image enhancement - southeast universitycse.seu.edu.cn/personalpage/bao.list/enhancement.pdf ·...
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Image Enhancement
Image Qualities
• Gray distribution
– Gray level mapping
• Noise level
– Image smoothing
• Contour sharpness
– Image sharpening
2011-fall LIST 2
Gray Histogram
2011-fall LIST 3
Histogram h(rk) = nk rk=[0, L-1]
kyx
k ryxfcountn ),(),(
nnrhk
k
k
k )(
normalized histogram :
n
n
n
rhrp kkk
)()(
1)(0 krp
1)( k
krpprobability density
Gray Histogram
2011-fall LIST 4
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Gray Histogram
2011-fall LIST 5
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Gray Histogram
2011-fall LIST 6
0
0.5
1
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2.5
x 104
0 50 100 150 200 250
Gray Histogram
2011-fall LIST 7
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Gray Histogram
2011-fall LIST 8
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Gamma Correction
2011-fall LIST 9
inout II
Gamma Correction
2011-fall LIST 10
Gray Mapping
2011-fall LIST 11
2011-fall LIST 12
2011-fall LIST 13
Histogram Equalization
2011-fall LIST 14
PDF:
Histogram Equalization
2011-fall LIST 15
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2011-fall LIST 16
R
B
G (0,0,0)
(1,0,0)
(0,1,0)
(0,0,1)
Red
Blue
Green
Yello
Black
White
Cyan
Magenta
红 黄
绿
青
品红
蓝
RGB
2011-fall LIST 17
Additive System Subtractive System
2011-fall LIST 18
HSI
Color Image Histogram Equalization
2011-fall LIST 19
2011-fall LIST 20
1. Z Chen, R R Abidi, D L Page, and M A Abidi, 'Gray-level grouping (GLG) : an automatic method for optimized image contrast enhancement – part I : the basic method', IEEE Trans Image Proc, 15(8), 2006 : 2290-2302
2. N Bassiou, C Kotropoulos, ‘Color image histogram equalization by absolute discounting back-off’, Computer Vision and Image Understanding, Vol 107, 2006: 108-122
Assignment
Image Smoothing
Spectrum Properties
2011-fall LIST 22
0 50 100 150 200 250 30050
100
150
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gray levels on line 256
0 50 100 150 200 250 3000
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spectrum on line 256
Spectrum Properties
2011-fall LIST 23
0 50 100 150 200 250 30050
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Gaussian noise
μ = 0 σ=0.01
2011-fall LIST 24
0 50 100 150 200 250 30050
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gray levels spectrum
original signal
with noise
0 50 100 150 200 250 3000
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Image Averaging
2011-fall LIST 25
tt
tnN
ItIN
I )(1
)(1
Original Image without noise: I
Samples of original image with noise : I(t), (t=0,1,...,N-1)
)()( tnItI n(t) → Gaussian distribution
sample 8 frames averaging 16 frames averaging
64frames averaging 128frames averaging
2011-fall 26 LIST
2011-fall 27 LIST
Lowpass Filter
2011-fall LIST 28
G(u,v) = H(u,v) F(u,v)
H(u,v) : filter transfer function
F(u,v) : image in frequency domain
G(u,v) : output in frequency domain
g(x,y) = h(x,y) f(x,y)
h(x,y) : point spread function
Linear Filter H(·)
F(u,v) G(u,v)
u
|F(u)|
u0 0
0
1)u(H
(|u|≤u0)
otherwise
Understanding of Lowpass Filter H(u)
Noise ↔ Edge
Lowpass Filter
2011-fall LIST 29
Ideal lowpass filter
point spread function
0 20 40 60 80 100 120 140-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
Lowpass Filter
2011-fall LIST 30
Gaussian filter
22 2/)( uAeuH 22222)( xAexh
0 20 40 60 80 100 120 1400
0.1
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1
0 20 40 60 80 100 120 1400.2
0.25
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0.35
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0.45
0.5
0.55
Lowpass filter
2011-fall LIST 31
Average filter
0 20 40 60 80 100 120 140-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
transfer function
0 20 40 60 80 100 120 1400
0.1
0.2
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1
point spread function
otherwise
axaxh
0
)2/2/(1)(
2/
2/
2)(a
a
uxj dxeuH
uj
ee aujauj
2
u
au
)sin(
2011-fall LIST 32
0 50 100 150 200 250 3000
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0 50 100 150 200 250 30020
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average filter
original image 3x3 5x5
2011-fall LIST 33
0 50 100 150 200 250 3000
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Gaussian filter
original image σ=0.5
0 50 100 150 200 250 30040
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0 50 100 150 200 250 30020
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σ=1.0
Median Filter
2011-fall LIST 34
nonlinear filter
median value
2011-fall LIST 35
0 50 100 150 200 250 3000
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3x3 median filter original image
0 50 100 150 200 250 3000
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5x5 median filter
Image Sharpening
Edges
2011-fall LIST 37
x
G(x)
x
G(x)
x
G(x)
Ideal Edge
Sharp Edge
Blurred Edge
Edge ↔ Noise
2011-fall LIST 38
2011-fall LIST 39
2011-fall LIST 40
Median Filter Gaussian Filter Average Filter
2011-fall LIST 41
Median Filter Gaussian Filter
Average Filter
2011-fall LIST 42
Gaussian Filter
2011-fall LIST 43
2011-fall LIST 44
Unsharp Masking
2011-fall LIST 45
Low Pass
High Pass
+
×
Input f(x,y) Output g(x,y)
α
2011-fall LIST 46
2011-fall LIST 47
2011-fall LIST 48
2011-fall LIST 49
Contrast Enhancement
2011-fall LIST 50
2011-fall LIST 51
2011-fall LIST 52
2011-fall LIST 53
2011-fall LIST 54
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