  How to represent a face pattern? While it is presented in a continuous way in
our visual system, computers often store and process the face image in a
discrete manner with 2D arrays of pixels. In this study, we attempt to learn a
continuous representation for face images with explicit functions. First, we
propose an explicit model (EmFace) for human face representation in the form of
a finite sum of mathematical terms, where each term is an analytic function
element. Further, to estimate the unknown parameters of EmFace, a novel neural
network, EmNet, is designed with an encoder-decoder structure and trained using
the backpropagation algorithm, where the encoder is defined by a deep
convolutional neural network and the decoder is an explicit mathematical
expression of EmFace. Experimental results show that EmFace has a higher
representation performance on faces with various expressions, postures, and
other factors, compared to that of other methods. Furthermore, EmFace achieves
reasonable performance on several face image processing tasks, including face
image restoration, denoising, and transformation.
