Learning Continuous Face Representation with Explicit Functions

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.

GmFace: A Mathematical Model for Face Image Representation Using Multi-Gaussian

Establishing mathematical models is a ubiquitous and effective method to understand the objective world. Due to complex physiological structures and dynamic behaviors, mathematical representation of the human face is an especially challenging task. A mathematical model for face image representation called GmFace is proposed in the form of a multi-Gaussian function in this paper. The model utilizes the advantages of two-dimensional Gaussian function which provides a symmetric bell surface with a shape that can be controlled by parameters. The GmNet is then designed using Gaussian functions as neurons, with parameters that correspond to each of the parameters of GmFace in order to transform the problem of GmFace parameter solving into a network optimization problem of GmNet. The face modeling process can be described by the following steps: (1) GmNet initialization; (2) feeding GmNet with face image(s); (3) training GmNet until convergence; (4) drawing out the parameters of GmNet (as the same as GmFace); (5) recording the face model GmFace. Furthermore, using GmFace, several face image transformation operations can be realized mathematically through simple parameter computation.