Facial Expression Classification using Gabor and Log-Gabor Filters
Nectarios Rose
School of Computer Science & Mathematics
Victoria University of Technology, Footscray Park Campus, VIC 3011, Australia
nckrose@aol.com
Abstract
Facial expression classification has achieved good
results in the past using manually extracted facial points
convolved with Gabor filters. In this paper, classification
performance was tested on feature vectors composed of
facial points convolved with Gabor and Log-Gabor
filters, as well as with whole image pixel representation of
static facial images. Principal Component Analysis was
performed on these feature vectors, and classification
accuracies compared using Linear Discriminant Analysis.
Experiments carried out on two databases show
comparable performance between Gabor and Log-Gabor
filters, with a classification accuracy of around 85%. This
was achieved on low-resolution images, without the need
to precisely locate facial points on each face image.
1. Introduction
Research in facial expression recognition has been
motivated by a desire to develop more sophisticated
human computer interaction tools. Potential benefits
include distance education learning, automobile driver
alertness monitoring, lie detection, affect assessment in
health, and for constructing more entertaining and
interactive games. There have been various approaches to
face expression analysis including geometric techniques
which involve representing the face in terms of distances,
angles and areas between features such as eyes, nose or
chin [1][2][3]. Other papers have applied Gabor filters to
points on a facial image, and one compared and achieved
better results than geometric techniques [4].
Gabor filters are based on physiological studies of
simple cells in the human visual cortex. The cells are
selectively tuned to orientation as well as spatial
frequency, and their response can be approximated by 2-
D Gabor filters. Studies in the past have achieved good
results in using these filters to improve classification
automatically using labelled elastic graph matching, or by
manually extracting the precise location of points on the
face [4][5]. It has been suggested that Log-Gabor filters,
which are based on Gaussian transfer functions
symmetrical on the log-frequency scale, can more
efficiently encode natural images [7]. This paper
compares novel classification accuracy using whole
image pixel based representation, Gabor and Log-Gabor
filtered images. This approach relies on convolving Gabor
and Log-Gabor filters on approximately rather than
precisely located facial points.
2. Gabor filters
A Gabor filter can be represented by the following
equation:
g(x,y)= s(x,y)w(x,y) (1)
where s(x,y) is a complex sinusoidal known as the carrier,
and w(x,y) is a 2-D Gaussian-shaped function known as
the envelope. There are various forms to define this
function, one normalized 2-D form being [6]:
{}
22222
22
(, ; , ) exp exp 2 (2)
yx x y
ffxfy
gxyf j fx
θπ
πσ σ σ σ
⎧⎫
⎡⎤
′′
⎪⎪
′
= − +
⎢⎥
⎨⎬
⎢⎥
⎪⎪
⎣⎦
⎩⎭
cos sin
sin cos
xx y
yx y
θθ
θθ
′
=+
′
=− +
where f is the frequency of a sinusoidal wave plane along
the x-axis, ș is the anti-clockwise rotation of the Gaussian
envelope of the sinusoid, and ı
x
and ı
y
are the spatial
widths of the Gaussian envelope along the x and y axes
respectively. Normalization of a set of Gabor features of
different orientation and frequency at a specific point can
be carried out for illumination invariance.
This function can also be represented in the frequency
domain. One such Fourier domain representation to define
the even symmetric filter is given by:
2222
22 22
() ()
11
(,) exp exp
22
oo
uv uv
ff ff
vv
Guv A A
σσ σσ
⎧⎫⎧⎫
⎡⎤⎡⎤
−+
⎪⎪⎪⎪
= − + + − + (3)
⎨⎬⎨⎬
⎢⎥⎢⎥
⎪⎪⎪⎪
⎣⎦⎣⎦
⎩⎭⎩⎭
Proceedings of the 7th International Conference on Automatic Face and Gesture Recognition (FGR’06)
0-7695-2503-2/06 $20.00 © 2006
IEEE
