AIM 1521
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
ARTIFICIAL INTELLIGENCE LABORATORY
and
CENTER FOR BIOLOGICAL AND COMPUTATIONAL LEARNING
A.I. Memo No. 1521
C.B.C.L. Paper No. 112
December, 1994
Example-based Learning for View-based
Human Face Detection
Kah-Kay Sung and Tomaso Poggio
This publication can be retrieved by anonymous ftp to publications.ai.mit.edu.
Abstract
Finding human faces automatically in an image is a dicult yet important rst step to a fully automatic
face recognition system. It is also an interesting academic problem because a successful face detection
system can provide valuable insight on how one might approach other similar object and pattern detection
problems. This paper presents an example-based learning approach for locating vertical frontal views of
human faces in complex scenes. The technique models the distribution of human face patterns by means
of a few view-based \face" and \non-face" prototype clusters. At each image location, a di erence feature
vector is computed between the local image pattern and the distribution-based model. A trained classi er
determines, based on the di erence feature vector, whether or not a human face exists at the current image
location. We show empirically that the prototypes we choose for our distribution-based model, and the
distance metric we adopt for computing di erence feature vectors, are both critical for the success of our
system.
Copyright c Massachusetts Institute of Technology, 1994
This report describes research done at the Arti cial Intelligence Laboratory and within the Center for Biological and Computational Learning in the Department of Brain and Cognitive Sciences at the Massachusetts Institute of Technology. This research
is sponsored by grants from ARPA-ONR under contract N00014-92-J-1879; and by a grant from the National Science Foundation under contract ASC-9217041 (this award includes funds from ARPA provided under the HPCC program). Additional
support is provided by the North Atlantic Treaty Organization, ATR Audio and Visual Perception Research Laboratories,
Mitsubishi Electric Corporation, Sumitomo Metal Industries, and Siemens AG. Support for the A.I. Laboratory's arti cial
intelligence research is provided by ARPA-ONR contract N00014-91-J-4038. Tomaso Poggio is supported by the Uncas and
Helen Whitaker Chair at MIT's Whitaker College.
1 Introduction
Feature and pattern detection in images is a classical
computer vision problem with many potential applications, ranging from automatic target recognition to industrial inspection tasks in assembly lines. While there
has been some successful pattern detection systems in
the past, especially those using pictorial templates [4]
[10] [11] or geometric models [7] for describing objects,
most such systems are limited by some serious constraints. For example, in some systems, the target objects must be rigid or at least made up of rigid parts. In
others, lighting must be controlled or the imaging geometry must be known.
This paper presents a new feature and pattern detection technique for nding slightly deformable objects under reasonable amounts of lighting variation. To demonstrate our technique, we focus on the speci c problem
of nding human faces in images. We have developed
a generic human face detection system that operates
successfully under a reasonably wide range of lighting
conditions and imaging environments. Our system detects vertically oriented and unoccluded frontal views
of human faces in grey-level images. It handles faces
within a range of scales as speci ed by the user, and
works under di erent lighting conditions, even with moderately strong shadows. We stress that our ultimate
goal is to propose a general methodology for taking on
feature detection tasks in multiple domains, including
hand-printed character recognition, industrial inspection, medical image analysis and terrain classi cation,
where target patterns may not be rigid or geometrically
parameterizable, and where imaging conditions may not
be within the user's control.
1.1 The Face Detection Problem
We begin by describing the problem of human face detection. Given as input an arbitrary image, which could
be a digitized video signal or a scanned photograph, determine whether or not there are any human faces in the
image, and if there are, return an encoding of the location and spatial extent of each human face in the image.
An example encoding might be to t each face in the
image with a bounding box, and return the image coordinates of the box corners. A related problem to face
detection is face recognition: given an input image of a
face, compare the input face against models in a library
of known faces and report if a match is found. In recent
years, the face recognition problem has attracted much
attention because of its many possible applications in
automatic access control systems and human-computer
interfaces.
Why is automatic face detection an interesting problem? Applications wise, face detection has direct relevance to the face recognition problem, because the rst
important step of a fully automatic human face recognizer is usually one of identifying and locating faces in
an unknown image. So far, the focus of face recognition
research has been mainly on distinguishing individual
faces from others in a database. The task of nding
faces in an arbitrary background is usually avoided by
either hand segmenting the input image, or by capturing 1
faces against a known uniform background.
Face detection also has potential applications in
human-computer interfaces and surveillance systems.
For example, a face nder can make workstations with
cameras more user friendly by turning monitors on and
keeping them active whenever there is someone in front
of the terminal. In some security and census systems,
one could determine the number of people in a scene by
counting the number of visible human faces.
From an academic standpoint, face detection is interesting because faces make up a challenging class of naturally structured but slightly deformable objects. There
are many other object classes and phenomena in the real
world that share similar characteristics, for example different hand or machine printed instances of the character
`A', tumor anomalies in MRI scans and material defects
in industrial products. A successful face detection system can provide valuable insight on how one might approach other similar pattern and feature detection problems.
Face detection is dicult for three main reasons.
First, although most faces are similarly structured with
the same facial features arranged in roughly the same
spatial con guration, there can be a large component of
non-rigidity and textural di erences among faces. For
the most part, these elements of variability are due to
the basic di erences in \facial appearance" between individuals | person `A' has a larger nose than person
`B', person `C' has eyes that are farther apart than person `D', while person `E' has a darker skin complexion
than person `F'. Even between images of the same person's face, there can still be signi cant geometrical or
textural di erences due to changes in expression and the
presence or absence of facial makeup. As such, traditional xed template matching techniques and geometric model-based object recognition approaches that work
well for rigid and articulate objects tend to perform inadequately for detecting faces.
Second, face detection is also made dicult because
certain common but signi cant features, such as glasses
or a moustache, can either be present or totally absent
from a face. Furthermore, these features, when present,
can cloud out other basic facial features (eg. the glare
in one's glasses may de-emphasize the darkness of one's
eyes) and have a variable appearance themselves (eg.
glasses come in many di erent designs). All this adds
more variability to the range of permissible face patterns that a comprehensive face detection system must
handle.
Third, face detection can be further complicated by
unpredictable imaging conditions in an unconstrained
environment. Because faces are essentially 3-dimensional
structures, a change in light source distribution can cast
or remove signi cant shadows from a particular face,
hence bringing about even more variability to 2D facial
patterns.
1.2 Existing work
As discussed above, the key issue and diculty in face
detection is to account for the wide range of allowable facial pattern variations in images. There have been three
main approaches for dealing with allowable pattern variations, namely: (1) the use of correlation templates, (2)
deformable templates, and (3) spatial image invariants.
Correlation Templates Fixed correlation templates
work like matched lters. They compute a di erence
measurement between a xed target pattern and candidate image locations, and the output is thresholded for
matches.
While the class of all face patterns is probably too varied to be modeled by xed correlation templates, there
are some face detection approaches that use a bank of
several correlation templates to detect major facial subfeatures in the image [2] [3]. The assumption here is that
the degree of non-rigidity in these facial subfeatures is
small enough to be adequately described by a few xed
templates. At a later stage, the technique infers the
presence of faces by analyzing the spatial relationship
between the detected subfeatures.
A closely related approach to correlation templates is
that of view-based eigen-spaces [12]. The approach assumes that the set of all possible face patterns occupies
a small and easily parameterizable sub-space in the original high dimensional input image vector space. To detect
faces, the approach rst recovers a representation of the
sub-space of face patterns as a reference for matching.
An image pattern is classi ed as \a face" if its distance
from the sub-space of faces is below a certain threshold,
according to an appropriate distance metric.
Typically, the approach approximates the sub-space
of face patterns using clusters and their principal components from one or more sets of face images. Mathematically, each set of face images is modeled as a cluster
of points in the original high-dimensional input image
vector space, and each cluster is characterized by the
principal components of the distribution of its elements.
The principal components, or eigenvectors, capture the
di erent types of variation that can occur between face
images in the set, with the largest eigenvectors usually
corresponding to the key variations types | those due to
illumination changes and predominant di erences in facial appearance between individuals. The face sub-space
is formed using only a subset of the largest eigenvectors
from each of the clusters, so as to preserve only the semantically meaningful variations. One commonly used
distance metric is the Euclidean distance of a pattern
from the nearest face sub-space location, which may be
interpreted as a di erence measure between the observed
pattern and some \typical" face pattern [12]. So far, this
approach has only been demonstrated on images with
not-so-cluttered backgrounds.
The view-based eigen-space approach has also been
used for detecting and locating individual facial subfeatures. The purpose of these sub-feature detectors has
mainly been one of registering mugshot faces with model
faces for recognition, rather than as a preprocessor for
face detection.
Deformable Templates Deformable templates are
similar in principle to classical correlation templates, except that the former has some built-in non-rigidity component. To nd faces in an image with a deformable tem- 2
plate, one essentially ts the template to di erent parts
of the image and thresholds the output for matches.
One deformable template approach uses hand constructed parameterized curves and surfaces to model the
non-rigid elements of faces and facial subfeatures, such as
the eyes, nose and lips [20]. The parameterized curves
and surfaces are xed elastically to a global template
frame to allow for minor positional variations between
facial features. The matching process attempts to align
the template with one or more pre-processed versions of
the image, such as the peak, valley and edge maps. An
energy functional constrains alignment by attracting the
parameterized curves and surfaces to corresponding image features, while penalizing deformation \stress" in the
template. The best t con guration is found by minimizing the the energy functional, and the minimumvalue
also serves as a closeness measure for the match.
Image Invariants Image-invariance schemes assume
that even though faces may vary greatly in appearance
for a variety of reasons, there are some spatial image relationships common and possibly unique to all face patterns. To detect faces, one has to compile such a set of
image invariants and check for positive occurrences of
these invariants at all candidate image locations.
One image-invariance scheme is based on a set of observed brightness invariants between di erent parts of
a human face [15]. The underlying observation is that
that while illumination and other changes can signi cantly alter brightness levels at di erent parts of a face,
the local ordinal structure of brightness distribution remains largely unchanged. For example, the eye regions
of a face are almost always darker than the cheeks and
the forehead, except possibly under some very unlikely
lighting conditions. Similarly, the bridge of the nose
is always brighter than the two anking eye regions.
The scheme encodes these observed brightness regularities as a ratio template, which it uses to pattern match
for faces. A ratio template is a coarse spatial template
of a face with a few appropriately chosen sub-regions,
roughly corresponding to key facial features. The brightness constraints between facial parts are captured by
an appropriate set of pairwise brighter-darker relationships between corresponding sub-regions. An image pattern matches the template if it satis es all the pairwise
brighter-darker relationships.
1.3 Example-based Learning and Face
Detection
In this paper, we formulate the face detection problem
as one of learning to recognize face patterns from examples. We use an initial database of about 1000 face
mugshots to construct a distribution-based generic face
model with all its permissible pattern variations in a
high dimensional image window vector space. We then
train a decision procedure on a sequence of \face" and
\non-face" examples, to empirically discover a set of operating parameters and thresholds that separates \face"
patterns from \non-face" patterns. Our learning-based
approach has the following distinct advantages over existing techniques:
First, our modeling scheme does not depend much
on domain speci c knowledge or special hand-crafting
techniques to parameterize face patterns and their various sources of variation. This immediately eliminates
one potential source of modeling error | that due to
inaccurate or incomplete knowledge. Unlike deformable
template approaches or image invariance techniques that
build models based on prior knowledge of facial structure, our scheme essentially builds models that describe
the distribution of face patterns it receives. Therefore,
as long as we provide our scheme with a suciently comprehensive set of example face patterns, we can expect
our face models to be more accurate and more descriptive than the manually synthesized ones.
Second, unlike most non learning-based approaches
that typically obtain their operating parameters and
thresholds manually from a few trial cases, our detection scheme derives its parameters and thresholds automatically from a large number of input-output examples. This makes our scheme potentially superior in two
ways: (1) For a given set of free thresholds and parameters, we can expect our scheme to arrive at a statistically
more reliable set of operating values because it is able to
process a wider sample of training data automatically.
(2) Because our scheme automatically learns thresholds
and parameters, it can be easily made to learn appropriate high-dimensional and non-linear relationships on
image measurements for distinguishing between \face"
and \non-face" patterns. These relationships, even if
they do exist, may be too complex for human observers
to discover manually.
Our resulting system also has the following desirable
characteristics. Performance wise, it can be made arbitrarily robust by increasing the size and variety of its
training examples. Both false positive and false negative
detection errors can be easily corrected by further training with the wrongly classi ed patterns. Functionality
wise, the system is also highly extensible. For instance,
to detect human faces over a wider range of poses, we
can apply the same example-based learning technique to
create a few separate systems that each model and identify faces at a di erent pose, and have the systems run
in parallel.
2 System Overview and Approach
In our view-based approach, faces are treated as a
class of local target patterns to be detected in an image.
Because faces are essentially structured objects with the
same key features geometrically arranged in roughly the
same fashion, it is possible to de ne a semantically stable \canonical" face structure in the image domain for
the purpose of pattern matching. Figure 1(a) shows the
canonical face structure adopted by our system. It corresponds to a square portion of the human face whose
upper boundary lies just above the eyes and whose lower
edge falls just below the mouth. The face detection task
thus becomes one of appropriately representing the class
of all such \face-like" window patterns, and nding instances of these patterns in an image.
Our system detects faces by exhaustively scanning an
image for these face-like window patterns at all possible scales. Figure 2(a) describes the system's task at
one xed scale. The image is divided into multiple,
possibly overlapping sub-images of the current window
size. At each window, the system attempts to classify
the enclosed image pattern as being either \a face" or
\not a face". This involves taking a set of local image measurements to extract pertinent information from
the enclosed pattern, and using a pre-de ned decision
procedure to determine, based on the measurements obtained, whether or not the enclosed pattern \resembles"
our canonical face structure. Each time a \matching"
window pattern is found, the system reports a face at the
window location, and the scale as given by the current
window size. Multiple scales are handled by examining
and classifying windows of di erent sizes. Our system
performs an equivalent operation by examining and classifying xed sized window patterns on scaled versions of
the image. The idea is to resize the image appropriately, so that the desired window size scales to the xed
window dimensions assumed by the image measurement
routines.
Clearly, the most critical part of our system is the
algorithm for classifying window patterns as \faces" or
\non-faces". The rest of this paper focuses on the algorithm we developed. Figure 2(b) shows the key components of the algorithm. Basically, the approach is one of
appropriately modeling the distribution of canonical face
patterns in some high dimensional image window vector
space, and learning a functional mapping of input pattern measurements to output classes from a representative set of \face" and \non-face" window patterns. More
speci cally, our approach works as follows:
1. We require that the window pattern to be classi ed
be 19 19 pixels in size and appropriately masked
(see Figure 1). All window patterns of di erent
dimensions must rst be re-scaled to this size and
masked before further processing. Matching with a
xed sized window simpli es our algorithm because
it allows us to use the same classi cation procedure
for all scales. The masking operation applies some
prior domain knowledge to the matching problem
by ignoring certain near-boundary pixels that may
fall outside the spatial boundaries of a face.
2. Using a database of canonical \face" window patterns and a similar database of \non-face" window
patterns, we construct a distribution-based model
of canonical face patterns in the masked 19 19
dimensional image window vector space. Our modeling scheme uses a few \face" pattern prototypes
to piece-wise approximate the distribution manifold
of canonical face patterns in the masked 19 19 dimensional image window vector space. It also uses a
few \non-face" pattern prototypes to help capture
the concavities in the distribution manifold more
accurately. Together, these \face" and \non-face"
pattern prototypes serve as a distribution-based
model for the class of canonical face views. The
\face" pattern prototypes are synthesized oine by
performing clustering on the example database of
\face" window patterns, and the \non-face" prototypes are similarly synthesized from the database
of \non-face" window patterns. The prototypes are
3
Figure 1: (a): A \canonical" face pattern. (b): A 19 19 mask for eliminating near-boundary pixels of canonical face
patterns. (c): The resulting \canonical" face pattern after applying the mask.
hard-wired into the face detection system at compile time. Each prototype is a multi-dimensional
Gaussian cluster with a centroid location and a covariance matrix that describes the local data distribution around the centroid.
3. For each new window pattern to be classi ed, we
compute a set of image measurements as input to
the \face" or \non-face" decision procedure. Each
set of image measurements is a vector of distances
from the new window pattern to the window pattern prototypes in the image window vector space.
To compute our vector of distances, we de ne and
use a new \Mahalanobis-like" distance metric for
measuring the distance between the input window
pattern and each prototype center. The distance
metric takes into account the shape of each prototype cluster, in order to penalize distances orthogonal to the local data distribution. The resulting
vector of distances coarsely encodes the new window pattern's location relative to the overall distribution of canonical face patterns in the image
window vector space. It serves as a notion of \difference" between the new window pattern and the
class of all canonical face patterns.
4. We train a multi-layer perceptron (MLP) net to
identify new window patterns as \faces" or \nonfaces" from their vector of distance measurements.
When trained, the multi-layer perceptron net takes
as input a vector of distance measurements and outputs a `1' if the vector arises from a face pattern,
and a `0' otherwise. We use a combined database
of 47316 \face" and \non-face" window patterns to
train the multi-layer perceptron classi er.
The following sections describe our window pattern
classi cation algorithm in greater detail. Section 3 describes our distribution-based model for canonical face
window patterns. It explains the pre-processing and
clustering operations we perform for synthesizing \face"
and \non-face" window pattern prototypes. Section 4
describes our distance metric for computing classi er input vectors. Section 5 discusses the classi er training
process, and in particular, our method of selecting a
comprehensive but tractable set of training examples.
In Section 6, we identify the algorithm's critical components in terms of generating correct results, and evaluate 4
the system's overall performance.
3 A Distribution-based Face Model
Our window classi cation algorithm identi es faces by
comparing each new masked window pattern with a
canonical face model, and declaring a \face" when the
match is good. This section describes our canonical face
model. We use a distribution-based modeling scheme
that tries to represent canonical faces as the set of all
masked 19 19 pixel patterns that are canonical face
views. More speci cally, our distribution-based modeling scheme works as follows: Suppose we treat each
unmasked pixel of a 19 19 image as a vector dimension, then the class of all 19 19 pixel images forms
a vector space whose dimensionality equals the number
of unmasked image pixels. Each 19 19 image pattern
maps to a speci c vector space location, and the set of
all 19 19 pixel canonical face patterns maps to a xed
region in this multi-dimensional vector space. So, in theory, one can model the class of all canonical face views by
identifying the portion of this multi-dimensional image
vector space that corresponds to canonical face patterns,
and representing the region in some tractable fashion.
3.1 Identifying and Representing the
Canonical Face Manifold
In practice, one does not have the set of all 19 19
pixel canonical face patterns to recover the sub-space
of canonical face views exactly. Figure 3 explains how
we localize and represent the region of canonical face
patterns with limited data. Basically, we use a reasonably large example database of canonical face patterns
and a carefully chosen database of non-face patterns to
infer the spatial extent of canonical face views in the
multi-dimensional image vector space. We assume that
our \face" database contains a suciently representative
sample of canonical face patterns that evenly populates
the actual vector sub-space of canonical face views. So
by building a model of the \face" sample distribution,
one can still obtain a coarse but fairly reliable representation of the actual canonical face manifold. Our \nonface" data samples are specially selected patterns that lie
near the boundaries of the canonical face manifold. We
use the \non-face" patterns to help localize and re ne the
boundaries of the canonical face manifold by explicitly
Figure 2: Overview of our face detection system. (a): The system's task at each scale. The image is divided into many
possibly overlapping windows. Each window pattern gets classi ed as either \a face" or \not a face", based on a set of
local image measurements. (b): The key components of the Face Pattern Recognizer block in greater detail. The Face
Pattern Recognizer block classi es new patterns as \faces" or \non-faces". The algorithm uses a distribution-based model
to represent the space of all possible canonical face patterns. For each new pattern to be classi ed, it computes a set of
\di erence" measurements between the new pattern and the canonical face model. A trained classi er identi es the new
pattern as being either \a face" or \not a face", based on the set of \di erence" measurements.
carving out regions around the \face" sample distribution that do not correspond to canonical face views. We
shall explain how we synthesize our special database of
\non-face" patterns in Section 5.2.
Our approach uses six prototype \face" clusters to
piece-wise approximate the multi-dimensional distribution of canonical face patterns, and six \non-face" clusters to model the distribution of \non-face" patterns.
Qualitatively, one can view the six \face" clusters as a
coarse distribution-based representation of the canonical face manifold. The six \non-face" clusters help dene boundaries in and around the manifold by carving out nearby regions in the vector space that do not
correspond to face patterns. Each prototype cluster is
a multi-dimensional Gaussian with a centroid location
and a covariance matrix that describes the local data
distribution. We adopt a piece-wise continuous modeling scheme because we believe that the actual face
pattern manifold is continuous and smoothly varying in
our multi-dimensional image vector space { i.e., more often than not, a face pattern with minor spatial and/or
grey-level perturbations still looks like another valid face
pattern. Similarly, a non-face pattern with minor variations would most likely still appear as a non-face pattern.
The piecewise smooth modeling scheme serves two important functions. First, it performs generalization by
applying a prior smoothness assumption to the observed
data sample distribution. This results in a stored data
distribution function that is well de ned even in regions
of the image vector space where no data samples have
been observed. Second, it serves as a tractable scheme
for representing an arbitrary data distribution by means
of a few Gaussian basis functions.
The bottom right image of Figure 3 shows the 12
prototype centroids in our canonical face model. The 5
six \face" prototypes are synthesized by clustering the
database of canonical face patterns, while the six \nonface" prototypes are similarly derived from the database
of non-face patterns. The rest of this section describes
our process for synthesizing prototypes in greater detail.
3.2 Preprocessing
The rst step of synthesizing prototypes is to normalize
the sample window patterns in the databases. Normalization compensates for certain sources of image variation. It reduces the range of possible window patterns
the subsequent stages have to consider, thus making the
modeling and classi cation tasks easier. Our preprocessing stage consists of the following sequence of image window operations:
1. Window resizing: Recall that our scheme performs modeling and classi cation on 19 19 greylevel window patterns. We choose a 19 19 window
size to keep the dimensionality of the window vector space manageably small, but also large enough
to preserve details that distinguish between \face"
and \non-face" window patterns. This operation
re-scales square window patterns of di erent sizes
to 19 19 pixels.
2. Masking: We use the 19 19 binary pixel mask
in Figure 1(b) to zero-out some near-boundary pixels of each window pattern. For \face" patterns,
these masked pixels usually correspond to background pixels irrelevant to the description of a face.
Zeroing out these pixels ensures that our modeling scheme does not wrongly encode any unwanted
background structure in our canonical face representation. It also reduces the dimensionality of our
image window vector space, which helps to make
Figure 3: Our distribution-based canonical face model. Top Row: We use a representative sample of canonical face
patterns to approximate the volume of canonical face views in a masked 19 19 pixel image vector space. We model
the \face" sample distribution with 6 multi-dimensional Gaussian clusters. Center Row: We use a selection of nonface patterns to help re ne the boundaries of our Gaussian mixture approximation. We model the \non-face" sample
distribution with 6 Gaussian clusters. Bottom Row: Our nal model consists of 6 \face" clusters and 6 \non-face"
clusters. Each cluster is de ned by a centroid and a covariance matrix. The 12 centroids are shown on the right. Note:
All the distribution plots are ctitious and are shown only to help with our explanation. The 12 centroids are real.
6
the modeling and classi cation tasks a little more
tractable.
3. Illumination gradient correction: This operation subtracts a best- t brightness plane from the
unmasked window pixels. For face patterns, it does
a fair job at reducing the strength of heavy shadows
caused by extreme lighting angles.
4. Histogram equalization: This operation adjusts for several geometry independent sources of
window pattern variation, including changes in illumination brightness and di erences in camera response curves.
Notice that the same preprocessing steps must also
be applied to all new window patterns being classi ed at
runtime.
3.3 Modeling the Distribution of \Face"
Patterns | Clustering for Positive
Prototypes
We use a database of 4150 normalized canonical \face"
patterns to synthesize 6 \face" pattern prototypes in
our multi-dimensional image vector space. The database
consists of 1067 real face patterns, obtained from several
di erent image sources. We arti cially enlarge the original database by adding to it slightly rotated versions of
the original face patterns and their mirror images. This
helps to ensure that our nal database contains a reasonably dense and representative sample of canonical face
patterns.
Each pattern prototype is a multi-dimensional Gaussian cluster with a centroid location and a covariance
matrix that describes the local data distribution around
the centroid. Our modeling scheme approximates the
observed \face" sample distribution with only a small
number of prototype clusters because the sample size is
still very small compared to the image vector space dimensionality (4150 data samples in a 283 dimensional
masked image vector space). Using a large number of
prototype clusters could lead to over tting the observed
data distribution with poor generalization results. Our
choice of 6 pattern prototypes is somewhat arbitrary.
The system's performance, i.e. its face detection rate
versus the number of false alarms, does not change much
with slightly fewer or more pattern prototypes.
We use a modi ed version of the k-means clustering
algorithm to compute 6 face pattern centroids and their
cluster covariance matrices from the enlarged database
of 4150 face patterns. Our clustering algorithm di ers
from the traditional k-means algorithm in that it ts
directionally elongated (i.e. elliptical) Gaussian distributions to the data sample instead of isotropic Gaussian
distributions. We adopt a non-isotropic mixture model
because we believe the actual face data distribution may
in fact be locally more elongated along certain vector
space directions than others.
To implement our elliptical k-means clustering algorithm, we use an adaptively changing normalized Mahalanobis distance metric instead of a standard Euclidean
distance metric to partition the data sample into clusters. The normalized Mahalanobis distance metric re-
Figure 4: An example of a naturally occuring \non-face"
pattern that resembles a face. Left: The pattern viewed
in isolation. Right: The pattern viewed in the context of
its environment.
turns a directionally dependent distance value between
a new pattern ~x (in column vector form) and a Gaussian
cluster centroid ~ (also as a column vector). It has the
form:
Mn(~x; ~) = 12 (d ln2 + ln jj + (~x ; ~ )T ;1(~x ; ~));
where is the covariance matrix that encodes the cluster's shape and directions of elongation. The normalized
Mahalanobis distance di ers from the Euclidean distance
in that it reduces the penalty of pattern di erences along
a cluster's major directions of data distribution. This
penalty adjustment feature allows the clustering algorithm to form elliptical clusters instead of spherical clusters where there is a non-isotropic local data distribution. Section 4.2 explains the normalized Mahalanobis
distance metric in greater detail.
The following is a crude outline of our elliptical kmeans clustering algorithm:
1. Obtain k (6 in our case) initial pattern centers by
performing vector quantization with euclidean distances on the enlarged face database. Divide the
data set into k partitions (clusters) by assigning
each data sample to the nearest pattern center in
euclidean space.
2. Initialize the covariance matrices of all k clusters to
be the identity matrix.
3. Re-compute pattern centers to be the centroids of
the current data partitions.
4. Using the current set of k pattern centers and their
cluster covariance matrices, re-compute data partitions by re-assigning each data sample to the nearest pattern center in normalized Mahalanobis distance space. If the data partitions remain unchanged or if the maximum number of inner-loop
(i.e. Steps 3 and 4) iterations has been exceeded,
proceed to Step 5. Otherwise, return to Step 3.
5. Re-compute the covariance matrices of all k clusters
from their respective data partitions.
6. Using the current set of k pattern centers and their
cluster covariance matrices, re-compute data partitions by re-assigning each data sample to the nearest pattern center in normalized Mahalanobis distance space. If the data partitions remain unchanged or if the maximum number of outer-loop
7
Figure 5: An illustration on how \negative" prototypes can help model concavities in a distribution with fewer Gaussian
basis functions. Left: A hypothetical data distribution in 2 dimensions with a concave surface. Center: The
distribution can be reasonably approximated with one positive Gaussian prototype encircling the distribution and one
negative prototype carving out the concave region. Right: To model the same distribution with only positive prototypes,
one has to use more Gaussian basis functions. The di erence in number of basis functions can be a lot larger in a higher
dimensional space.
(i.e. Steps 3 to 6) iterations has been exceeded,
proceed to Step 7. Otherwise, return to Step 3.
7. Return the current set of k pattern centers and their
cluster covariance matrices.
The inner loop (i.e. Steps 3 and 4) is analogous to the
traditional k-means algorithm. Given a xed distance
metric, it nds a set of k pattern prototypes that stably
partitions the sample data set. Our algorithm di ers
from the traditional k-means algorithm because of Steps
5 and 6 in the outer loop, where we try to iteratively
re ne and recover the cluster shapes as well.
\face" pattern distribution. The system's face detection
rate versus false alarm ratio does not change much with
slightly fewer or more \non-face" pattern prototypes.
We use our elliptical k-means clustering algorithm to
obtain 6 \non-face" prototypes and their cluster covariance matrices from a database of 6189 face-like patterns.
The database was incrementally generated in a \bootstrap" fashion by rst building a reduced version of our
face detection system with only \face" prototypes, and
collecting all the false positive patterns it detects over a
large set of random images. Section 5.2 elaborates further on our \boot-strap" data generation technique.
3.4 Modeling the Distribution of \Non-Face"
Patterns | Clustering for Negative
Prototypes
3.5 Summary and Remarks
There are many naturally occuring \non-face" patterns
in the real world that look like faces when viewed in isolation. Figure 4 shows one such example. In our multidimensional image window vector space, these \facelike" patterns lie along the boundaries of the canonical
face manifold. Because we are coarsely representing the
canonical face manifold with 6 Gaussian clusters, some
of these face-like patterns may even be located nearer the
\face" cluster centroids than some real \face" patterns.
This may give rise to misclassi cation problems, because
in general, we expect the opposite to be true, i.e. face
patterns should lie nearer the \face" cluster centroids
than non-face patterns.
In order to avoid possible misclassi cation, we try to
obtain a comprehensive sample of these face-like patterns
and explicitly model their distribution using 6 \nonface" prototype clusters. These \non-face" clusters carve
out negative regions around the \face" clusters that do
not correspond to face patterns. Each time a new window pattern lies too close to a \non-face" prototype, we
favor a \non-face" hypothesis even if the pattern also lies
near a \face" prototype. Our choice of using exactly 6
pattern prototypes to model the \non-face" distribution
is also somewhat arbitrary, as in the case of modeling the
One of the key diculties in face detection is to account
for the wide range of permissible face pattern variations
that cannot be adequately captured by geometric models, correlation templates and other classical parametric
modeling techniques. Our approach addresses this problem by modeling the distribution of frontal face patterns
directly in a xed 19 19 pixel image vector space. We
infer the actual distribution of face patterns in the image vector space from a suciently representative set of
face views, and a carefully chosen set of non-face patterns. The distribution-based modeling scheme statistically encodes observable face pattern variations that
cannot otherwise be easily parameterized by classical
modeling techniques. To generalize from the slow varying nature of the face pattern distribution in the image
vector space, and to construct a tractable model for the
face pattern distribution, we interpolate and represent
the observed distribution in a piecewise-smooth fashion
using a few multi-dimensional Gaussian clusters.
Our nal distribution-based model consists of 6 \face"
clusters for coarsely approximating the canonical face
pattern manifold in the image vector space, and 6 \nonface" clusters for representing the distribution of a specially selected \non-face" data sample. The non-face
patterns come from non-face regions in the image vector
8 space near the canonical face manifold. We propose two
Figure 6: The measurements returned from matching a test pattern against our distribution-based model. (a): Each
set of measurements is a vector of 12 distances between the test pattern and the model's 12 cluster centroids. (b): Each
distance measurement between the test pattern and a cluster centroid is a 2-value distance metric. The rst component is a
Mahalanobis distance between the test pattern's projection and the cluster centroid in a subspace spanned by the cluster's
75 largest eigenvectors. The second component is the Euclidean distance between the test pattern and its projection in
the subspace. So, the entire set of 12 distance measurements is a vector of 24 values.
possibly related ways of reasoning about the 6 \non-face"
pattern clusters:
1. The 6 \non-face" clusters explicitly model the distribution of face-like patterns that are not actual
faces | i.e. \near miss" patterns that the face detection system should classify as \non-faces". They
de ne and represent a separate \near-miss" pattern
class in the multi-dimensional vector space, just like
how the 6 \face" clusters encode a \canonical face"
pattern class. Test patterns that fall under this
\near-miss" class are classi ed as non-faces.
2. The 6 \non-face" clusters carve out regions in and
around the \face" clusters that should not correspond to face patterns. They help shape the boundaries in our Gaussian mixture model of the canonical face manifold. More interestingly, they can also
help one model concavities in the canonical face
manifold with fewer Gaussian basis functions (see
Figure 5). This advantage of using \non-face" clusters becomes especially critical when one has too
few face data samples to model a concave distribution region with a large number of Gaussian \face"
clusters.
4 Matching Patterns with the Model
To detect faces, our system rst matches each candidate window pattern in an input image against our
distribution-based canonical face model. Each match
returns a set of measurements that captures a notion
of \similarity" or \di erence" between the test pattern
and the face model. At a later stage, a trained classi er
determines, based on the set of \match" measurements,
whether or not the test pattern is a frontal face view.
This section describes the set of \match" measurements we compute for each new window pattern. Each
set of measurements is a vector of 12 distances between
the test window pattern and the model's 12 cluster centroids in our multi-dimensional image vector space (see
Figure 6(a)). One way of interpreting our vector of distances is to treat each distance measurement as the test
pattern's actual distance from some key reference location on or near the canonical face pattern manifold. The
set of all 12 distances can then be viewed as a crude \difference" notion between the test pattern and the entire
\canonical face" pattern class.
4.1 A 2-Value Distance Metric
We now de ne a new metric for measuring distance
between a test pattern and a prototype cluster centroid.
Ideally, we want a metric that returns small distances
between face patterns and the \face" prototypes, and either large distances between non-face patterns and the
\face" prototypes, or small distances between non-face
patterns and the \non-face" centers. We propose one
such measure that normalizes distances by taking into
account both the local data distribution around a prototype centroid, and the reliability of the local distribution
estimate. The measure scales up distances orthogonal
to a cluster's major axes of elongation, and scales down
distances along the cluster's major elongation directions.
We argue that such a distance measure should meet our
ideal goals reasonably well, because we expect most face
patterns on the face manifold to lie along the major axes
of one or more \face" clusters, and hence register small
distances with one or more \face" prototypes. Similarly,
we expect most non-face patterns to lie either far away
9 from all the \face" clusters or along the major axes of
Figure 7: Graphs of eigenvalues in decreasing order of magnitude. Left: Decreasing eigenvalues for 6 \Face" clusters.
Right : Decreasing eigenvalues for 6 \Non-Face" clusters.
one or more \non-face" clusters, and hence either register large distances with all the \face" prototypes or small
distances with some \non-face" prototypes.
Our proposed distance measure consists of two output components (see Figure 6(b)). The rst value is
a Mahalanobis-like distance between the test pattern
and the prototype centroid, de ned within a lowerdimensional sub-space of our masked 19 19 pixel image
vector space. The sub-space is spanned by the 75 largest
eigenvectors of the prototype cluster. This distance component is directionally weighted to re ect the test pattern's location relative to the major elongation directions in the local data distribution around the prototype center. The second value is a normalized Euclidean
distance between the test pattern and its projection in
the lower-dimensional sub-space. This is a uniformly
weighted distance component that accounts for pattern
di erences not included in the rst component due to
possible modeling inaccuracies. We elaborate further on
the two components below.
4.2 The Normalized Mahalanobis Distance
Mn(~x; ~) = 21 (d ln2 + ln jj + (~x ; ~ )T ;1(~x ; ~)):
Here, d is the vector space dimensionality and jj means
the determinant of .
The normalized Mahalanobis distance is simply the
negative natural logarithm of the best- t Gaussian distribution described above. It is normalized in the sense
that it originates directly from a probability density
distribution that integrates to unity. Our modi ed kmeans clustering algorithm in Section 3 uses the normalized Mahalanobis distance metric instead of the standard
form because of stability reasons. Notice that for a given
spatial displacement between a test pattern and a prototype centroid, the standard Mahalanobis distance tends
to be smaller for long clusters with large covariance matrices than for small clusters. So, if one uses a standard
Mahalanobis distance metric to perform clustering, the
larger clusters will constantly increase in size and eventually overwhelm all the smaller clusters.
As a distance metric for establishing the class identity of test patterns, the Mahalanobis distance and its
normalized form are both intuitively pleasing for the following reason: They both measure pattern di erences in
a distribution dependent manner, unlike the Euclidean
distance which measures pattern di erences in an absolute sense. More speci cally, the distances they measure are indicative of how the test pattern ranks relative
to the overall location of other known patterns in the
pattern class. In this sense, they capture very well the
notion of \similarity" or \dis-similarity" between a test
pattern and a pattern class.
We begin with a brief review of the Mahalanobis distance. Let ~x be a column vector test pattern, ~ be a
column vector prototype centroid, and be the covariance matrix describing the local data distribution near
the centroid. The Mahalanobis distance between the test
pattern and the prototype centroid is given by:
M(~x; ~) = (~x ; ~)T ;1(~x ; ~):
Geometrically, the Mahalanobis distance can be interpreted as follows. If one models the prototype cluster
with a best- t multi-dimensional Gaussian distribution,
then one gets a best- t Gaussian distribution centered
at ~ with covariance matrix . All points at a given Ma- 4.3 The First Distance Component |
Distance within a Normalized
halanobis distance from ~ occupy a constant density surLow-Dimensional Mahalanobis Subspace
face in this multi-dimensional vector space. This interpretation of the Mahalanobis distance leads to a closely
As mentioned earlier, our distance metric consists of
related distance measure, which we call the normalized 2 output values as shown in Figure 6(b). The rst
Mahalanobis distance, given by:
10 value, D1, is a Mahalanobis-like distance between the
Figure 8: The eigen-image model of faces by Turk and Pentland [19] [12]. The approach represents the space of all
face views (i.e. the \Face Space") as a linear combination of several orthonormal eigen-images. The eigen-images are
computed by performing PCA on an example database of face patterns. The modeling scheme assumes that all face views
lie within the \face space", and each face view corresponds to a set of coecients that describes its appearance as a linear
combination of the eigen-images. One can use the coecients as features to recognize faces of di erent individuals. One
can also determine whether or not a test pattern is a face by computing and thresholding d, a measure of how badly the
eigen-images reconstruct the test pattern.
test pattern and the prototype center. This distance is orthogonal in direction to the cluster's 75 most signi de ned within a 75-dimensional sub-space of our masked cant eigenvectors. We omit the smaller eigenvectors in
19 19 pixel image vector space, spanned by the 75 this directionally dependent distance measure because
largest eigenvectors of the current prototype cluster. Ge- we believe that their corresponding eigenvalues may be
ometrically, we can interpret the rst distance value as signi cantly inaccurate due to the small number of data
follows: The test pattern is rst projected onto the 75 samples available to approximate each cluster. For indimensional vector sub-space. We then compute the nor- stance, we have, on the average, fewer than 700 data
malized Mahalanobis distance between the test pattern's points to approximate each \face" cluster in a 283 diprojection and the prototype center as the rst output mensional masked image vector space. Using the smaller
value. Like the standard Mahalanobis distance, this rst eigenvectors and eigenvalues to compute a distribution
value locates and characterizes the test pattern relative dependent distance can therefore easily lead to meaningless results.
to the cluster's major directions of data distribution.
Figure 7 plots the eigenvalues of our 12 prototype clusMathematically, the rst value is computed as follows:
Let ~x be the column vector test pattern, ~ be the pro- ters in decreasing order of magnitude. Notice that for all
totype pattern, E75 be a matrix with 75 columns, where 12 curves, only a small number of eigenvectors are sigcolumn i is a unit vector in the direction of the cluster's ni cantly larger than the rest. We use the following criith largest eigenvector, and W75 be a diagonal matrix terion to arrive at 75 \signi cant" eigenvectors for each
of the corresponding 75 largest eigenvalues. The covari- cluster: We eliminate from each cluster the maximum
ance matrix for the cluster's data distribution in theT75 possible number of trailing eigenvectors, such that the
dimensional subspace is given by 75 = (E75W75E75), sum of all eliminated eigenvalues is still smaller than the
largest eigenvalue in the cluster. This criterion leaves
and the rst distance value is:
us with approximately 75 eigenvectors for each cluster,
D1(~x; ~) = 21 (75 ln2 + ln j75j + (~x ; ~)T ;751(~x ; ~)): which we standardize at 75 for the sake of simplicity.
Second Distance Component |
We emphasize again that this rst value is not a \com- 4.4 The
Distance
from the Low-Dimensional
plete" distance measure in our masked 19 19 pixel imMahalanobis
Subspace
age vector space, but rather a \partial" distance measure
in a subspace of the current cluster's 75 most signi - The second output value of our distance metric is a stancant eigenvectors. The measure is not \complete" in the dard Euclidean distance between the test pattern and
sense that it does not account for pattern di erences in its projection in the 75 dimensional sub-space. This
certain image vector space directions, namely di erences 11 distance component accounts for pattern di erences not
Figure 9: The view-based model of volcanos by Burl et.
al. [4]. The approach assumes that the set of all volcano
patterns lies within a low dimensional model space, spanned
by a small number of the largest principal component vectors from a volcano image database. Each pattern in the
model space corresponds to a set of coecients that describes the pattern's appearance as a linear combination of
the principal component images. Not all linear combinations of principal component images are volcano patterns,
so one can detect volcanos by learning from examples the
range of coecient values that corresponds to volcanos.
captured by the rst component, namely pattern di erences in the smaller eigenvector directions. Because we
may not have a reasonable estimate of the smaller eigenvalues, we simply assume an isotropic Gaussian sample
data distribution in the smaller eigenvector directions,
and hence a Euclidean distance measure.
Using the notation from the previous sub-section, we
can show that the second component is simply the L2
norm of the displacement vector between ~x and its projection x~p :
D2 (~x; ~) = jj(~x ; x~p )jj = jj(I ; E75E75T )(~x ; ~)jj:
Notice that on its own, the second distance value is
also not a \complete" distance measure in our masked
19 19 pixel image vector space. Speci cally, it does
not account for pattern di erences in the subspace of
the cluster's 75 most signi cant eigenvectors. It complements the rst output value to form a \complete"
distance measure that captures pattern di erences in all
directions of our masked 1919 pixel image vector space.
4.5 Relationship between our 2-Value Distance
and the Mahalanobis Distance
totype cluster 1 . Recall from Section 4.2 that the Mahalanobis distance and its normalized form arise from
tting a multi-dimensional full-covariance Gaussian to a
sample data distribution. For high dimensional vector
spaces, modeling a distribution with a full-covariance
Gaussian is often not feasible because one usually has
too few data samples to recover the covariance matrix
accurately. In a d dimensional vector space, each fullcovariance Gaussian requires d parameters to de ne its
centroid and another d(d + 1)=2 more parameters to dene its covariance matrix. For d = 283, this amounts to
40469 parameters!
One way of reducing the number of model parameters
is to use a restricted Gaussian model with a diagonal covariance matrix, i.e., a multi-dimensional Gaussian distribution whose elongation axes are aligned to the vector space axes. In our domain of 19 19 pixel images,
this corresponds to a model whose individual pixel values
may have di erent variances, but whose pair-wise pixel
values are all uncorrelated. Clearly, this is a very poor
model for face patterns which are highly structured with
groups of pixels having very highly correlated intensities.
An alternative way of simplifying the Gaussian model
is to preserve only a small number of \signi cant" eigenvectors in the covariance matrix. One can show that
a d dimensional Gaussian with h principal components
has a covariance matrix of only h(2d ; h + 1)=2 free
parameters. This can easily be a tractable number of
model parameters if h is small. Geometrically, the operation corresponds to projecting the original d dimensional Gaussian cluster onto an h dimensional subspace,
spanned by the cluster's h most \signi cant" elongation
directions. The h dimensional subspace projection preserves the most prominent correlations between pixels
in the target pattern class. To exploit these pixel-wise
correlations for pattern classi cation, one computes a directionally weighted Mahalanobis distance between the
test pattern's projection and the Gaussian centroid in
this h dimensional subspace | D1 of our 2-Value distance metric.
The orthogonal subspace is spanned by the d ; h remaining eigenvectors of the original Gaussian cluster.
Because this subspace encodes pixel correlations that are
less prominent and possibly less reliable due to limited
training data, we simply assume an isotropic Gaussian
distribution of data samples in this subspace, i.e. a diagonal covariance matrix Gaussian with equal variances
along the diagonal. The isotropic Gaussian distribution requires only 1 free parameter to describe its variance. To measure distances in this subspace of isotropic
data distribution, we use a directionally independent Euclidean distance | D2 of our 2-Value distance metric.
We can thus view our 2-Value distance metric as a
robust approximate Mahalanobis distance that one uses
when there is insucient training data to accurately recover all the eigenvectors and eigenvalues of a Gaussian
model. The approximation degrades gracefully by using
its limited degrees of freedom to capture the most prominent pixel correlations in the data distribution. Notice
There is an interesting relationship between our 2-Value
1 See [8] for a similar interpretation and presentation. Our
distance metric and the \complete" normalized Mahalanobis distance involving all 283 eigenvectors of a pro- 12 explanation here is adapted from theirs.
Figure 10: One of the multi-layer perceptron (MLP) net architectures we trained to identify face patterns from our vector
of distance measurements. The net has 12 pairs of input units to accept the 12 pairs of distance values from our matching
stage. When trained, the output unit returns a 1 for face patterns and a 0 otherwise. Notice that this net has one special
layer of hidden units that combines each 2-Value distance pair into a single distance value. Our experiments show that
the detailed net architecture is really not crucial in this application.
combination coecients. Because the technique assumes
that all face patterns actually lie within the \face space",
one can use the set of linear combination coecients as
features to parameterize and recognize faces of di erent
individuals (see Figure 8). Similarly, one can determine
or not a given pattern is a face by measuring
4.6 Relationship between our 2-Value Distance whether
how well or poorly the eigen-images reconstruct the patand some PCA-based Classical Distance
tern | i.e., the pattern's distance (d in Figure 8) from
Measures
the \face space" [12].
In another recent application of classical techniques,
Our 2-Value distance metric is also closely related to the
classical distance measures used by principal components Burl et. al. [4] have used a di erent PCA based approach
analysis (PCA, also called Karhunen-Loeve expansion) for a terrain classi cation task on nding volcanos in
based classi cation schemes [5] [6] [18]. We examine two SAR images of Venus. Their system builds a low dimensional view-based volcano model, parameterized by a
such distance measures below.
A standard way of modeling a 3D object for pattern small number of the largest principal component vectors
recognition is to represent its space of 2D views using a from an example set of volcano images (see Figure 9).
few basis images, obtained by performing principal com- Within this low-dimensional model space, Burl et. al.
ponents analysis on a comprehensive set of 2D views. further observe that not all reconstructible patterns are
The modeling approach assumes that all possible 2D actual volcano views; i.e., not all linear combinations of
views of the target object lie within a low dimensional principal component images are volcano patterns. Thus,
sub-space of the original high dimensional image space. to detect volcanos, they use the set of linear combinaThe low dimensional sub-space is linearly spanned by tion coecients as classi cation features, and learn from
the principal components. Each new view of the target examples the range of coecient values, i.e. distances
object can be represented by a set of coecients that within the volcano model space, that actually correspond
describes the view as a linearly weighted superposition to volcano patterns.
One can relate our 2-Value distance metric to
of the principal components.
Kirby and Sirovich [16] [9] have used principal compo- the above PCA based classi cation techniques as folnents analysis methods to build low-dimensional mod- lows: Suppose we treat each Gaussian cluster in our
els for characterizing the space of human faces. As a distribution-based model as locally representing a subrepresentative recent example, let us consider Turk and class of \face" or \non-face" patterns, then the cluster's
Pentland's application of PCA techniques to face recog- 75 largest eigenvectors can be viewed as a set of basis imnition [19] and facial feature detection [12]. To opti- ages that linearly span the sub-class. Each new pattern
mally represent their \face space", Turk and Pentland in the sub-class corresponds to a set of 75 coecients in
compute an orthonormal set of eigen-images from an ex- the model space.
Our distance component D2 is the Euclidean distance
ample database of face patterns to span the space. New
face views are represented by projecting their image pat- between a test pattern and the cluster's 75 largest eigenterns onto the set of eigen-images to obtain their linear 13 vector subspace. Assuming that the 75 eigenvectors are
that as the data sample size increases, one can preserve
a larger number of principal components in the Gaussian
model. This results in D1 becoming increasingly like the
\complete" Mahalanobis distance with D2 vanishing in
size and importance.
Figure 11: Arti cially generating virtual examples of face patterns. For each original face pattern in our training database,
we can generate a few new face patterns using some simple image transformations. We arti cially enlarge our face database
in this fashion to obtain a more comprehensive sample of face patterns.
the \basis views" that span our target sub-class, this distance component measures how poorly the basis views
reconstruct the test pattern, and hence how \di erent"
the test pattern is relative to the entire target sub-class.
This distance is analogous to Turk and Pentland's distance to \face space" metric (i.e. d in Figure 8), which
quanti es the \di erence" between a test pattern and
the class of face views.
The distance component D1 is a Mahalanobis distance
between the cluster centroid and a test pattern's projection in the 75 largest eigenvector subspace. Here, we
implicitly assume, like Burl et. al., that not all reconstructible patterns in our 75 eigenvector model space
are views of the target sub-class, and that all views of
the target sub-class are located within a certain Mahalanobis distance from the cluster centroid. This constrains the range of model coecients that correspond
to actual target patterns, just like how Burl et. al. constrain by learning their range of model parameters that
correspond to actual volcano views.
Thus, our D1 and D2 distance measurements correspond to di erent classical classi cation criteria used
also recently. As far as we know, this paper presents the
rst attempt to combine these two measures for pattern
classi cation.
distance vector arises from a \face" pattern, and a `0'
otherwise.
In our current system, the hidden units are partially
connected to the input terminals and output unit as
shown in Figure 10. The connections exploit some prior
knowledge of the problem domain. Notice in particular
that there is one layer of hidden units that combines each
2-Value distance pair into a single distance value. Our
experiments in the next section will show that the number of hidden units and network connectivity structure
do not signi cantly a ect the classi er's performance.
We train our multi-layer perceptron classi er on feature distance vectors from a database of 47316 window
patterns. There are 4150 positive examples of \face"
patterns in the database and the rest are \non-face"
patterns. The net is trained with a standard backpropagation learning algorithm [14] until the output error stabilizes at a very small value. For the particular
multi-layer perceptron net architecture in Figure 10, we
actually get a training output error of 0.
5.2 Generating and Selecting Training
Examples
In many example-based learning applications, how well
a learner eventually performs on its task depends heavily on the quality of examples it receives during training.
An ideal learning scenario would be to give the learner
5 The Classi er
as large a set of training examples as possible, in order
The classi er's task is to identify \face" test patterns to attain a comprehensive sampling of the input space.
from \non-face" patterns based on their match feature Unfortunately, there are some real-world considerations
vectors of 12 distance measurements. Our approach that could seriously limit the size of training databases,
treats the classi cation stage as one of learning a func- such as shortage of free disk space and computation retional mapping from input feature distance vectors to source constraints.
output classes using a representative set of training exHow do we build a comprehensive but tractable
amples.
database of \face" and \non-face"" patterns? For \face"
patterns, the task at hand seems rather straight forward.
5.1 A Multi-Layer Perceptron Classi er
We simply collect all the frontal views of faces we can nd
We use a Multi-Layer Perceptron (MLP) net to perform in mugshot databases and other image sources. Because
the desired classi cation task. The net has 12 pairs of we do not have access to many mugshot databases and
input terminals, one output unit and 24 hidden units. the size of our mugshot databases are all fairly small, we
Each hidden and output unit computes a weighted sum do not encounter the problem of having to deal with an
of its input links and performs sigmoidal thresholding unmanageably large number of \face" patterns. In fact,
on its output. During classi cation, the net is given a to make our set of \face" patterns more comprehensive,
vector of the current test pattern's distance measure- we even arti cially enlarged our data set by adding virments to the 12 prototype centers. Each input terminal tual examples [13] of faces to the \face" database. These
pair receives the distance values for a designated proto- virtual examples are mirror images and slightly rotated
type pattern. The output unit returns a `1' if the input 14 versions of the original face patterns, as shown in Fig-
Figure 12: Some false detects by an earlier version of our face detection system, marked by solid squares on the two
images above. We use these false detects as new negative examples to re-train our system in a \boot-strap" fashion.
end of each iteration, we can re-cluster our \face" and
ure 11.
For \non-face" patterns, the task we have seems more \non-face" databases to generate new prototype patterns
tricky. In essence, every square non-canonical face win- that might model the distribution of face patterns more
dow pattern of any size in any image is a valid \non-face" accurately.
pattern. Clearly, even with a few source images, our set
of \non-face" patterns can grow intractably large if we 6 Results and Performance Analysis
are to include all valid \non-face" patterns in our trainWe implemented and tested our face detection system
ing database.
To constrain the number of \non-face" examples in on a wide variety of images. Figure 13 shows some samour database, we use a \boot-strap" strategy that in- ple results. The system detects faces over a fairly large
crementally selects only those \non-face" patterns with range of scales, beginning with a window size of 19 19
pixels and ending with a window size of 100 100 pixels.
high information value. The idea works as follows:
successive scales, the window width is enlarged
1. Start with a small and possibly incomplete set of Between
by
a
factor
of 1:2.
\non-face" examples in the training database.
The system writes its face detection results to an out2. Train the multi-layer perceptron classi er with the put image. Each time a \face" window pattern is found
current database of examples.
in the input, an appropriately sized dotted box is drawn
3. Run the face detector on a sequence of random at the corresponding window location in the output imimages. Collect all the \non-face" patterns that age. Notice that many of the face patterns in Figure 13
the current system wrongly classi es as \faces" (see are enclosed by multiple dotted boxes. This is because
Figure 12). Add these \non-face" patterns to the the system has detected those face patterns either at a
few di erent scales or at a few slightly o set window
training database as new negative examples.
positions or both.
4. Return to Step 2.
The upper left and bottom right images of Figure 13
At the end of each iteration, the \boot-strap" strat- show that our system works reliably without making
egy enlarges the current set of \non-face" patterns with many false positive errors (none in this case), even for
new \non-face" patterns that the current system classi- fairly complex scenes. Notice that the current system
es wrongly. We argue that this strategy of collecting does not detect Geordi's face. This is because Geordi's
wrongly classi ed patterns as new training examples is face di ers signi cantly from the notion of a \typical"
reasonable, because we expect these new examples to face pattern in our training database of faces | his eyes
improve the classi er's performance by steering it away are totally occluded by an opaque metallic visor. The
upper right input-output image pair demonstrates that
from the mistakes it currently commits.
Notice that if necessary, we can use the same \boot- the same system detects real faces and hand-drawn faces
strap" technique to enlarge the set of positive \face" pat- equally well, while the bottom left image shows that
terns in our training database. Also, notice that at the 15 the system nds faces successfully at two very di erent
Figure 13: Some face detection results by our system. The upper left and bottom right images show that the system
nds faces in complex scenes without making many false detects. The upper right image pair shows that the same system
detects real faces and hand drawn faces equally well. The bottom left image shows the system working successfully at two
very di erent scales. Notice that in the cards image, the system detects only the vertically oriented face patterns as it is
meant to at this time.
16
scales.
pairs of input terminals. The single perceptron unit
computes a sigmoidally thresholded weighted sum
6.1 Measuring the System's Performance
of its input feature distance vector. It represents
the simplest possible architecture in the family of
To quantitatively measure our system's performance, we
multi-layer perceptron net classi ers, and its purran our system on two test databases and counted the
pose here is to provide an \extreme case" perfornumber of correct detections versus false alarms. All the
mance gure for multi-layer perceptron net classiface patterns in both test databases are new patterns not
ers in this problem domain.
found in the training data set. The rst test database
consists of 301 frontal and near-frontal face mugshots
2. A nearest neighbor classi er. We perform nearof 71 di erent people. All the images are high quality
est neighbor classi cation on feature distance vecdigitized images taken by a CCD camera in a laborators to identify new test patterns. The nearest
tory environment. There is a fair amount of lighting
neighbor classi er works as follows: For each trainvariation among images in this database, with about 10
ing pattern, we compute and store its 24 value feaimages having very strong lighting shadows. We use this
ture distance vector and output class at compile
database to obtain a \best case" detection rate for our
time. When classifying a new test pattern, we comsystem on high quality input patterns.
pute its 24 value feature distance vector and return
The second database contains 23 images with a total
the output class of the closest stored feature vector
of 149 face patterns. There is a wide variation in quality
in Euclidean space. The nearest neighbor classi er
among the 23 images, ranging from high quality CCD
provides us with a performance gure for a di erent
camera pictures to low quality newspaper scans. Most
classi er type in this problem domain.
of these images have complex background patterns with The Distance Metric The second experiment invesfaces taking up only a very small percentage of the total tigates how using a di erent distance metric for comimage area. We use this database to obtain an \average
feature distance vectors in the matching stage
case" performance measure for our system on a more puting
a
ects
the
system's performance. We compare our 2representative sample of input images.
distance metric with three other distance meaFor the rst database, our system correctly nds Value
(1) the normalized Mahalanobis distance within
96:3% of all the face patterns and makes only 3 false sures:
a
75
dimensional
subspace spanned by the prodetects. All the face patterns that it misses have either totype cluster's 75vector
largest
| i.e. the rst
strong illumination shadows or fairly large o -plane ro- component only (D ) of oureigenvectors
2-Value distance metric, (2)
1
tation components or both. Even though this high de- the Euclidean distance
between the test pattern and its
tection rate applies only to high quality input images, projection in the 75 dimensional
subspace | i.e. the secwe still nd the result encouraging because often, one ond component only (D ) of our 2-Value
distance metric,
2
can easily replace poorer sensors with better ones to ob- and (3) the standard normalized Mahalanobis
distance
tain comparable results. For the second database, our (M ) between the test pattern and the prototype
cenn
system achieves a 79:9% detection rate with 5 false posi- troid within the full image vector space.
tives. The face patterns it misses are mostly either from
conduct this experiment, we repeat the previous
low quality newspaper scans or hand drawn pictures. We setToof classi
experiments three additional times, once
consider this behavior acceptable because the system is for each newerdistance
we are comparing. Each
merely degrading gracefully with poorer image quality. new set of experiments dimetric
ers from the original set as follows: During the matching stage, we use one of the three
6.2 Analyzing the System's Components
measures above instead of the original 2-Value
We conducted the following additional experiments to distance
distance
to compute feature distance vectors beidentify the key components of our face detection algo- tween newmetric
test
patterns
and the 12 prototype centroids.
rithm. Speci cally, we examined how the following three Notice that because the three
distance measures are
aspects of our system a ects its performance in terms of all single-value measurements,new
our
feature distance
face detection rate versus false alarm ratio: (1) The clas- vectors have only 12 values insteadnew
of
24
values. This
si er architecture, (2) our 2-Value distance metric versus means that we have to modify the classi er architectures
other distance measures for computing feature distance accordingly by reducing the number of input terminals
vectors, and (3) the importance of \non-face" prototypes from 24 to 12.
in our distribution-based face model.
\Non-Face" Prototypes This experiment looks at
Classi er Architecture The rst experiment investi- how di erently the system performs with and without
gates how varying the classi er's architecture a ects our \non-face" prototypes in the distribution-based model.
system's overall performance. To do this, we create two We compare results from our original system, whose face
new systems with di erent classi er architectures, and model contains both \face" and \non-face" prototypes,
compare their face detection versus false alarm statistics against results from two new systems whose internal
with those of our original system. Our two new classi er models contain only \face" prototypes. The two new
architectures are:
systems are:
1. A system with 12 \face" prototypes and
1. A single perceptron unit. We replace the origno \non-face" prototypes. In this system, we
inal multi-layer perceptron net in Figure 10 with a
x the total number of pattern prototypes in the
single perceptron unit connected directly to the 12 17
Classi er Architecture
Multi-Layer Single Unit Nearest Nbr
96.3% 3 96.7% 3 65.1%
1
79.9% 5 84.6% 13
D1
91.6% 21 93.3% 15 97.4% 208
( rst component) 85.1% 114 85.1% 94
D2
91.4% 4 92.3% 3 53.9%
1
(second component) 65.1% 5 68.2% 5
Mn
84.1% 9 93.0% 13 71.8%
5
(Std. Mahalanobis) 42.6% 5 58.6% 11
Distance Metric
2-Value
Table 1: Summary of performance gures from Experiments 1 (Classi er Architecture) and 2 (Distance Metric). Detection
rates versus number of false positives for di erent classi er architectures and distance metrics. The four numbers for each
entry are: Top Left: detection rate for rst database. Top Right: number of false positives for rst database. Bottom
Left: detection rate for second database. Bottom Right: number of false positives for second database. Notice that
we did not test the nearest neighbor architecture on the second database. This is because the test results from the rst
database already show that the nearest neighbor classi er is signi cantly inferior to the other 2 classi ers in this problem
domain.
canonical face model, and hence the dimensionality
of the feature distance vector the matching stage
computes. We obtain the 12 \face" prototypes
by performing elliptical k-means clustering with 12
centers on our enlarged canonical face database of
4150 patterns (see Section 3.3). The matching stage
computes the same 2-Value distance metric that our
original system uses; i.e., for each prototype cluster, D1 is the normalized Mahalanobis distance in
a subspace of the 75 largest eigenvectors, and D2
is the Euclidean distance between the test pattern
and the subspace.
2. A system with only 6 \face" prototypes. In
this system, we preserve only the \face" prototypes
from the original system. The matching stage computes the same 2-Value distances between each test
pattern and the 6 \face" centroids. Notice that the
resulting feature distance vectors have only 6 pairs
of values.
We generate two sets of performance statistics for each
the two new systems above. For the rst set, we use a
trained multi-layer perceptron net with 12 hidden units
to classify new patterns from their feature distance vectors. For the second set, we replace the multi-layer perceptron net classi er with a trained single perceptron
unit classi er.
somewhat higher face detection rate with a lot more false
alarms, or a much lower face detection rate with somewhat fewer false alarms than the other two classi ers.
Because we do not have a reasonable measure of relative
importance between face detection rate and number of
false alarms, we empirically rank the performance gures by visually examining their corresponding output
images. In doing so, we nd that the two network-based
classi ers produce results that are a lot more visually
appealing than the nearest neighbor classi er.
It is interesting that the two network-based classi ers
we tested produce very similar performance statistics,
especially on the rst test database. The similarity here
suggests that the system's performance depends most
critically on the classi er type, i.e. a perceptron net,
and not on the speci c net architecture. It is also somewhat surprising that one can get very encouraging performance gures even with an extremely simple single
perceptron unit classi er, especially when using our 2Value distance metric to compute feature distance vectors. This suggests that the distance vectors we get with
our 2-Value distance metric are a linearly very separable
set of features for \face" and \non-face" patterns.
Why does the nearest neighbor classi er have a much
lower face detection rate than the other two networkbased classi ers when used with our 2-Value distance
metric? We believe this has to do with the much larger
6.3 Performance Figures and Interpretation
number of non-face patterns in our training database
Table 1 summarizes the performance statistics for than face patterns (43166 non-face patterns versus 4150
both the classi er architecture and distance metric ex- face patterns). The good performance gures from the
periments, while Table 2 shows how the system performs single perceptron classi er suggest that the two pattern
classes are linearly highly separable in our 24 value feawith and without \Non-Face" model prototypes.
ture distance vector space. Assuming that roughly the
Classi er Architecture The horizontal rows of Ta- same fraction of face and non-face patterns lie along
ble 1 show how di erent classi er architectures a ect the linear class boundary, we get a boundary population
the system's face detection rate versus false alarm in- with 10 times more non-face samples than face samples.
stances. Quantitatively, the two network-based classi- A new face pattern near the class boundary will thereers have very similar performance gures, while the fore have a very high chance of lying nearer a non-face
nearest neighbor classi er produces rather di erent per- sample than a face sample, and hence be wrongly clasformance statistics. Depending on the distance metric si ed by a nearest neighbor scheme. Notice that despite
being used, the nearest neighbor classi er has either a 18 the huge di erence in number of face and non-face train-
Composition of Prototypes
Classi er
6 Face &
12 Face
6 Face
Architecture
6 Non-Face
Multi-layer Perceptron 96.3% 3 85.3% 21 59.7% 17
79.9% 5 69.6% 74 60.9% 41
Single Perceptron
96.7% 3 52.1% 6 66.6% 25
84.6% 13 49.7% 16 55.4% 56
Table 2: Summary of performance gures for Experiment 3 (\Non-Face" Prototypes). Detection rates versus number of
false positives for di erent classi er architectures and composition of prototypes in distribution-based model. The four
numbers for each entry are: Top Left: detection rate for rst database. Top Right: number of false positives for rst
database. Bottom Left: detection rate for second database. Bottom Right: number of false positives for second
database.
ing patterns, a perceptron classi er can still locate the with a \partial" D2 distance metric almost always outface vs. non-face class boundary accurately if the two performs a similar classi er with a \complete" Mahapattern classes are indeed linearly highly separable, and lanobis distance metric. At rst glance, the observation
can be surprising because unlike the \complete" Mahahence still produce good classi cation results.
distance, the D2 metric alone does not account
The Distance Metric The vertical columns of Ta- lanobis
for pattern di erences in certain image vector space dible 1 show how the system's performance changes with rections. More speci cally, the D2 metric only measures
di erent distance metrics in the pattern matching stage. a pattern's Euclidean distance from a cluster's 75 most
Both the multi-layer perceptron net and single per- signi cant eigenvector subspace, and does not account
ceptron classi er systems produce better performance for pattern di erences within the subspace. We believe
statistics with our 2-Value distance metric than with the this comparison truly reveals that without sucient data
other three distance measures, especially on images from to accurately recover a full Gaussian covariance matrix,
the second test database. The observation should not at the resulting Mahalanobis distance can be a very poor
all be surprising. Our 2-Value distance metric consists notion of \pattern di erence".
of both D1 and D2 , two of the three other distance measures we are comparing against. A system that uses our \Non-Face" Prototypes Table 2 summarizes the
2-Value distance should therefore produce performance performance statistics for comparing systems with and
gures that are at least as good as a similar system that without \non-face" prototypes. As expected, the sysuses either D1 or D2 only. In fact, since our 2-Value tems with \non-face" prototypes clearly out-perform
distance systems actually produce better classi cation those without \non-face" prototypes. Our results sugresults than the systems using only D1 or D2, one can gest that not only are the \non-face" prototypes an adfurther arm that the two components D1 and D2 do ditional set of features for face detection, they are in fact
not mutually contain totally redundant information.
a very discriminative set of additional features.
Our 2-Value distance metric should also produce classi cation results that are at least as good as those ob- 7 Conclusion
tained with a Mahalanobis distance metric. This is because both metrics treat and quantify distance in essen- We have successfully developed a system for nding untially the same way | as a \di erence" notion between occluded vertical frontal views of human faces in images.
a test pattern and a local data distribution. Further- The approach is view based. It models the distribution of
more, the \di erence" notions they use are based on face patterns by means of a few prototype clusters, and
two very similar Gaussian generative models of the local learns from examples a set of distance parameters for
data distribution. In our experiments with perceptron- distinguishing between \face" and \non-face" test patbased classi ers, the 2-Value distance metric actually terns. We stress again, however, that our ultimate goal
out-performs the Mahalanobis distance metric consis- is to develop our face detection approach into a general
tently. We suggest two possible reasons for this di er- methodology for taking on feature detection and pattern
ence in performance: (1) As discussed in Section 4.5, we recognition tasks in multiple domains.
have too few sample points in our local data distribution
We plan to further our work in the following two dito accurately recover a full Gaussian covariance matrix rections. First, we would like to demonstrate the full
for computing Mahalanobis distances. By naively trying power of our face detection approach by building a more
to do so, we get a distance measure that poorly re ects comprehensive face detection system. One obvious exthe \di erence" notion we want to capture. (2) The lo- tension would be to have the system detect faces over a
cal data distribution we are trying to model may not be wider range of poses instead of just near-frontal views.
truly Gaussian. Our 2-Value distance metric provides We believe that our current approach can in fact be used
an additional degree of freedom that better describes a without modi cation to perform this new task. All we
test pattern's location relative to the local non-Gaussian need is a means of obtaining or arti cially generating a
data distribution.
suciently large example database of human faces at the
It is interesting that even a network-based classi er 19 di erent poses [1].
Second, we would like to demonstrate the versatility
and generality of our approach by building a few more
feature and pattern detection applications in other problem domains. Some possibilities include industrial inspection applications for detecting defects in manufactured products and terrain feature classi cation applications for SAR imagery. We believe that the key to
making this work would be to nd appropriate transformation spaces for each new task, wherein the target
pattern classes would be reasonably stable.
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