Annals of Mathematical Sciences and Applications

Volume 7 (2022)

Number 1

An optimal transportation-based recognition algorithm for 3D facial expressions

Pages: 49 – 96

DOI: https://dx.doi.org/10.4310/AMSA.2022.v7.n1.a3

Authors

Tiexiang Li (School of Mathematics, Southeast University, Nanjing, China; and Nanjing Center for Applied Mathematics, Nanjing, China)

Pei-Sheng Chuang (Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan)

Mei-Heng Yueh (Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan)

Abstract

Facial expression recognition (FER) is an active topic that has many applications. The development of effective algorithms for FER has been a competitive research field in the last two decades. In this paper, we propose a fully automatic 3D FER method based on the sparse approximation of 2D feature images. For a prescribed feature defined on the 3D facial surface, we apply a parameterization that not only maps the facial surface onto the unit disk but also locally preserves the feature. To ensure the uniqueness of the solution, some aligning constraints are further taken into account while computing the desired parameterization. The facial surface associated with the feature is then converted into the 2D image of the parameter domain. To recognize the expression of a test facial image, we apply an existing 2D expression recognition model, which is built upon sparse representation. Numerical experiments indicate that the accuracy of the proposed FER algorithm reaches 71.42% on a benchmark facial expression database, which is promising for practical applications.

Keywords

facial expression recognition, optimal mass transportation, projected gradient descent method

2010 Mathematics Subject Classification

Primary 52C26, 68U05. Secondary 65D18.

Received 17 January 2022

Accepted 5 February 2022

Published 7 April 2022