使用非负矩阵因子化夸张面部表情

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"文章提出了一种通过夸张映射来放大面部表情的方法，这种映射利用非负矩阵分解来定义，可以将面部运动转化为夸张的运动。通过输入夸张率来模拟三维面部表情，以表现变化的程度。实验验证了夸张映射和面部表情模拟的有效性。该研究属于图像处理和成像系统领域，具体涉及100.0100和110.0110这两个分类。" 面部表情在诸如视频游戏、电影、社交代理、商业广告以及人类学等众多领域中广泛应用，尤其是人脸，它在传达情绪和信息方面起着至关重要的作用。传统的面部表情捕捉技术能够记录并再现真实世界中的面部运动，但通常局限于忠实于原始数据，缺乏表现力和吸引力。本文提出的是一种新的方法，旨在通过夸张的方式来增强面部表情的动态效果。这一方法的核心是“夸张映射”，它基于非负矩阵分解（Non-negative Matrix Factorization, NMF）来构建。NMF是一种数学工具，常用于数据挖掘和信号处理，能够从非负数据集中提取关键特征。在面部表情的应用中，NMF被用来分析和提取面部运动的关键模式，然后这些模式被用来创建夸张的面部运动。夸张映射允许用户通过控制夸张率来调整模拟的面部表情程度。夸张率作为一个输入参数，可以细腻地控制表情的变化，从微妙的微妙情绪到戏剧化的强烈反应，从而增加表情的视觉冲击力和情感表达力。这一技术对于创造具有鲜明个性的虚拟角色或者增强动画效果特别有用。实验结果显示，该方法能够有效地实现面部表情的放大，并且保持了表情的真实性与连贯性。实验的验证表明，夸张映射可以成功地应用到面部表情模拟中，提高了面部动画的视觉吸引力和艺术表现力。同时，这种方法对于进一步研究如何更自然、更生动地表达情感，以及在人机交互和虚拟现实等领域中增强用户体验具有重要意义。这篇研究通过非负矩阵分解驱动的夸张映射，为面部表情的数字化处理提供了一个创新工具，有望推动数字娱乐、教育、心理咨询等领域的面部表情应用达到新的高度。同时，由于其灵活性和可控性，该技术对于定制化和个性化内容的创作也具有极大的潜力。

January 10, 2010 / Vol. 8, No. 1 / CHINESE OPTICS LETTERS 29

Exaggeration of facial expressions from facial motion

capture data

Seongah Chin (ªªª)

∗

and Chung-Yeon Lee (ooo¿¿¿,,,)

Division of Multimedia, College of Engineering, Sungkyul University,

#147-2 Anyang-8 Dong. Manan-Gu, Anyang City, 430-742, Korea

∗

E-mail: solideo@sungkyul.edu

Received June 17, 2009

We propose a method for exaggerating facial expressions derived from exaggeration mappings that trans-

form facial motions into exaggerated motions. The exaggeration mapping of facial motions is deﬁned

by non-negative matrix factorization. Three-dimensional facial expressions are simulated using the exag-

gerating rate as an input value to convey the degree of variation. Experiments show the validity of the

exaggeration mapping and facial expression simulations.

OCIS co des: 100.0100, 110.0110.

doi: 10.3788/COL20100801.0029.

Facial expressions have been widely used for characters,

digital actors, and virtual humans in various ﬁelds such as

video games, movies, social agents, commercials, and an-

thropology. The human face, in particular, plays a signif-

icant role in non-verbal communication, with a plethora

of expressions that vary by personality. Most researchers

in the area of facial expression synthesis seem to focus on

realistic expressions or retargeting

[1−3]

, rather than exag-

gerating expressions. To draw attention to subjects, it is

very important to exaggerate facial expressions, but this

is a labor-intensive process. As a consequence, a method

for automatic exaggerated facial expression synthesis is

a must. Exaggeration is considered to be similar to plac-

ing more emphasis on the key features of an object. It

should be noted that the larger accentuated features are

found before the lesser features are determined. However

to our knowledge, no published articles have reported on

the exaggeration of facial expressions. In this letter, we

propose a method to exaggerate facial expressions de-

rived from facial motions acquired by motion capture. In

this transformation, we employ non-negative matrix fac-

torization (NMF) to realize exaggeration mapping. The

proposed method is validated by showing some experi-

mental results.

Exaggeration mapping is used to transform a facial mo-

tion composed of feature points on a face acquired by

motion capture into an exaggerated facial motion. The

fundamental idea of this approach to the exaggeration

mapping of facial motions is to place more emphasis on

those features with relatively more movements. The ﬁrst

step is proper data factorization. NMF is suitable for

parts-based data factorization because of its advantages

over principal component analysis (PCA) or vector quan-

tization (VQ) with respect to its use of non-negative con-

straints. In addition, NMF learns parts of faces, whereas

PCA and VQ learn holistically. These constraints lead to

a parts-based representation computed only by additive,

rather than subtractive, combinations

[4,5]

The mapping method primarily comprises two proce-

dures. Firstly, NMF decomposes a facial motion matrix

into a basis and its weight matrix. Then, a facial motion

is exaggerated by multiplying both the weights and resid-

uals acquired from the NMF decomposition by a speciﬁc

exaggeration rate.

Cross-cultural research presents six universal expres-

sions — surprise, fear, disgust, anger, happiness, and sad-

ness — for which a sequence of facial markers, called a fa-

cial motion, is factorized in order to exaggerate individual

facial markers of the facial motion. Each motion consists

of the three-dimensional (3D) movements of markers at-

tached to the principal facial muscles of an actor. These

facial motions are regarded as an n × m matrix M, each

column of which consists of the x, y, and z coordinates of

the markers. Given a facial motion denoted by M, NMF

decomposes M into two matrices B and E, as

iµ

≈ (BE)

iµ

a=1

aµ

, (1)

to approximate the facial motions. The dimensions of

the factorized matrices B and E are n × r and r × m,

respectively, with r satisfying (n + m)r < nm.

Each column of the matrix B contains a basis vector,

while each column of E includes the weights correspond-

ing to the measurement column in M using the basis from

B. To estimate the factorization matrices, an objective

function has to be deﬁned. This objective function works

out the likelihood of computing the facial motions in M

from the basis B and encodings E. The objective func-

tion that we used is given as

H =

i=1

µ=1

iµ

log(BE)

iµ

− (BE)

iµ

]. (2)

Solutions for NMF begin with initializing the non-

negative conditions for B and E. Continuing the iter-

ation of the update rules in

← B

iµ

(BE)

iµ

aµ

, (3)

aµ

← E

aµ

iµ

(BE)

iµ

, (4)

M ﬁnds an approximate factorization M ≈ BE by con-

verging to a local maximum of the objective function

1671-7694/2010/010029-04

° 2010 Chinese Optics Letters

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