GmFace: An explicit function for face image representation

Abstract

Establishing mathematical models is a ubiquitous and effective method to understand the objective world. Due to the complex physiological structures and dynamic behaviors, the mathematical representation of the human face is an especially challenging task. In this paper, an explicit function called GmFace is proposed for face image representation in the form of a multi-Gaussian function. The model utilizes the advantages of two-dimensional Gaussian function which provides a symmetric bell surface with a controllable shape. 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. Furthermore, using GmFace, several face image transformation operations can be realized mathematically through simple parameter computation. Experimental results demonstrate that GmFace has a superior representation ability for face images compared to convolutional autoencoder (CAE), principal component analysis (PCA) and discrete cosine transform (DCT) method.