Method of Modelling Facial Action Units Using Partial Differential Equations



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.


Facial Action Coding System (FACS) Boundary Value Approach Order Elliptic Partial Differential Equations Facial Expression Data Non-uniform Rational B-splines (NURBS) 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Centre for Visual ComputingSchool of Engineering and Informatics, University of BradfordBradfordUK

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