Skip to main content
SpringerLink
Log in

Method of Modelling Facial Action Units Using Partial Differential Equations

  • Chapter
  • First Online:
Advances in Face Detection and Facial Image Analysis

Abstract

In this paper we discuss a novel method of mathematically modelling facial action units for accurate representation of human facial expressions in 3-dimensions. Our method utilizes the approach of Facial Action Coding System (FACS). It is based on a boundary-value approach, which utilizes a solution to a fourth order elliptic Partial Differential Equation (PDE) subject to a suitable set of boundary conditions. Here the PDE surface generation method for human facial expressions is utilized in order to generate a wide variety of facial expressions in an efficient and realistic way. For this purpose, we identify a set of boundary curves corresponding to the key features of the face which in turn define a given facial expression in 3-dimensions. The action units (AUs) relating to the FACS are then efficiently represented in terms of Fourier coefficients relating to the boundary curves which enables us to store both the face and the facial expressions in an efficient way.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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. I.A. Essa, A.P. Pentland, Coding, analysis, interpretation, and recognition of facial expressions. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 757–763 (1997)

    Article  Google Scholar 

  2. H. Ugail, Partial Differential Equation for Geometric Design (Springer, London, 2011)

    Book  MATH  Google Scholar 

  3. Y. Sheng, P. Willis, G. Castro, H. Ugail, Facial geometry parameterisation based on partial differential equations. Math. Comput. Model. 54(5–6), 1536–1548 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Noh, U. Neumann, A survey of facial modeling and animation techniques. USC Technical Report (1998), pp. 99–705

    Google Scholar 

  5. F.I. Parke, Computer generated animation of faces, in ACM 72, Proceedings of the ACM Annual Conference, vol. 1 (1972), pp. 451–457

    Google Scholar 

  6. D. Terzopoulus, K. Waters, Physically-based facial modeling. J. Vis. Comput. Animat. 1(4), 73–80 (1990)

    Article  Google Scholar 

  7. F.I. Parke, Parameterized models for facial animation. IEEE Comput. Graph. Appl. 2(9), 61–68 (1982)

    Article  Google Scholar 

  8. T. Beier, S. Neely, Feature-based image metamorphosis. ACM SIGGRAPH Comput. Graph. 26, 35–42 (1992)

    Article  Google Scholar 

  9. M. Oka, K. Tsutsui, A. Ohba, Y. Karauchi, T. Tago, Real-time manipulation of texture-mapped surfaces. ACM Comput. Graph. 21(4), 181–188 (1987)

    Article  Google Scholar 

  10. Y. He, Y. Zhao, D. Jiang, H. Sahli, Speech driven photo-realistic face animation with mouth and jaw dynamics, in Signal and Information Processing Association Annual Summit and Conference (APSIPA), 2013 Asia-Pacific. IEEE, Kaohsiung (ACM, 2013), pp. 1–4

    Google Scholar 

  11. V. Blanz, T. Vetter, A morphable model for the synthesis of 3D faces, in Proc. 26th Annu. Conf. Comput. Graph. Interact. Tech., SIGGRAPH 99 (1999), pp. 187–194

    Google Scholar 

  12. L. Zhang, S. Member, D. Samaras, Face recognition from a single training image under arbitrary unknown lighting using spherical harmonics. IEEE Trans. Pattern Anal. Mach. Intell. 28(3), 351–363 (2006)

    Article  Google Scholar 

  13. B. Moghaddam, J. Lee, H. Pfister, R. Machiraju, Model-based 3D face capture with shape-from-silhouettes, in IEEE Work Analysis and Modelling of Faces and Gesture Recognition (2003), pp. 20–27

    Google Scholar 

  14. S. Romdhani, T. Vetter, Estimating 3D shape and texture using pixel intensity, edges, specular highlights, texture constraints and a prior, in IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit., vol. 2 (2005), pp. 20–27

    Google Scholar 

  15. H. Yu, O.G.B. Garrod, P.G. Schyns, Perception-driven facial expression synthesis. Comput. Graph. 36(3), 152–162 (2012)

    Article  Google Scholar 

  16. S. Villagrasa, A.S. Sánchez, Face! 3D facial animation system based on facs, in IV Iberoamerican Symposium in Computer Graphics - SIACG 2009 (2009), pp. 202–207

    Google Scholar 

  17. A. Wojdel, L.J.M. Rothkrantz, Parametric generation of facial expressions based on FACS. Comput. Graph. Forum 24(4), 743–757 (2005)

    Article  Google Scholar 

  18. P. Havaldar, Performance driven facial animation, in ACM SIGGRAPH 2006 (2006), pp. 1–20

    Google Scholar 

  19. M. Hoch, G. Fleischmann, B. Girod, Modeling and animation of facial expressions based on B-splines. Vis. Comput. 11(2), 87–95 (1994)

    Article  Google Scholar 

  20. D. Huang, H. Yan, Modeling and animation of human expressions using NURBS curves based on facial anatomy. Signal Process. Image Commun. 17(6), 457–465 (2002)

    Article  Google Scholar 

  21. D. Huang, H. Yan, NURBS curve controlled modelling for facial animation. Comput. Graph. 27(3), 373–385 (2003)

    Article  Google Scholar 

  22. E. Elyan, H. Ugail, Reconstruction of 3D human facial images using partial differential equations. J. Comput. 2(8), 1–8 (2007)

    Article  Google Scholar 

  23. G.G. Castro, H. Ugail, P. Willis, Y. Sheng, Parametric representation of facial expressions on PDE-based surfaces, in Proc. of the 8th IASTED International Conference Visualization, Imaging, and Image Processing (VIIP 2008) (2008), pp. 402–407

    Google Scholar 

  24. G.G. Castro, H. Ugail, P. Willis, I. Palmer, A survey of partial differential equations in geometric design. Vis. Comput. 24(3), 213–225 (2008)

    Article  Google Scholar 

  25. E. Elyan, H. Ugail, Interactive surface design and manipulation using PDE-method through autodesk maya plug-in, in International Conference on Cyberworlds 2009 (2009), pp. 119–125

    Google Scholar 

  26. H. Ugail, Method of trimming PDE surfaces. Comput. Graph. 30(2), 225–232 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. M.I.G. Bloor, M.J. Wilson, Spectral approximations to PDE surfaces. Comput. Aided Des. 28(2), 145–152 (1996)

    Article  Google Scholar 

  28. Y. Sheng, P. Willis, G. Castro, H. Ugail, PDE face: a novel 3D face model, in Proc. of the 8th IASTED International Conference Visualization, Imaging, and Image Processing (VIIP 2008) (2008), pp. 408–415

    Google Scholar 

  29. D. Cosker, E. Krumhuber, A. Hilton, A FACS valid 3D dynamic action unit database with applications to 3D dynamic morphable facial modeling, in IEEE International Conference on Computer Vision (ICCV) 2011. IEEE, Barcelona (Elsevier, 2011), pp. 2296–2303

    Google Scholar 

  30. Y. Sheng, P. Willis, G. Castro, H. Ugail, PDE-based facial animation: making the complex simple, in Advances in Visual Computing. Lecture Notes in Computer Science, vol. 5359 (Springer, Heidelberg, Germany, 2008), pp. 723–732

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Visual Computing, School of Engineering and Informatics, University of Bradford, Bradford, BD7 1DP, UK

    Hassan Ugail & Nur Baini Ismail

Authors
  1. Hassan Ugail
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nur Baini Ismail
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hassan Ugail .

Editor information

Editors and Affiliations

  1. Automatic Control, Silesian University of Technology, Kawulok, Poland

    Michal Kawulok

  2. Computer Science, Louisiana State University in Shreveport, Shreveport, Louisiana, USA

    M. Emre Celebi

  3. Silesian University of Technology, Gliwice, Poland

    Bogdan Smolka

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Ugail, H., Ismail, N.B. (2016). Method of Modelling Facial Action Units Using Partial Differential Equations. In: Kawulok, M., Celebi, M., Smolka, B. (eds) Advances in Face Detection and Facial Image Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-25958-1_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25958-1_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25956-7

  • Online ISBN: 978-3-319-25958-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation