Input
• Training examples S = {(x
i
, z
i
), i = 1, · · · , N }.
• T is the total number of weak classifiers to be trained.
Initialize
• Initialize example score F
0
(x
i
) =
1
2
ln
³
N
+
N
−
´
,
where N
+
and N
−
are the number of positive and
negative examples in the training data set.
Adaboost Learning
For t = 1, · · · , T :
1. For each Haar-like feature h(x) in the pool, find the
optimal threshold H and confidence score c
1
and c
2
to minimize the Z score L
t
(8).
2. Select the best feature with the minimum L
t
.
3. Update F
t
(x
i
) = F
t−1
(x
i
) + f
t
(x
i
), i = 1, · · · , N ,
4. Update W
+1j
, W
−1j
, j = 1, 2.
Output Final classifier F
T
(x).
Figure 3. Adaboost learning pseudo code.
1 2 3
Input
sub-windows
Further
processing
T
T T
F
F
F
Rejected sub-windows
Figure 4. The attentional cascade.
Eq. (8) is referred as the Z score in [80]. In practice, at
iteration t + 1, for every Haar-like feature h(x), we find the
optimal threshold H and confidence score c
1
and c
2
in order
to minimize the Z score L
t+1
. A simple pseudo code of the
AdaBoost algorithm is shown in Fig. 3.
2.3. The Attentional Cascade Structure
Attentional cascade is a critical component in the Viola-
Jones detector. The key insight is that smaller, and thus
more efficient, boosted classifiers can be built which reject
most of the negative sub-windows while keeping almost all
the positive examples. Consequently, majority of the sub-
windows will be rejected in early stages of the detector,
making the detection process extremely efficient.
The overall process of classifying a sub-window thus
forms a degenerate decision tree, which was called a “cas-
cade” in [92]. As shown in Fig. 4, the input sub-windows
pass a series of nodes during detection. Each node will
make a binary decision whether the window will be kept
for the next round or rejected immediately. The number of
weak classifiers in the nodes usually increases as the num-
ber of nodes a sub-window passes. For instance, in [92], the
first five nodes contain 1, 10, 25, 25, 50 weak classifiers, re-
spectively. This is intuitive, since each node is trying to
reject a certain amount of negative windows while keeping
all the positive examples, and the task becomes harder at
late stages. Having fewer weak classifiers at early stages
also improves the speed of the detector.
The cascade structure also has an impact on the training
process. Face detection is a rare event detection task. Con-
sequently, there are usually billions of negative examples
needed in order to train a high performance face detector.
To handle the huge amount of negative training examples,
Viola and Jones [92] used a bootstrap process. That is, at
each node, a threshold was manually chosen, and the par-
tial classifier was used to scan the negative example set to
find more unrejected negative examples for the training of
the next node. Furthermore, each node is trained indepen-
dently, as if the previous nodes does not exist. One argu-
ment behind such a process is to force the addition of some
nonlinearity in the training process, which could improve
the overall performance. However, recent works showed
that it is actually beneficial not to completely separate the
training process of different nodes, as will be discussed in
Section 4.
In [92], the attentional cascade is constructed manually.
That is, the number of weak classifiers and the decision
threshold for early rejection at each node are both specified
manually. This is a non-trivial task. If the decision thresh-
olds were set too aggressively, the final detector will be
very fast, but the overall detection rate may be hurt. On the
other hand, if the decision thresholds were set very conser-
vatively, most sub-windows will need to pass through many
nodes, making the detector very slow. Combined with the
limited computational resources available in early 2000’s,
it is no wonder that training a good face detector can take
months of fine-tuning.
3. Feature Extraction
As mentioned earlier, thanks to the rapid expansion in
storage and computation resources, appearance based meth-
ods have dominated the recent advances in face detection.
The general practice is to collect a large set of face and non-
face examples, and adopt certain machine learning algo-
rithms to learn a face model to perform classification. There
are two key issues in this process: what features to extract,
and which learning algorithm to apply. In this section, we
first review the recent advances in feature extraction.
The Haar-like rectangular features as in Fig. 2 (a-f) are
very efficient to compute due to the integral image tech-
nique, and provide good performance for building frontal
face detectors. In a number of follow-up works, researchers
extended the straightforward features with more variations
in the ways rectangle features are combined.
For instance, as shown in Fig. 5, Lienhart and Maydt[49]
generalized the feature set of [92] by introducing 45 degree
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