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Method of modelling facial action units using partial differential equations
Ugail, Hassan Ismail, N.B.
Ugail, Hassan
Ismail, N.B.
Publication Date
2016
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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.
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Ugail H and Ismail NB (2016) Method of modelling facial action units using partial differential equations. In: Kawulok M, Celebi E M and Smolka B (Eds.) Advances in face detection and facial image analysis. Springer. 129-143.
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