數位影像中熵的計算與應用
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Transcript 數位影像中熵的計算與應用
數位影像中熵的計算與應用
義守大學
資訊工程學系
黃健興
Outline
Entropy
Applications
Conclusions
• Definition
• Entropy of images
• Visual Surveillance System
• Background Extraction
Concept of Entropy
Rudolf Julius Emanuel Clausius , 1864
化學及熱力學
• 測量在動力學方面不能做功的能量總數
• 計算一個系統中的失序現象
• 描述系統狀態的函數
• 經常用熵的參考值和變化量進行分析比較
Information Theory
Claude Elwood Shannon , 1948
運用機率論與數理統計的方法研究資訊
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編碼學
密碼學與密碼分析學
數據傳輸
數據壓縮
檢測理論
估計理論
數據加密
Definition
H ( X ) E ( I ( X ))
• E is the expected value,
• I is the information content of X.
n
n
i 1
i 1
H ( X ) p( xi ) I ( xi ) p( xi ) logb p( xi )
• p denotes the probability mass function of X
Advantage
Whole Image
Histogram
Entropy
• M×N Matrix
• N×1 Vector
• Single value
Entropy of Image
Pixel Color
Pixel Distribution
Texture
• Horizontal
• Vertical
The Statistic of gray-level
Position Information
Normalize the size of image
Edge Detection
• Sobel
• Canny
Horizontal Projection
Vertical Projection
Sobel Edge Detection
Sobel Filter
m1
m4
m7
m2
m5
m8
m3
m6
m9
1 2
0
0
1
2
1
0
1
1
2
1
0
2
1
0
1
0
1
45
0
0
0
1
2
1
9 0
0
1
2
0
1
2
1
0
1
2
1
0
135
Sobel Edge Detection(cont.)
s0 m7 2m8 m9 m1 2m2 m3
s45 m6 2m8 m9 m1 2m2 m4
s90 m3 2m6 m9 m1 2m4 m7
s135 m2 2m3 m6 m4 2m7 m8
S s0 s45 s90 s135 T
S s0 s45 s90 s135 T
Sobel Edge Detection(cont.)
Horizontal Projection
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0
0 0
240
0
0 7 2 2 2 7 0 0
Horizontal Projection(cont.)
Vertical Projection
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0
0 0
0 7 2 2 2 2 2 7 0 0
0
320
Vertical Projection(cont.)
Local Binary Pattern
Pattern Texture T t ( g0 gc ,...,g p1 gc )
• Pattern T t( g , g ,...,g )
• Center Pixel gc
• Surrounding Pixel gi(i=0, 1,…,p-1)
• T t(s(g g ),...,s(g g ))
c
0
c
p1
0
p1
c
1 x 0
s ( x)
0 x 0
• Label
p 1
LBPP,R ( xc , yc ) s( g p g c )2 p
p 0
Local Binary Pattern(cont.)
g0
g3
g5
g1
gc
g6
g2
g4
g7
0 0
1 gc
0 0
0
1
0
g 0 g c 0 g1 g c 0 g 2 g c 0
g3 gc 0
gc
g4 gc 0
g5 gc 0 g6 gc 0 g7 gc 0
LBPP,R ( xc , yc ) 0 20 0 21 0 22 1 23 1 24 0 25 0 26 0 27 24
Definition
H ( X ) E ( I ( X ))
• E is the expected value,
• I is the information content of X.
n
n
i 1
i 1
H ( X ) p( xi ) I ( xi ) p( xi ) logb p( xi )
• p denotes the probability mass function of X
Applications
Visual Surveillance System
Background Extraction
• variance of video information
• Block for pixel
Visual Surveillance System
F2
F 20
F 63
F 45
F 68
F 60
F 69
Visual Surveillance System
Gray Prediction – GM(1,1)
Gray Prediction – GM(1,1) (cont.)
Step 1: X 0 x0 1, x0 2,, x0 n
1
1
1
1
n
X
x
1
,
x
2
,
,
x
Step 2:
k
x 1 k x 0 i
i 0
k 1,2, , n
1 1
1
k 1
z
k
x
k
x
Step 3:
2
k 2,3,, n
1
Gray Prediction – GM(1,1) (cont.)
Step 4:
Step 5:
z 1 2
1
z 3
B
1
z n
x 0 2
0
x 3
Y
0
x n
1
1
1
x0 k az1 k u
a
a BT B
u
1
BT YN
Gray Prediction – GM(1,1) (cont.)
Step 6:
dxt
axt u
dt
1
u ak u
0
x k 1 x 1 a e a
k 1,2,, n
0
1
1
Step 7: x k 1 x k 1 x k
0
u
0
a
ak
k
1
x
1
1
e
e
x
a
k 1,2, , n
Visual Surveillance System
Visual Surveillance System
Background Extraction
Non-recursive approaches
• Selective update using temporal averaging
• Selective update using temporal median
• Selective update using non-foreground pixels
• Non-parametric model
• Time Interval (It-L,It-L+1,It-1)
• Probability Density Function
1 t 1
f ( I t u ) K (u I i )
L i t L
Background Extraction
Recursive approaches
• Kalman filter
• Mixture of Gaussians (MoG)
• Parametric model f (I u) w
• Matching I T
• Updata w (1 )w
t
t
i, j
i , j 1
K
i 1
i, j
i , j 1
i , j 1
i , j (1 p) i , j 1 pIt
i2, j (1 p) i2, j 1 p( I t i , j )
p (u; i , j ; i , j )
(u; i , j ; i , j )
Improved Method
Treat the n×n block as a pixel
Improved Method(cont.)
Conclusions
Reduce Memory Size
Enhanced Performance
• Quantize the content of image
• Judgment of the variance