Eigenspace-based Face Recognition: A comparative
study of different approaches
Javier Ruiz-del-Solar and Pablo Navarrete
Department of Electrical Engineering, Universidad de Chile.
Email:{jruizd, pnavarre}@ing.uchile.cl
Abstract
Eigenspace-based Face Recognition corresponds to one of the most successful methodologies for the
computational recognition of faces in digital images. Starting with the Eigenface-Algorithm different
eigenspace-based approaches for the recognition of faces have been proposed. They differ mostly in the
kind of projection method used (standard-, differential- or kernel-eigenspace), in the projection algorithm
employed, in the use of simple or differential images before/after projection, and in the similarity matching
criterion or classification method employed. The aim of this paper is to present an independent,
comparative study among some of the main eigenspace-based approaches. We believe that carrying out
independent studies is relevant, since comparisons are normally performed using the own implementations
of the research groups that have proposed each method, which does not consider completely equal working
conditions for the algorithms. Very often, more than a comparison between the capabilities of the methods,
a contest between the abilities of the research groups is performed. This study considers theoretical aspects
as well as simulations performed using the Yale Face Database, a database with few classes and several
images per class, and FERET, a database with many classes and few images per class.
1
1. Introduction
Face Recognition is a high dimensional pattern recognition problem. Even low-resolution face images
generate huge dimensional feature spaces (20,000 dimensions in the case of a 100x200 pixels face image).
In addition to the problems of large computational complexity and memory storage, this high
dimensionality makes very difficult to obtain statistical models of the input space using well-defined
parametric models. Moreover, this last aspect is further stressed given the fact that only few samples for
each class (1-3) are normally available for the system training. However, the intrinsic dimensionality of the
face space is much lower than the dimensionality of the image space, since faces are similar in appearance
and contain significant statistical regularities. This fact is the starting point of the use of eigenspace-based
methods for reducing the dimensionality of the input face space. Standard- as well as differential- and
kernel-eigenspace approaches have been presented in the literature to overcome the mentioned problems.
Given that similar troubles are normally found in many biometric applications, we believe that some of the
eigenspace-based methods to be outlined and compared in this work can be applied in the implementation
of other biometric systems (signature, fingerprint, iris, etc.).
Eigenspace-based methods, mostly derived from the Eigenface-algorithm [19], project input faces onto
a dimensional reduced space where the recognition is carried out, performing a holistic analysis of the
faces. Different eigenspace-based methods have been proposed. They differ mostly in the kind of
projection/decomposition approach used (standard-, differential- or kernel-eigenspace), in the projection
algorithm employed, in the use of simple or differential images before/after projection, and in the similarity
matching criterion or classification method employed. The aim of this paper is to present an independent,
comparative study among some of these different approaches. We believe that carrying out independent
studies is relevant, because comparisons are normally performed using the own implementations of the
research groups that have proposed each method (e.g. in FERET contests), which does not consider
completely equal working conditions (e.g. exactly the same pre-processing steps). Very often, more than a
2
comparison between the capabilities of the methods, a contest between the abilities of the research groups
is performed. Additionally, not all the possible implementations are considered (e.g. p projection methods
with q similarity criteria), but only the ones that some groups have decided to use.
This study corresponds to an extension of the one presented in [12]. It considers standard, differential
and kernel eigenspace methods. In the case of the standard ones, three different projection algorithms,
Principal Component Analysis - PCA, Fisher Linear Discriminant - FLD and Evolutionary Pursuit – EP,
and five similarity matching criteria, Euclidean-, Cosines- and Mahalanobis-distance, SOM-Clustering and
Fuzzy Feature Contrast – FFC, were considered. In the case of differential eigenspace methods, two
approaches were used: the pre-differential [13] and the post-differential [15]. In both cases two
classification methods, Bayesian and Support Vector Machine – SVM classification, were employed.
Finally, regarding kernel eigenspace methods [9], Kernel PCA - KPCA and Kernel Fisher Discriminant -
KFD were used together with the five similarity measures employed in the standard eigenspace methods.
This comparative study considers theoretical aspects as well as simulations performed using the Yale
Face Database, a database with few classes and several images per class, and FERET, a database with
many classes and few images per class. It is important to use both kinds of databases for performing such a
study, because, as it will be shown in this work, some properties of the methods, as for example their
generalization ability, change depending on the number of classes taken under consideration.
Pre-processing aspects as face alignment, masking, illumination compensation and so on, are kept
unchanged in all the approaches and their different implementations.
This paper is structured as follows. In section 2 different approaches for the eigenspace-based
recognition of faces are described. In section 3 a comparative study among these approaches is presented.
Finally, some conclusions of this work are given in section 4.
2. Eigenspace-based Recognition of Faces
3
Standard eigenspace-based approaches project input faces onto a dimensional reduced space where the
recognition is carried out. In 1987 Sirovich and Kirby used PCA in order to obtain a reduced representation
of face images [17]. Then, in 1991 Turk and Pentland used PCA projections as the feature vectors to solve
the problem of face recognition, using the Euclidean distance as similarity function [19]. This system, later
called Eigenfaces, was the first eigenspace-based face recognition approach and, from then on, many
eigenspace-based systems have been proposed using different projection methods and similarity functions.
In particular, Belhumeur et al. proposed in 1997 the use of FLD as projection algorithm in the so-called
Fisherfaces system [1]. In all standard eigenspace-based approaches a similarity function, which works as a
nearest-neighbor classifier [3], is employed.
In 1997 Pentland and Moghaddam proposed a differential eigenspace-based approach that allows the
application of statistical analysis in the recognition process [13]. The main idea is to work with differences
between face images, rather than with single face images. In this way the recognition problem becomes a
two-class problem, because the so-called “differential image” contains information of whether the two
subtracted images belong to the same class or to different classes. In this case the number of training
images per class increases so that statistical information becomes available, and a statistical classifier can
be used for performing the recognition. The system proposed in [13] used Dual-PCA projections and a
Bayesian classifier. Following the same approach, a system using Single-PCA projections and a SVM
classifier was proposed in [15].
In the differential approach all the face images need to be stored in the database, which slows down the
recognition process. This is a serious drawback in practical implementations. To overcome this drawback a
so-called post-differential approach was proposed in [15]. Under this approach, differences between
reduced face vectors instead of differences between face images are used. This allows to decrease the
number of computations and the required storage capacity (only reduced face vectors are stored in the
4
database), without losing the recognition performance of the differential approaches. Both, Bayesian and
SVM classifiers were used to implement this approach in [15].
On the other hand, kernel eigenspace methods were proposed for increasing the generalization ability of
eigenspace methods by increasing the dimensionality of the input space instead of using differences of face
images or reduced vectors. In this case KPCA and KFD, non-linear extensions of PCA and FLD
respectively, are used as projection algorithms. The main idea behind these projection algorithms is to use
linear methods applied to high-dimensional mapped vectors instead of the original vectors, and at the same
time to avoid the explicit mapping of these vectors by means of the so-called “kernel-trick” (same strategy
is employed in SVM). As in the case of the standard eigenspace methods, a similarity function, which
works as a nearest-neighbor classifier, is employed. A kernel-based system for the recognition of faces was
proposed in [10]. This system uses either KPCA or KFD as projection algorithm.
Standard-, differential- and kernel-eigenspace approaches for the recognition of faces are described in
the following subsections.
2.1. Standard Eigenspace Face Recognition
Fig. 1 shows the block diagram of a generic, standard eigenspace-based face recognition system.
Standard eigenspace-based approaches approximate the face vectors (face images) by lower dimensional
feature vectors. These approaches consider an off-line phase or training, where the projection matrix
(
W ∈
R
N
× m
), the one that achieve the dimensional reduction, is obtained using all the database face images.
In the off-line phase, the mean face (
x ) and the reduced representation of each database image (
p
) are also
calculated. The recognition process works as follows. A preprocessing module transforms the face image
into a unitary vector (normalization module in the case of Fig. 1) and then performs a subtraction of the
mean face. The resulting vector is projected using the projection matrix that depends on the eigenspace
method been used (PCA, FLD, etc.). This projection corresponds to a dimensional reduction of the input,
k
5
