Learning Continuous Face Representation with Explicit Functions

TL;DR

This paper introduces EmFace, a continuous face representation model using explicit mathematical functions, estimated via a neural network, outperforming traditional discrete methods in various face processing tasks.

Contribution

The paper presents EmFace, a novel explicit mathematical model for continuous face representation, and a neural network, EmNet, to estimate its parameters, enabling improved face image processing.

Findings

EmFace outperforms other methods in representing faces with various expressions and postures.

EmFace achieves effective results in face image restoration, denoising, and transformation.

The explicit function-based model provides a continuous representation aligning with human visual perception.

Abstract

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.