Learning to represent 2D human face with mathematical model

Abstract

Abstract How to represent a human face pattern? While it is presented in a continuous way in human visual system, computers often store and process it in a discrete manner with 2D arrays of pixels. The authors attempt to learn a continuous surface representation for face image with explicit function. First, an explicit model (EmFace) for human face representation is proposed 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 from massive face images, where the encoder is defined by a deep convolutional neural network and the decoder is an explicit mathematical expression of EmFace. The authors demonstrate that our EmFace represents face image more accurate than the comparison method, with an average mean square error of 0.000888, 0.000936, 0.000953 on LFW, IARPA Janus Benchmark‐B, and IJB‐C datasets. Visualisation results show that, EmFace has a higher representation performance on faces with various expressions, postures, and other factors. Furthermore, EmFace achieves reasonable performance on several face image processing tasks, including face image restoration, denoising, and transformation.

Keywords

• artificial neural networks
• face analysis
• image processing
• mathematics computing