Transcript Adaboost_20110510

AdaBoost
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Classifier
• Simplest classifier
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Adaboost: Agenda
• (Adaptive Boosting, R. Scharpire, Y. Freund,
ICML, 1996):
• Supervised classifier
• Assembling classifiers
– Combine many low-accuracy classifiers (weak
learners) to create a high-accuracy classifier (strong
learners)
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Example 1
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Adaboost: Example (1/10)
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Adaboost: Example (2/10)
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Adaboost: Example (3/10)
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Adaboost: Example (4/10)
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Adaboost: Example (5/10)
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Adaboost: Example (6/10)
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Adaboost: Example (7/10)
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Adaboost: Example (8/10)
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Adaboost: Example (9/10)
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Adaboost: Example (10/10)
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Adaboost
• Strong classifier = linear combination of T
weak classifiers
(1) Design of weak classifier ht (x)
(2) Weight for each classifier (Hypothesis
weight)  t
(3) Update weight for each data (example
distribution)
• Weak Classifier: < 50% error over any distribution
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Adaboost: Terminology (1/2)
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Adaboost: Terminology (2/2)
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Adaboost: Framework
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Adaboost: Framework
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Adaboost
• Strong classifier = linear combination of T
weak classifiers
(1) Design of weak classifier ht (x)
(2) Weight for each classifier (Hypothesis
weight)  t
(3) Update weight for each data (example
distribution)
• Weak Classifier: < 50% error over any distribution
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Adaboost: Design of weak classifier (1/2)
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Adaboost: Design of weak classifier (2/2)
• Select a weak classifier with the smallest weighted
error
m
ht  arg min  j  i 1 Dt (i )[ yi  h j ( xi )]
h j H
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• Prerequisite:  t 
2
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Adaboost
• Strong classifier = linear combination of T
weak classifiers
(1) Design of weak classifier ht (x)
(2) Weight for each classifier (Hypothesis
weight)  t
(3) Update weight for each data (example
distribution)
• Weak Classifier: < 50% error over any distribution
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Adaboost: Hypothesis weight (1/2)
• How to set  t ?
1 , if yi  H(xi )
i  0, else

1 , if yi f(xi )  0
1
 
0, else
N i 
1
1 exp( yi f(xi ))
  exp( yi f(xi ))  DT 1 (i) 
N
N i
 Zt
1
training error( H ) 
N
  DT 1 (i ) Z t
i
i
i
  Zt
i
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Adaboost: Hypothesis weight (2/2)
1 1 t
 t  ln(
)
2
t
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Adaboost
• Strong classifier = linear combination of T
weak classifiers
(1) Design of weak classifier ht (x)
(2) Weight for each classifier (Hypothesis
weight)  t
(3) Update weight for each data (example
distribution)
• Weak Classifier: < 50% error over any distribution
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Adaboost: Update example distribution
(Reweighting)
y * h(x) = 1
y * h(x) = -1
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Reweighting
In this way, AdaBoost “focused on” the
informative or “difficult” examples.
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Reweighting
In this way, AdaBoost “focused on” the informative or
“difficult” examples.
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Summary
1
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 t  ln(
1 t
t
t=1
)
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Example 2
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Example (1/5)
Original Training set : Equal Weights to all training samples
Taken from “A Tutorial on Boosting” by Yoav Freund and Rob Schapire
Example (2/5)
ROUND 1
Example (3/5)
ROUND 2
Example (4/5)
ROUND 3
Example (5/5)
Example 3
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1
2
 t  ln(
1 t
t
)
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1
2
 t  ln(
1 t
t
)
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1
2
 t  ln(
1 t
t
)
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1
2
 t  ln(
1 t
t
)
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1
2
 t  ln(
1 t
t
)
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1
2
 t  ln(
1 t
t
)
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Example 4
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Adaboost:
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Application
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Discussion
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Discrete Adaboost (DiscreteAB)
(Friedman’s wording)
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Discrete Adaboost (DiscreteAB)
(Freund and Schapire’s wording)
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Adaboost with Confidence Weighted
Predictions (RealAB)
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Adaboost Variants Proposed By Friedman
• LogitBoost
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Adaboost Variants Proposed By Friedman
• GentleBoost
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Reference
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Robust Real-time Object Detection
Key word : Features extraction,
Integral Image , AdaBoost , Cascade
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Outline
1. Introduction
2. Features
2.1 Features Extraction
2.2 Integral Image
3. AdaBoost
3.1 Training Process
3.2 Testing Process
4. The Attentional Cascade
5. Experimental Results
6. Conclusion
7. Reference
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1. Introduction
This paper brings together new algorithms and
insights to construct a framework for robust and
extremely rapid object detection.
Frontal face detection system achieves :
1. High detection rates
2. Low false positive rates
Three main contributions:
1. Integral image
2. AdaBoost : Selecting a small number of important features.
3. Cascaded structure
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2. Features
 Based on the simple features value.
 Reason :
1. Knowledge-based system is difficult to learn using a finite
quantity of training data.
2. Much faster than Image-based system.
ps. Feature-based: Use extraction features like eye, nose pattern.
Knowledge-based: Use rules of facial feature.
Image-based: Use face segments and predefined face pattern.
[3] A.S.S.Mohamed, Ying Weng, S. S Ipson, and Jianmin Jiang, ”Face Detection based on Skin Color in Image by Neural
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Networks”, ICIAS 2007, pp. 779-783, 2007.
2.1 Feature Extraction (1/2)
 Filter:
Ex: haar-like filter
Filter type.
 Feature:
a. pattern 的座標位置.
EX: eye , nose
b. pattern 的大小
 Feature value:
Feature value = Filter  Feature
EX:
convolution
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2.1 Feature Extraction (2/2)
• Haar-like filter: The sum of the pixels which lie within the
white rectangles are subtracted from the sum of pixels in
the grey rectangles.
Figure 1
Filter C
Feature

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Filter type
＋ －＋
feature value
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2.2 Integral Image (1/6)
 Integral image
1. Rectangle features
2. Computed very rapidly
 II(x , y) : sum of the pixels above and to the left of (x , y).
ii( x, y) 

'
'
i( x , y )
x'  x , y '  y
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2.2 Integral Image (2/6)
Known:
A: Sum of the pixels within rectangle A.
B: Sum of the pixels within rectangle B.
C: Sum of the pixels within rectangle C.
D: Sum of the pixels within rectangle D.
Location 1 value is A. Location 2 value is A+B.
Location 3 value is A+C.
Location 4 value is A+B+C+D.
Equation: 1 = A
3=A+C
2 = A + B.
4=A+B+C+D
Figure 2: Integral image
Q : The sum of the pixels within rectangle D = ?
A : 4  A B C  D  D  4 A B C
 D  4  ( A  B)  C  D  4  2  C
 D  4  2  (3  A)  D  4  2  (3  1)  4  1  (2  3)
The sum within D can be computed as 4 + 171- (2 + 3).
2.2 Integral Image (3/6)
Sum of the pixels
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2.2 Integral Image (4/6)
 Using the following pair of recurrences to get integral image
s( x, y )  s ( x, y  1)  i ( x, y )
(1)
ii ( x, y )  ii ( x  1, y )  s ( x, y )
(2)
ii ( x, y )
i ( x, y )
is the integral image.
ii (1, y )  0
is the original image.
s ( x, y ) is the cumulative row sum.
ps.
ii ( x, y ):
s ( x, 1)  0
ii( x, y)    i( x' , y ' )
x'  x y '  y
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2.2 Integral Image (5/6)
i ( x, y )
original image
s ( x, y )
cumulative row sum
1
3
4
7
2
4
6
10
6 13 18
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s( x, y )  s ( x, y  1)  i ( x, y )
(1)
ii ( x, y )  ii ( x  1, y )  s ( x, y )
(2)
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ii ( x, y )
integral image
2.2 Integral Image (6/6)
i ( x, y )
original image
s ( x, y )
cumulative row sum
(3*3)
s ( x, y ) = s( x, y  1) +
s (0, 0) = s (0, 1) +
s(1, 0) = s(1, 1) +
s(2, 0) = s (2, 1) +
s(0,1) = s (0, 0)
+
s (1,1) = s(1, 0)
+
i ( x, y )
i (0, 0)
i (1, 0)
i (2, 0)
i (0,1)
i (1,1)
ii ( x, y )
integral image
(3*3)
=0+1=1
=0+1=1
=0+4=4
=1+2=3
=1+2=3
(3*3)
ii ( x, y ) = ii ( x  1, y ) + s ( x, y )
ii (0, 0) = ii ( 1, 0) + s (0, 0) =0+1=1
ii (1, 0)
ii (2, 0)
ii (0,1)
ii (1,1)
= ii (0, 0)
+ s (1, 0) =1+1=2
= ii (1, 0)
+ s (2, 0) =2+4=6
= ii ( 1,1)
+ s (0,1) =0+3=3
= ii (0,1)
+ s (1,1) =3+3=6
+ i (2, 2) =7+1=8
…
…
s(2, 2) = s(2,1)
ii (2, 2) = ii (1, 2)
+ s (2, 2) =10+8=18
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3. AdaBoost (1/2)
 AdaBoost (Adaptive Boosting) is a machine learning algorithm.
 AdaBoost works by choosing and combining weak classifiers
together to form a more accurate strong classifier !
– Weak classifier:
Feature value
positive , if filter(X )<
h( X )  
negative , otherwise
Image set
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Threshold
3. AdaBoost (2/2)
 Subsequent classifiers built are tweaked in favor of those
instances misclassified by previous classifiers. [4]
 The goal is to minimize the number of features that need to
be computed when given a new image, while still achieving
high identification rates.
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[4] AdaBoost - Wikipedia, the free encyclopedia , http://en.wikipedia.org/wiki/AdaBoost
3.1 Training Process - Flowchart
1. Input:
Training image set X
Face
(24x24)
l張
Non-Face
(24x24)
m張
2. Feature Extraction:
Using haar-like filter
feature
設每張 image 可
extract 出 N 個 feature value
共有N*(l+m) 個 feature value
Candidate threshold θ
3. AdaBoost Algorithm:
3.0. Image weight initialization
1
, for postive

 2l
wi  
, i  1,..., n
 1 , for negative

 2m
3.1. Normalize image weight
wt ,i 
wt ,i
n
 wt , j
, i  1,..., n
j 1
3.2. Error calculation
n
 i , j   wt ,k hi , j  xk   yk , i  1,...n, j  1,...N
k 1
3.3. Select a weak classifier ht with the lowest error εt
3.4. Image weight adjusting
4. Output:
A strong classifier
(24x24)
 wt ,i t , if xi is classified correctly
wt 1,i  
 wt ,i , otherwise
T
H T ( x)    t ht ( x)
t 1
Weak classifier
Weak classifier weight
T個
weak classifiers
3.2 Training Process - Input
1. Input:
Training data set 以 X 表示 . 設有 l 張 positive image , m 張 negative
image , 共 n (n=l+m) 張 image.
1 , postive/face
X  ( x1 , y1 ), ( x2 , y2 ),..., ( xn , yn ) , yi  
0 , negative/non-face
{
…
1
1
0
1
0
}
1
設每張 image 可以 extract 出 N 個 local feature ,
f j ( xi ) 表示 image
裡的第 j 個 local feature value , 共有 N * n 個 local feature value.
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3.2 Training Process - Feature Extraction (1/2)
2. Feature Extraction: Using haar-like filter
Haar-like filter :
n 張 image
…
…

…
…
…
…
…
f: feature number
convolution
Candidate feature value
(n*N 個)
Ps. 1張 image 可 extract 出 N 個 feature value
∴N=4*f
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3.2 Training Process - Feature Extraction (2/2)
Define weak classifiers
h: i , j
Ex : 3 face & 1 non-face image
extract by 5th feature
Face
1 , if pi , j f j ( xk )  pi , ji , j
hi , j ( xk )  
0 , otherwise
Non-face
i, j
: 即 image i 的第 j 個 local feature value
f j ( xk ) : 即 image k 的第 j 個 local feature value
Polarity :
1 , if  i , j  0.5
pi , j  
1 , otherwise
θ1,5 θ2,5 θ3,5 θ4,5
h1,5 h2,5 h3,5 h4,5
ε1,5 ε2,5 ε3,5 ε4,5
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3.2 Training Process - AdaBoost Algorithm (1/4)
3. AdaBoost Algorithm:
3-0. Image weight initialization :
1
, for postive/face image

 2l
wi  
, i  1,..., n
1

, for negative/non-face image

 2m
l is the quantity of positive images.
m is the quantity of negative images.
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3.2 Training Process - AdaBoost Algorithm (2/4)
Iterative: t = 1, … ,T
T : weak classifier number
3-1. Normalize image weight:
wt ,i
wt ,i  n
, i  1,..., n
 wt , j
Training data set X
j 1
3-2. Error calculation :
Candidate weak classifier
n
error rate
 i , j   wt ,k hi , j  xk   yk , i  1,...n, j  1,...N
k 1
3-3. Select a weak classifier
positive or negative
with
ht the lowest error rate .  t
3-4. Image weight adjusting :
wt 1,i
 wt ,i t , if xi is classified correctly


where  t = t
1- t
 wt ,i , otherwise
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3.2 Training Process – Output (1/2)
T
1 T

positive/face ,   t ht ( x)    t
H T ( x)  
2 t 1
t 1
negative/non-face , otherwise

1
threshold
 t  log
t
Weak classifier weight
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3.2 Training Process – Output (2/2)
Weak classifier weight (  t 
ε
1 t
t
)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
250 α
200
Fig. B
Weak classifier weight (  t
1 t
 log(
)
t
ε
如 Fig. B，當ε (error rate)在 0
~ 0.1 區間內與其他如 0.1 ~
0.5 區間內即使ε有相同的變
化量，所對應到的α (weak
classifier weight)變化量差異也
相當大，如此一來當ε越趨近
於 0 時，即使ε只有些微改變，
在 strong classifier 中其比重也
會劇烈加大。因此，取 log 是
為了縮小 weight 彼此間差距，
使 strong classifier 中的各個
weak classifiers 均佔有一定比
重。
)
ε
0.6
0.5
0.001
0.4
0.3
0.2
0.1
0
0
Fig. C
0.5
1
1.5
2
2.5
3
3.5
4
4.5
α
1 

999
0.005
199
0.101
8.9
0.105
8.52
log(
1 

2.99
800
)
0.7
2.29
0.94
0.38
0.93
0.01
AdaBoost Algorithm –
Image Weight Adjusting Example
If  1,3 取最小 , 則  
1,3
0.167

 0.2
1  1,3 1  0.167
t =1 時
W1
W2
W3
W4
W5
W6
初始值
0.167
0.167
0.167
0.167
0.167
0.167
經分類後
O
O
O
O
X
O
0.167
0.167*0.2
0.5
0.1
Update wt 1 0.167*0.2 0.167*0.2 0.167*0.2 0.167*0.2
Normalize
0.1
0.1
0.1
0.1
Weight 變化
wt 1,i
 wt ,i t , if xi is classified correctly

 wt ,i , otherwise
每一輪都將分對的 image 調低其weight ，經過
Normalize 後，分錯的 image的 weight 會相對提高，
如此一來，常分錯的 image 就會擁有較高 weight。
如果一張 image 擁有較高 weight 表示在進行分類
評估時，會著重在此 image。
3.3 Testing Process - Flowchart
Test Image
1. Extract Sub-windows
Downsampling
…
(360*420)
(24*28)
(228*336)
(360*420)
About 100000
sub-windows
(24*24)
…

2. Strong Classifier (24*24)Detection
Load T weak classifiers
Strong Classifier
…
h1
h2
h3
Sub-window

hT
T
1 T

positive
,

h
(
x
)



t
t t
H T ( x)  
2 t 1
t 1
negative , otherwise

Accept windows
Result Image
…
3. Merge Result
average
coordinate
…
For all
sub-windows
Reject windows
…
4. The Attentional Cascade (1/5)
 Advantage: Reducing testing computation time.
 Method: Cascade stages.
 Idea: Reject as many negatives as possible at the earliest stage. More complex
classifiers were then used in later stages.
 The detection process is that of a degenerate decision tree, so called “cascade”.
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Stage
True positive
False positive
True negative
False negative
Figure 4 : Cascade Structure
4. The Attentional Cascade (2/4)
θ
Stage 1
θ
Stage 2
θ
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Stage 3
4. The Attentional Cascade (3/4)
 True positive rates (detection rates):
將 positive 判斷為 positive 機率
True Positive
True Positive  False Negative
 False positive rates (FP):
將 negative 判斷為 positive 機率
False Positive
False Positive  True Negative
 True negative rates:
將 negative 判斷為 negative 機率
True Negative
False Positive  True Negative
 False negative rates (FN):
將 positive 判斷為 negative 機率
FP
False Negative
True Positive  False Negative
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+
FN
=> Error Rate
4. The Attentional Cascade (4/4)
 Training a cascade of classifiers:
 Involves two types of tradeoffs :
1. Higher detection rates
2. Lower false positive rates
 More features will achieve higher detection rates and
lower false positive rates. But classifiers require more time
to compute.
 Define an optimization framework:
1. the number of stages
2. the number of features in each stage
3. the strong classifier threshold in each stage
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4. The Attentional Cascade - Algorithm (1/3)
4. The Attentional Cascade - Algorithm (2/3)
 f : Maximum acceptable false positive rate. (最大 negative 辨識成 positive 錯誤百分比)
 d : Minimum acceptable detection rate. (最小辨識出 positive 的百分比)
 Ft arg et: Target overall false positive rate. (最後可容許的 false positive rate)
 Initial value:
P : Total positive images
N : Total negative images
f = 0.5
d = 0.9999
Ft arg et  106
F0  1.0
初始 False positive rate.
D0  1.0
初始 Detection rate.
Threshold = 0.5
AdaBoost threshold
Threshold adjust weight
104
The number of cascade stage
Threshold_EPS =
i=0
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4. The Attentional Cascade - Algorithm (3/3)
 Iterative:
While( Fi  Ft arg et )
{
i=i+1
f : Maximum acceptable false positive rate
d : Minimum acceptable detection rate
Ft arg et : Target overall false positive rate
Add Stage
ni  0, Fi  Fi 1
P : Total positive images
N : Total negative images
i : The number of cascade stage
While( Fi  f * Fi )1
Fi : False positive rate at ith stage
{
ni : The number of features at ith stage
Di : Detection rate at ith stage
Add Feature
ni  ni  1
( Fi , D)i = AdaBoost(P,N, ) ni
Get New Di , Fi
While( Di  d * Di )1
{
Threshold = Threshold – Threshold_EPS
Di = Re-computer current strong classifier
detection rate with Threshold (this also affects
)
}
Threshold , 則Di ,Fi
}
If( Fi  Ft arg et)
N = false detections with current cascaded detector on the N
}
N = Fi *N
Fi
5. Experimental Results (1/3)
 Face training set:
 Extracted from the world wide web.
 Use face and non-face training images.
 Consisted of 4916 hand labeled faces.
 Scaled and aligned to base resolution of 24 by 24 pixels.
 The non-face sub-windows come from 9544 images which were
manually inspected and found to not contain any faces.
Fig. 5: Example of frontal upright face
images used for training
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5. Experimental Results (2/3)
 In the cascade training:
 Use 4916 training faces.
 Use 10,000 non-face sub-windows.
 Use the AdaBoost training procedure.
 Evaluated on the MIT+CMU test set:
 An average of 10 features out of a stage are evaluated per sub-window.
 This is possible because a large majority of sub-windows are rejected by
the first or second stage in the cascade.
 On a 700 Mhz Pentium III processor, the face detector can process a 384
by 288 pixel image in about .067 seconds .
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5. Experimental Results (3/3)
θ
Fig. 6: Create the ROC curve (receiver operating characteristic) the threshold of
the final stage classifier is adjusted from
.
 to 
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Reference
[1] P. Viola and M. Jones, “Rapid Object Detection Using A Boosted Cascade of
Simple Features”, Proc. IEEE Conf. Computer Vision and Pattern
Recognition, vol.1, pp. 511-518, 2001
[2] P. Viola and M. Jones, “Robust Real-time Object Detection”, IEEE
International Journal of Computer Vision, vol.57, no.2, pp.137-154, 2001.
[3] A.S.S.Mohamed, Ying Weng, S. S Ipson, and Jianmin Jiang, ”Face Detection
based on Skin Color in Image by Neural Networks”, ICIAS 2007, pp. 779783, 2007.
[4] AdaBoost - Wikipedia, the free encyclopedia ,
http://en.wikipedia.org/wiki/AdaBoost
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