Boosting for Fast Face Recognition

Boosting for Fast Face Recognition
Boosting for Fast Face Recognition
Guo-Dong Guo and Hong-Jiang Zhang
Microsoft Research China
5F, Beijing Sigma Center
No. 49, Zhichun Road, Haidian District
Beijing 100080, P. R. China
E-mail: guodong guoyahoo:om
Abstract
We propose to use the AdaBoost algorithm for face
recognition. AdaBoost is a kind of large margin classifiers
and is efficient for on-line learning. In order to adapt the
AdaBoost algorithm to fast face recognition, the original
Adaboost which uses all given features is compared with
the boosting along feature dimensions. The comparable
results assure the use of the latter, which is faster for
classification. The AdaBoost is typically a classification
between two classes. To solve the multi-class recognition
problem, a majority voting (MV) strategy can be used to
combine all the pairwise classification results. However,
the number of pairwise comparisons n n
= is huge,
when the number of individuals n is very large in the face
database. We propose to use a constrained majority voting
(CMV) strategy to largely reduce the number of pairwise
comparisons, without losing the recognition accuracy.
Experimental results on a large face database of 1079 faces
of 137 individuals show the feasibility of our approach for
fast face recognition.
(
1) 2
Keywords: Face recognition, large margin classifiers, AdaBoost, constrained majority voting (CMV), principal component analysis (PCA).
1. Introduction
Face recognition technology can be used in a wide range
of applications such as identity authentication, access control, and surveillance. Interests and research activities in
face recognition have increased significantly over the past
few years [8] [1]. Two issues are central for face recognition, i.e., what features to use to represent a face, and how
to classify a new face based on the chosen representation.
Principal Component Analysis (PCA), is a classical technique for signal representation [9]. Turk and Pentland [11]
developed a well known face recognition method, the eigenfaces, based on the PCA technique for face representation.
Some other complex methods such as ICA or non-linear approaches [6] can also be used to extract face features. Here,
we focus on the classification problem, and choose to use
the simple and efficient PCA technique [11] for face feature
extraction.
In the standard eigenfaces approach [11], the nearest
center (NC) criterion is used to recognize a new face. In
[5], a probabilistic visual learning (PVL) method is developed for face recognition. Another way of Bayesian classification of faces is proposed in [4], called probabilistic reasoning models (PRM), based on some assumptions of the
class distributions. More recently, the support vector machine (SVM) [12] is popular for visual object recognition
[7]. The SVM constructs a hyperplane between two classes
of examples based on the criterion of large margin. The
face recognition accuracy based on SVM is relatively high
[3]. However, in SVM, both the training and testing process is a little time consuming if the face database is very
large. Recently, Freund and Schapire [2] proposed another
kind of large margin classifiers, AdaBoost, to tackle the machine learning problems, which is fast and efficient for online learning. AdaBoost algorithm has the potential of fast
training and testing for real-time face recognition. Hence,
we concentrate on the AdaBoost algorithm and evaluate its
performance for face recognition.
In the next Section, we describe the AdaBoost algorithm
and give our strategies to adapt it for fast face recognition.
Then, the constrained majority voting is presented in Section 3 to tackle the multi-class recognition problems. Section 4 shows the experimental evaluations of AdaBoost in
face recognition. Finally, conclusions and discussions are
given in Section 5.
2. AdaBoost
Boosting is a method to combine a collection of weak
classification functions (weak learner) to form a stronger
classifier. AdaBoost is an adaptive algorithm to boost a sequence of classifiers, in that the weights are updated dynamically according to the errors in previous learning [2].
AdaBoost is a kind of large margin classifiers. Tieu and Viola [10] adapted the AdaBoost algorithm for natural image
retrieval. They made the weak learner work in a single feature each time. So after T rounds of boosting, T features are
selected together with the T weak classifiers. If Tieu and
Viola’s version can get comparable results with the original Freund and Schapire’s AdaBoost [2], it will be a better
choice for face recognition because of the reduced computation of T comparisons instead of T D in the original
AdaBoost [2], where D is the feature dimension. To make
it clear, we denote the original AdaBoost [2] as Boost.0.
Because of the space limit, we do not give the original AdaBoost algorithm [2] here. Readers can refer to [2] for a detailed explanation. Tieu and Viola’s version [10] is briefly
described as below:
AdaBoost Algorithm
Input: 1) n training examples x1 ; y1 ; : : : ; xn ; yn with
yi
or ; 2) the number of iterations T .
1
Initialize weights w1;i
or 21m for yi
or , respec2l
tively, with l m n.
Do for t
;:::;T:
1. Train one hypothesis hj for each feature j with wt ,
and error j P riwt hj xi 6 yi .
2. Choose ht hk such that 8j 6 k; k < j . Let
t k .
3. Update: wt+1;i
wt;i tei , where ei
or for
example xi classified correctly or incorrectly respectively,
t and 1
with t
t
1 t
t .
4. Normalize the weights so that they are a distribution,
Pnwt+1w;i .
wt+1;i
t+1;j
j =1
Output the final hypothesis,
(
=1 0
+ =
=1
=
=
=
)
=
[ ( )= ℄
()= ()
=
= log
hf (x) = 1
0
P
if Tt=1 t ht (x) otherwise
(
)
=1 0
=
=1 0
1
2
PT t=1 t
=
=0
= log
=0
= 0 01
01
= 01
= 0 01
=0
3. Multi-class Recognition
AdaBoost is typically used to solve two-class classification problems. In a multi-class scenario, we can use a majority voting (MV) strategy to combine all pair-wise classification results. However, it needs n(n2 1) pairwise comparisons, where n is the number of classes. In order to speed up
the process for fast face recognition, we first use the nearest
center criterion to rank all classes with respect to a given
query. The class labels appear on the top list if the class
centers are nearest to the query. Then, top m classes are
selected and used for voting. We call it Constrained Majority Voting (CMV), which can largely reduce the number of
comparisons. We compare the performance of CMV with
the majority voting which uses all pairs of classes.
We also show the face recognition results with the
method of probabilistic reasoning models (PRM) [4], which
is an approximation to the Bayesian classifier with the assumption that the covariance matrix is diagonal. The recognition accuracy of the standard eigenface is also shown for
comparison.
4. Experiments
(1)
It should be noted, however, a problem emerges when
Tieu and Viola’s boosting is used for face recognition. Since
it starts with the most discriminative feature and adds another one in next round of boosting, the algorithm may
begins with a feature having zero classification error, i.e.,
t
1
t
, then t
. So t
1 t
t can not
be defined, and the boosting should stop there [2]. Because boosting is based on the classification error in previous round [2]. It is explicit that very few rounds of boosting
and hence very small number of features are not sufficient
for the complicated task of face recognition. In fact, we
=0
find the phenomenon of zero boosting error in quite a few
cases. To solve this problem and make the boosting process
go forward, we define a small value for t instead of zero in
case of t
. We let t
: and : and compare their
effects on the recognition results. We call them Boost.1 and
Boost.2 respectively corresponding to different settings of
t values.
One suspicion still exits. That is, whether we need to
weight the features with the distribution wt in step 1 of AdaBoost. It should be clarified by experiments. For this purpose, we do not weight the features in Boost.1 and Boost.2,
and call it Boost.3 if the distribution wt is used to weight
: , if t
,
the features (and simultaneously set t
which is experimentally better than t
: ). The weak
learner is the simple nearest center classifier, as that in [10].
Different versions of AdaBoost from Boost.0 to Boost.3
are evaluated on a compound face database with 1079 face
images of 137 persons.
4.1. Face Database
The face database is a collection of five databases: (1).
The Cambridge ORL face database which contains 40 distinct persons. Each person has ten different images. (2).
The Bern database contains frontal views of 30 persons,
each with 10 images. (3). The Yale database contains 15
persons. For each person, ten of its 11 frontal view images
0.9
0.85
recognition accuracy
0.8
0.75
0.7
Boost.3
Boost.2
Boost.1
Boost.0
PRM
eigenface
0.65
0.6
Figure 1. Examples of face images in our face
database.
are randomly selected. (4). Five persons are selected from
the Harvard database, each with 10 images. (5). A database
composed of 179 images of 47 Asian students, each with
three or four images. The face images are cropped and
scaled to the same size of
pixels in our database.
The face images have large variations in facial expressions
and facial details, and changes in light, face size and pose.
Some face examples in the database are shown in Fig. 1.
The face database is divided into two non-overlapping
sets for training and testing. The training data consist of 544
images: five images per person are randomly chosen from
the Cambridge, Bern, Yale, and Harvard databases, and two
images per person are randomly selected from the Asian
students database. The remaining 535 images are used for
testing.
128 128
10
15
Firstly, the principal components are calculated from the
face images in the training set. The projection coefficients
of face images to these principal components are computed
and used as the features. Then, different algorithms are used
for face recognition with respect to the number of features
or rounds of boosting in AdaBoost. We compare the original Adaboost (Boost.0) with Boost.1 (
: , if ,
without using the distribution wt to weight a new coming
feature), Boost.2 which is the same as Boost.1 except for
setting : , if , and Boost.3 (using previous distribution wt to weight a new feature in boosting, and setting
: , if ). It is shown in Fig. 2 the recogni-
= 0 01
=0
20
25
30
number of features
35
40
45
50
Figure 2. Face recognition performance with
respect to rounds of boosting (or number of
features). Only a small number of boosting is
sufficient for AdaBoost.
tion rates of each algorithm with respect to rounds of boosting or the number of features (for PRM and eigenfaces).
We can observe several results: 1). The four versions of
boosting can give comparable results. This guarantee to use
the simple boostings instead of the original complex one.
In detail, the best recognition rate of Boost.0 is :
(T
, dim
), while Boost.1 is :
(T
or ), Boost.2 is :
(T
), and Boost.3 is :
(T
). The results of Boost.2 and Boost.3 are slightly
better than Boost.1, and comparable to Boost.0; 2). The
different behavior of Boost.1 to Boost.3 shows the effects
of various settings of interior parameters on the recognition performance. Boost.3 is preferable in small number
of boosting rounds (T ); 3). The recognition accuracy of Boost.3 is not lower than the approximate Bayesian
recognition
classification, PRM [4], which gives :
accuracy with
features. This demonstrates the acceptability of boosting for face recognition; 4). Both boosting and PRM can improve the recognition rates over the
standard eigenfaces, however, the boosting algorithms select less features to use (15 features are sufficient); 5). The
problem of over-fitting is serious for boosting on face data.
When T > , the performance deteriorates obviously. It
is interesting to observe that, when the round of boosting
is small (T ), the recognition performance is Boost.3
> Boost.2 > Boost.1, where “>” represents “better than”.
While Boost.3 degenerates more rapidly if the number of
boosting rounds becomes larger (T > ).
In above, we use majority voting to solve the multi-class
pairwise comrecognition problem. Thus it should do
parisons for a single query. In order to speed up the process,
= 10
15
= 15
= 30
85 23% = 15
84 11%
15
40
4.2. Experimental Results
=01 =0
= 01
=0
5
85 79%
15
15
15
9316
85 98%
= 10
85 98%
0.9
0.95
0.85
0.9
0.8
recognition accuracy
recognition accuracy
1
0.85
0.8
0.7
NCtop2
NCtop4
NCtop8
NCtop16
NCtop32
0.75
0.7
0.75
5
10
15
20
25
30
number of features
35
40
45
0.65
50
Figure 3. The recognition accuracy of top m
classes ranked by NC criterion with respect to
the number of features for m
; ; ; ; .
we propose to use a constrained majority voting (CMV)
strategy. To do it, we must firstly demonstrate the efficiency
of class ranking with the nearest center (NC) criterion. It is
shown in Fig. 3 the recognition rates of top m classes, for
m
; ; ; ; . The selection of m is arbitrary here,
and we just set m as the power of . We can find that top
classes (with 25 features) can cover :
correct classes.
Hence it is safe to use only a small number of classes to feed
into the multi-class solver – CMV.
In our experiments with CMV, we only use top 4 classes,
ranked by NC with 25 features. The number of pairto . The
wise comparisons is largely reduced from
recognition performance with CMV is shown in Fig. 4.
We try both Boost.2 and Boost.3 using CMV, denoted as
CMVBoost.2 and CMVBoost.3 respectively, and compare
their results with Boost.3 in Fig. 2, but here denoted as
MVBoost.3. It is interesting to observe that the boosting
behavior has changed somewhat with respect to boosting
rounds. The best results of boosting with CMV now correspond to 45 rounds of boosting. But the computation time
is still reduced explicitly as compared with MVBoost.3.
The best recognition rate of CMVBoost.2 is :
, and
, comparable to the MVBoost.3 of
CMVBoost.3 is :
:
(15 rounds of boosting).
2
32
98 88%
9316 6
85 98%
85 98%
5
10
15
20
25
30
rounds of boosting
35
40
45
50
Figure 4. The recognition accuracy of boosting by using the constrained majority voting (CMV) strategy, with respect to rounds of
boosting.
= 2 4 8 16 32
= 2 4 8 16 32
0.6
CMVBoost.3
CMVBoost.2
MVBoost.3
86 17%
5. Conclusions and Discussions
We have evaluated the AdaBoost algorithm for face
recognition. Boosting along dimensions can give comparable results as that using all features in each round. Hence
both learning and testing processes can be largely sped up.
=0
=01
in some beginning
To overcome the problem of t
rounds of boosting, two small values are tried for t . From
the experiments, it is better to set t
: than : . Further more, it makes little difference to weight the features
or not in the boosting process along the feature dimensions.
To further speed up the multi-class face recognition process, the constrained majority voting (CMV) strategy can
be used, which is faster than the traditional majority voting strategy using all pairs, without explicitly losing the
recognition accuracy. As a result, both CMVBoost.2 and
CMVBoost.3 can be used for fast face recognition. Additional observation is that over-fitting is a serious problem for
boosting on face data. Our experimental evaluations should
stimulate more research on boosting method itself for face
recognition, which can be expected to further improve the
face recognition accuracy.
0 01
More recently, a new web site on AdaBoost,
http://www.boosting.org, was just opened for researchers
to exchange their research results or do discussions. This is
useful to stimulate and speed up the research on boosting
methods and their applications.
6. Acknowledgements
The authors would like to thank Kinh Tieu and Gunnar
Ratsch for their helpful discussions on AdaBoost algorithm.
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