AdaBoost算法及应用

i 1
• Update distribution: Dt 1 (i )
T Output final classifier: sign H ( x) t ht ( x) t 1
ATTENTIONAL CASCADE


单独一个AdaBoost分类器即使很强，在误检率和检测时间上根本满足不 了真正的实时人脸检测系统的需要。采用级联检测策略能很好地解决这 个问题。Adaboost算法引入了一种瀑布型的分类器---级联分类器。 在级联分类器中，每一个待检测窗口只有通过了当前层的强分类器 （AdaBoost分类器）才能进入下一层。这样大量的待检测窗口只需要最 初几层简单的判断就可以被迅速淘汰，使得平均检测成本大大降低。多 层级联结构中，每一层的强分类器都是由AdaBoost算法训练来的。
f1 , d1
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Classifier 1 T
f2 , d2
Classifier 2 T
f3 , d3
Classifier 3 T
F, D
FACE
F NON-FACE
F NON-FACE
Weights Increased
BOOSTING ILLUSTRATION
Weak Classifier 2
BOOSTING ILLUSTRATION
Weights Increased
BOOSTING ILLUSTRATION
Weak Classifier 3
BOOSTING ILLUSTRATION
IMAGE SUB-WINDOW
Classifier 1
T
Classifier 2
T
Classifier 3
T
FACE
F NON-FACE
F NON-FACE
F NON-FACE
ATTENTIONAL CASCADE
ROC Curve

% Detection
Chain classifiers that are progressively more complex and have lower false positive rates
. . .
H T ( x) sign t ht ( x) t 1
训练一个弱分类器（特征f）就 是在当前权重分布的情况下，确定f 的最优阈值以及不等号的方向，使 得这个弱分类器（特征f）对所有训 strong classifier 练样本的分类误差最低。
1 pf ( x ) p h ( x, f , p , ) 0其他 T
. . .
T H T ( x) sign t ht ( x) t 1
hT ( x) {1, 1}
weak classifiers
slightly better than random
strong classifier
WEAKER CLASSIFIERS
h1 ( x) {1, 1} h2 ( x) {1, 1}
Given: ( x1 , y1 ),, ( xm , ym ) where xi X , yi {1, 1}
1 Initialization: D1 (i) m , i 1,, m
Dt (i):probability distribution of xi 's at time t
For t 1,, T :
• Find classifier ht : X {1, 1} which minimizes error wrt Dt ,i.e.,
ht arg min j where j Dt (i )[ yi h j ( xi )]
hj
m
minimize weighted error
Final classifier is a combination of weak classifiers
AdaBoost for Face Detection
ADABOOST & ITS APPLICATIONS
THE TASK OF FACE DETECTION
Many slides adapted from P. Viola
THE VIOLA/JONES FACE DETECTOR
2001年，Viola和Jones利用类Haar特征构造弱分类器，使 用AdaBoost算法把弱分类器组合成强分类器，采用 Cascade结构把强分类器串联组合成级联分类器，实现了 准实时的人脸检测。
P. Viola and M. Jones. Rapid object detection using a boosted cascade of simple features. CVPR 2001. P. Viola and M. Jones. Robust real-time face detection. IJCV 57(2), 2004.
THE ADABOOST ALGORITHM
Given: ( x1 , y1 ),, ( xm , ym ) where xi X , yi {1, 1}
1 Initialization: D1 (i) m , i 1,, m
For t 1,, T :
• Find classifier ht : X {1, 1} which minimizes error wrt Dt ,i.e.,
i 1
• Update distribution: Dt 1 (i )
T Output final classifier: sign H ( x) t ht ( x) t 1
BOOSTING ILLUSTRATION
Weak Classifier 1
BOOSTING ILLUSTRATION
ht arg min j where j Dt (i )[ yi h j ( xi )]
hj
m
• Weight classifier: t
1 1 t ln 2 t Dt (i ) exp[ t yi ht ( xi )] , Z t is for normalization Zt
hT ( x) {1, 1}
weak classifiers
slightly better than random
THE STRONG CLASSIFIERS
h1 ( x) {1, 1} h2 ( x) {1, 1}
. . .
T H T ( x) sign t ht ( x) t 1
特征3
1 1 1 分布 0.35 0.15 0.25 0.25 1 1
排序
结果 -1 1 错误率 0
错误率 0.15
标记
1
1
-1
1
“好中取最好” 最终选定特征3及其阈值构 成弱分类器
分布 0.15 0.25 排序 结果 1 1
0.35 0.25 -1 -1
错误率 0.25
特征2
THE ADABOOST ALGORITHM
hT ( x) {1, 1}
weak classifiers
slightly better than random
strong classifier
The AdaBoost Algorithm
ADABOOST & ITS APPLICATIONS
THE ADABOOSTRES
Feature Value (Pixel in white area)
(Pixel in black area) 将任意一个矩形放到人脸区域上，然后将
白色区域的像素和减去黑色区域的像素和， 得到的值我们暂且称之为人脸特征值。
Rectangle filters
Given: ( x1 , y1 ),, ( xm , ym ) where xi X , yi {1, 1}
1 Initialization: D1 (i) m , i 1,, m
For t 1,, T :
• Find classifier ht : X {1, 1} which minimizes error wrt Dt ,i.e.,
2×2 image
ADABOOST 在人脸检测中的应用
+1
1类
-1
…
-1类
计算特征值
特征值排序
1类 考虑方向 -1类 or
-1类
1类
穷举找到最佳阈值
发挥出每个Haar特征的最好效果
特征1
标记 1 -1 1 1 标记 -1 分布 0.15 0.35 排序 结果 -1 -1 0.25 0.25 1 1
• Weight classifier: t
1 1 t ln 2 t
i 1
for minimize exponential loss
• Update distribution: Dt 1 (i )
Dt (i ) exp[ t yi ht ( xi )] , Z t is for normalization Zt Give error classified patterns more chance for learning.
F f i , D di
i 1 i 1

K
K

The detection rate and the false positive rate of the cascade are found by multiplying the respective rates of the individual stages A detection rate of 0.9 and a false positive rate on the order of 106 can be achieved by a 10-stage cascade if each stage has a detection rate of 0.99 (0.9910 ≈ 0.9) and a false positive rate of about 0.30 (0.310 ≈ 6106 )