Eigenfaces vs Fisherfaces&Specific Linear Projection
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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 19, NO. 7, JULY 1997 711
Eigenfaces vs. Fisherfaces: Recognition
Using Class Specific Linear Projection
Peter N. Belhumeur, Joao
~
P. Hespanha, and David J. Kriegman
Abstract
—We develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression.
Taking a pattern classification approach, we consider each pixel in an image as a coordinate in a high-dimensional space. We take
advantage of the observation that the images of a particular face, under varying illumination but fixed pose, lie in a 3D linear
subspace of the high dimensional image space—if the face is a Lambertian surface without shadowing. However, since faces are
not truly Lambertian surfaces and do indeed produce self-shadowing, images will deviate from this linear subspace. Rather than
explicitly modeling this deviation, we linearly project the image into a subspace in a manner which discounts those regions of the
face with large deviation. Our projection method is based on Fisher’s Linear Discriminant and produces well separated classes in a
low-dimensional subspace, even under severe variation in lighting and facial expressions. The Eigenface technique, another method
based on linearly projecting the image space to a low dimensional subspace, has similar computational requirements. Yet, extensive
experimental results demonstrate that the proposed “Fisherface” method has error rates that are lower than those of the Eigenface
technique for tests on the Harvard and Yale Face Databases.
Index Terms
—Appearance-based vision, face recognition, illumination invariance, Fisher’s linear discriminant.
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1I
NTRODUCTION
Within the last several years, numerous algorithms have
been proposed for face recognition; for detailed surveys see
[1], [2]. While much progress has been made toward recog-
nizing faces under small variations in lighting, facial ex-
pression and pose, reliable techniques for recognition under
more extreme variations have proven elusive.
In this paper, we outline a new approach for face recogni-
tion—one that is insensitive to large variations in lighting
and facial expressions. Note that lighting variability includes
not only intensity, but also direction and number of light
sources. As is evident from Fig. 1, the same person, with the
same facial expression, and seen from the same viewpoint,
can appear dramatically different when light sources illumi-
nate the face from different directions. See also Fig. 4.
Our approach to face recognition exploits two observations:
1) All of the images of a Lambertian surface, taken from
a fixed viewpoint, but under varying illumination, lie
in a 3D linear subspace of the high-dimensional image
space [3].
2) Because of regions of shadowing, specularities, and
facial expressions, the above observation does not ex-
actly hold. In practice, certain regions of the face may
have variability from image to image that often devi-
ates significantly from the linear subspace, and, con-
sequently, are less reliable for recognition.
We make use of these observations by finding a linear
projection of the faces from the high-dimensional image
space to a significantly lower dimensional feature space
which is insensitive both to variation in lighting direction
and facial expression. We choose projection directions that
are nearly orthogonal to the within-class scatter, projecting
away variations in lighting and facial expression while
maintaining discriminability. Our method Fisherfaces, a
derivative of Fisher’s Linear Discriminant (FLD) [4], [5],
maximizes the ratio of between-class scatter to that of
within-class scatter.
The Eigenface method is also based on linearly project-
ing the image space to a low dimensional feature space [6],
[7], [8]. However, the Eigenface method, which uses princi-
pal components analysis (PCA) for dimensionality reduc-
tion, yields projection directions that maximize the total
scatter across all classes, i.e., across all images of all faces. In
choosing the projection which maximizes total scatter, PCA
retains unwanted variations due to lighting and facial
expression. As illustrated in Figs. 1 and 4 and stated by
Moses et al., “the variations between the images of the same
face due to illumination and viewing direction are almost
always larger than image variations due to change in face
identity” [9]. Thus, while the PCA projections are optimal
0162-8828/97/$10.00 © 1997 IEEE
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• The authors are with the Center for Computational Vision and Control, Dept.
of Electrical Engineering, Yale University, New Haven, CT 06520-8267.
E-mail: {belhumeur, kriegman}@yale.edu, hespanha@yale.edu.
M
anuscript received 15 Feb. 1996 revised 20 Mar. 1997. Recommended for accep-
tance by J. Daugman.
For information on obtaining reprints of this article, please send e-mail to:
transpami@computer.org, and reference IEEECS Log Number 104797.
Fig. 1. The same person seen under different lighting conditions can
appear dramatically different: In the left image, the dominant light
source is nearly head-on; in the right image, the dominant light source
is from above and to the right.
最大化类间分散度与类内的分散度之比
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