general definition - sharifee.sharif.edu/~miap/files/dip4miap(forview)f_enhancement.pdf · 2011. 2....
TRANSCRIPT
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20111
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• General Definition:
SystemH ,f x y ,g x y
, ,g x y H f x y
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E. Fatemizadeh, Sharif University of Technology, 20112
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Linearity
• Shift Invariant or Spatially Invariant:
• Causality: We do not care about it• Stability as before.
1 2 1 2, , , ,H af x y bf x y aH f x y bH f x y
0 0 0 0, , , ,g x y H f x y g x x y y H f x x y y
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20113
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Unit Impulse Function (Pinhole):
0 , 0,0,
, 0,0
, 1
x yx y
x y
x y dxdy
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20114
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Point Spread Function (Impulse Response):
• Linear Shift Invariant Systems:
0 0 0 0, ; , ,H x y x y H x x y y
0 0 0 0 0 0, ; , , ,
, ,
H x y x y H x x y y H x x y y
H x y H x y
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20115
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Convolution/Correlation Integral:
• Convolution/Corrlelation Summation:
, , , ,
, , , ,
f x y h x y f s t h x s y t dsdt
f x y h x y f s t h x s y t dsdt
1 1
0 0
1 1
0 0
, , , ,
, , , ,
M N
p q
M N
p q
f m n h m n f p q h m p n q
f m n h m n f p q h m p n q
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20116
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Discrete Fourier Transform:
1 1
0 0
1 1
0 0
1, , exp 2
1, , exp 21
M N
m n
M N
u v
um vnF u v f m n jM N
um vnf m n F
N
jN
M
u vM
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20117
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20118
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20119
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201110
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
10
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201111
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Fourier Transform Centering– fftshift in Matlab
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E. Fatemizadeh, Sharif University of Technology, 201112
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Example
Without Shift
With Shift
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E. Fatemizadeh, Sharif University of Technology, 201113
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Phase Importance in Digital Image Processing
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E. Fatemizadeh, Sharif University of Technology, 201114
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Phase Importance in Digital Image Processing
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E. Fatemizadeh, Sharif University of Technology, 201115
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
Double Rect
Double Sinc
• A Sample DFT:
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E. Fatemizadeh, Sharif University of Technology, 201116
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Fourier Spectrum
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E. Fatemizadeh, Sharif University of Technology, 201117
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Image Processing in Frequency Domain:
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E. Fatemizadeh, Sharif University of Technology, 201118
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Notch Filter Effect on DC Level
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E. Fatemizadeh, Sharif University of Technology, 201119
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Lowpass and Highpass effects
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E. Fatemizadeh, Sharif University of Technology, 201120
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Highboost (Highpass + Original)
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E. Fatemizadeh, Sharif University of Technology, 201121
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Ideal Low Pass Filtering:
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E. Fatemizadeh, Sharif University of Technology, 201122
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• An Image and its Spectrum (Circle Energy)!
92.0%
94.6%
96.4%
98.0%
99.5%
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201123
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
Blurring Effect of ILPF
(Back to BLPF)
(Back to GLPF)
-8%
-5.4% -3.6%
-2% -0.5%
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E. Fatemizadeh, Sharif University of Technology, 201124
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Origin of Ringing Effect
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E. Fatemizadeh, Sharif University of Technology, 201125
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Butterworth Low Pass Filtering
2
0
1,,
1
H u vD u v
D
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E. Fatemizadeh, Sharif University of Technology, 201126
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
BLPF Blurring Effect (ILPF)
(Back to GLPF)
D0=5
D0=15 D0=30
D0=80D0=230
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E. Fatemizadeh, Sharif University of Technology, 201127
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
BLPF(1) BLPF(2) BLPF(5) BLPF(20)
• Butterworth LPF Spatial Representation:
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E. Fatemizadeh, Sharif University of Technology, 201128
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Gaussian Low Pass Filter
2
20
,, exp
2D u v
H u vD
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E. Fatemizadeh, Sharif University of Technology, 201129
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
GLPF Blurring Effect (ILPF)
(BLPF)
D0=5
D0=15 D0=30
D0=80D0=230
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E. Fatemizadeh, Sharif University of Technology, 201130
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
IHPF
BHPF
GHPF
• Highpass filter
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E. Fatemizadeh, Sharif University of Technology, 201131
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
IHPF BHPF GHPF
• Ringing!
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E. Fatemizadeh, Sharif University of Technology, 201132
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
IHPF
Ringing
D0=15 D0=30 D0=80
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201133
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
BHPF
Ringing
D0=15 D0=30 D0=80
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201134
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
GHPF
Ringing
D0=15 D0=30 D0=80
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201135
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
Laplacian in (u,v) Image view
IDFT of –(u2+v2)
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E. Fatemizadeh, Sharif University of Technology, 201136
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
Original Laplacian
EnhancedLaplacian
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E. Fatemizadeh, Sharif University of Technology, 201137
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
Original Laplacian
A=2 A=2.7
, 1 ,hb hpH u v A H u v
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201138
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Combinational Processes:
Original BHPF
HFE
, ,hfe hpH u v a bH u v
HE
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201139
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Implementation‐Practical Consideration:
Ordinary ViewShifted View
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201140
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Zero Padding:– Convolution of N‐points signal and M‐Points signals will results a M+N‐1 points signal
– In Frequency Domain we need zero padding before Fourier transform.
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201141
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201142
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Zero Padding:
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ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201143
Medical Image Analysis and Processing
Image Enhancement in Frequency Domain
• Matlab Command– fft2, ifft2, fftshift, ifftshift– freqz2, – fspecial (average, disk , gaussian, laplacian, log, motion, prewitt, sobel, unsharp)