (2014)

    Article  Google Scholar 

  9. Bryan, R., Perona, P., Adolphs, R.: Perspective distortion from interpersonal distance is an implicit visual cue for social judgments of faces. PloS one 7 (9), e45,301 (2012)

    Article  Google Scholar 

  10. Burgos-Artizzu, X.P., Ronchi, M.R., Perona, P.: Distance estimation of an unknown person from a portrait. In: Proceedings of the ECCV, Zurich, pp. 313–327 (2014)

    Google Scholar 

  11. Cootes, T.F., Edwards, G.J., Taylor, C.J.: Active appearance models. In: Proceedings of the ECCV, Freiburg, pp. 484–498 (1998)

    Google Scholar 

  12. Flores, A., Christiansen, E., Kriegman, D., Belongie, S.: Camera distance from face images. In: Proceedings of the ISVC, Rethymnon, pp. 513–522 (2013)

    Google Scholar 

  13. Georghiades, A., Belhumeur, P., Kriegman, D.: From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Pattern Anal. Mach. Intell. 23 (6), 643–660 (2001)

    Article  Google Scholar 

  14. Gordon, C.C., Churchill, T., Clauser, C.E., Bradtmiller, B., McConville, J.T.: Anthropometric survey of US army personnel: methods and summary statistics 1988. Technical report NATICK/TR-89/044, DTIC Document (1989)

    Google Scholar 

  15. Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge university press, Cambridge/New York (2003)

    MATH  Google Scholar 

  16. Hill, H., Bruce, V.: A comparison between the hollow–face and ‘hollow–potato’ illusions. Perception 23, 1335–1337 (1994)

    Article  Google Scholar 

  17. Keller, M., Knothe, R., Vetter, T.: 3D reconstruction of human faces from occluding contours. In: Proceedings of the Mirage, Rocquencourt, pp. 261–273 (2007)

    Google Scholar 

  18. Kleinberg, K.F., Vanezis, P., Burton, A.M.: Failure of anthropometry as a facial identification technique using high-quality photographs. J. Forensic Sci. 52 (4), 779–783 (2007)

    Article  Google Scholar 

  19. Knothe, R., Romdhani, S., Vetter, T.: Combining PCA and LFA for surface reconstruction from a sparse set of control points. In: Proceedings of the International Conference on Automatic Face and Gesture Recognition, Southampton, pp. 637–644 (2006)

    Google Scholar 

  20. Latto, R., Harper, B.: The non-realistic nature of photography: further reasons why Turner was wrong. Leonardo 40 (3), 243–247 (2007)

    Article  Google Scholar 

  21. Lepetit, V., Moreno-Noguer, F., Fua, P.: EPnP: an accurate O(n) solution to the PnP problem. Int. J. Comput. Vis. 81 (2), 155–166 (2009)

    Article  Google Scholar 

  22. Liu, C.H., Chaudhuri, A.: Face recognition with perspective transformation. Vis. Res. 43 (23), 2393—2402 (2003)

    Article  Google Scholar 

  23. Liu, C.H., Ward, J.: Face recognition in pictures is affected by perspective transformation but not by the centre of projection. Perception 35 (12), 1637–1650 (2006)

    Article  Google Scholar 

  24. Lüthi, M., Albrecht, T., Vetter, T.: Probabilistic modeling and visualization of the flexibility in morphable models. In: Proceedings of the Thirteenth IMA Conference on Mathematics of Surfaces, York, pp. 251–264 (2009)

    Google Scholar 

  25. Patel, A., Smith, W.A.P.: 3D morphable face models revisited. In: Proceedings of the CVPR, Miami, pp. 1327–1334 (2009)

    Google Scholar 

  26. Paysan, P., Knothe, R., Amberg, B., Romdhani, S., Vetter, T.: A 3D face model for pose and illumination invariant face recognition. In: Proceedings of the IEEE International Conference on Advanced Video and Signal Based Surveillance (2009)

    Book  Google Scholar 

  27. Perona, P.: A new perspective on portraiture. J. Vis. 7 (9), 992–992 (2007)

    Article  Google Scholar 

  28. Porter, G., Doran, G.: An anatomical and photographic technique for forensic facial identification. Forensic Sci. Int. 114 (2), 97–105 (2000)

    Article  Google Scholar 

  29. Sagonas, C., Tzimiropoulos, G., Zafeiriou, S., Pantic, M.: 300 faces in-the-wild challenge: the first facial landmark localization challenge. In: Proceedings of the ICCV Workshop on Automatic Facial Landmark Detection in-the-Wild Challenge, Sydney, pp. 397–403 (2013)

    Google Scholar 

Download references

Acknowledgements

I would like to thank the reviewers for their thoughtful comments which helped improve the chapter significantly.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of York, York, UK

    William A. P. Smith

Authors
  1. William A. P. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to William A. P. Smith .

Editor information

Editors and Affiliations

  1. Institute for Applied Mathematics and Scientific Computing, Brandenburg University of Technology, Cottbus, Germany

    Michael Breuß

  2. Israel Institute of Technology Technion, Haifa, Israel

    Alfred Bruckstein

  3. School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece

    Petros Maragos

  4. INRIA, Grenoble Rhône-Alpes, Saint Ismier, France

    Stefanie Wuhrer

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Smith, W.A.P. (2016). The Perspective Face Shape Ambiguity. In: Breuß, M., Bruckstein, A., Maragos, P., Wuhrer, S. (eds) Perspectives in Shape Analysis. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-24726-7_14

Download citation

Publish with us

Policies and ethics

Search

Navigation