No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity...
Transcript of No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity...
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ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
1
Digital Image Processing
Intensity Transformations and Spatial Filtering
1
• Image Enhancement:
– No Explicit definition
• Methods
– Spatial Domain: • Linear
• Nonlinear
– Frequency Domain: • Linear
• Nonlinear
![Page 2: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/2.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
2
Digital Image Processing
Intensity Transformations and Spatial Filtering
2
• Spatial Domain Process
, ,g x y T f x y
![Page 3: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/3.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
3
Digital Image Processing
Intensity Transformations and Spatial Filtering
3
• For 1×1 neighborhood: – Contrast Enhancement/Stretching/Point Process
• For w×w neighborhood: – Filtering/Mask/Kernel/Window/Template Processing
s T r
![Page 4: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/4.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
4
Digital Image Processing
Intensity Transformations and Spatial Filtering
4
• Intensity Transformation Functions:
![Page 5: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/5.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
5
Digital Image Processing
Intensity Transformations and Spatial Filtering
5
• Image Negatives:
1s L r
![Page 6: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/6.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
6
Digital Image Processing
Intensity Transformations and Spatial Filtering
6
• Log Transform:
log 1s c r
![Page 7: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/7.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
7
Digital Image Processing
Intensity Transformations and Spatial Filtering
7
• Power-Law Transform:
s cr
![Page 8: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/8.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
8
Digital Image Processing
Intensity Transformations and Spatial Filtering
8
• Gamma Correction:
11.8 2.5
r
1.8 2.5r
1.8 2.5r
![Page 9: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/9.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
9
Digital Image Processing
Intensity Transformations and Spatial Filtering
9
Original =0.6
=0.4 =0.3
• Gamma Correction
– Too Dark Image
![Page 10: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/10.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
10
Digital Image Processing
Intensity Transformations and Spatial Filtering
10
=5
Original =3
=4
• Gamma Correction
– Too Bright Image
![Page 11: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/11.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
11
Digital Image Processing
Intensity Transformations and Spatial Filtering
11
Original
C. S. THR.
• Contrast Stretching
![Page 12: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/12.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
12
Digital Image Processing
Intensity Transformations and Spatial Filtering
12
• Gray Level Slicing
![Page 13: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/13.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
13
Digital Image Processing
Intensity Transformations and Spatial Filtering
13
• Example Using Fig 3.11 (a) Using Fig 3.11 (b)
![Page 14: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/14.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
14
Digital Image Processing
Intensity Transformations and Spatial Filtering
14
• Bit-Plane Slicing:
– Highlighting effect of a single bit!
![Page 15: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/15.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
15
Digital Image Processing
Intensity Transformations and Spatial Filtering
15
• Example:
– LSB -> MSB (Left to Right and Top to Bottom)
![Page 16: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/16.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
16
Digital Image Processing
Intensity Transformations and Spatial Filtering
16
Bits (7,8) Bits (6,7,8) Bits (5,6,7,8)
• Image Reconstruction from bit-planes
![Page 17: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/17.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
17
Digital Image Processing
Intensity Transformations and Spatial Filtering
17
• Histogram Processing:
– Enhancement based on statistical Properties:
• Local
• Global
– Histogram Definition:
, 0, 1 , 0,
1
k k k k
kk k
h r n r L n M N
np r n
n M N
![Page 18: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/18.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
18
Digital Image Processing
Intensity Transformations and Spatial Filtering
18
• Histogram Visual Meaning:
– Dark
– Light
– Low Contrast
– High Contrast
![Page 19: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/19.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
19
Digital Image Processing
Intensity Transformations and Spatial Filtering
19
• Histogram Equalization:
– Continuous Case.
– Seek for a suitable transform (Except for negative):
![Page 20: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/20.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
20
Digital Image Processing
Intensity Transformations and Spatial Filtering
20
• Effect of Point Process on Histogram:
• Special Case (CDF):
1 S r
s T r drP s P r
r T s ds
0
Uniform Distribution on [0, -1]
1 1
1 1, 0 1
1
r
r r
s r r
r
dT rdss T r L p w dw L p r
dr dr
drp s p r p r s L
ds p r
L
L
![Page 21: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/21.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
21
Digital Image Processing
Intensity Transformations and Spatial Filtering
21
• Concept Illustration:
![Page 22: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/22.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
22
Digital Image Processing
Intensity Transformations and Spatial Filtering
22
• Discrete Case
• Perfect equalization is NOT possible
0 0
1
min2
min
, 0,1,2, , 1
11 , 0,1, , 1
ˆ 0.5
ˆ 1 0.51
k kr k
k k
k k r j k
j J
k k k
k kk
k
n np r k L
MN n
LS T r L p r n k L
MN
S S round S
S SS L
L S
![Page 23: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/23.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
23
Digital Image Processing
Intensity Transformations and Spatial Filtering
23
• Numerical Example:
0
7k
k r j
j
S p r
𝑆𝑘 𝑆 𝑘
1.33 1
3.08 3
4.55 5
5.67 6
6.23 6
6.56 7
6.86 7
7.00 7
![Page 24: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/24.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
24
Digital Image Processing
Intensity Transformations and Spatial Filtering
24
• Numerical Examples (Cont.)
![Page 25: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/25.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
25
Digital Image Processing
Intensity Transformations and Spatial Filtering
25
• Real Experiment:
![Page 26: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/26.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
26
Digital Image Processing
Intensity Transformations and Spatial Filtering
26
• Gray-Level Transfer Function
![Page 27: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/27.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
27
Digital Image Processing
Intensity Transformations and Spatial Filtering
27
• Histogram Matching and Modification:
– Goal: Specify the shape of the histogram:
– Example: Pages: 133-136
?
0 1 1
0
1
1
r z
r
r
z
z
p r p z
s T r L p w dw
z G T r G s
G z L p t dt
![Page 28: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/28.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
28
Digital Image Processing
Intensity Transformations and Spatial Filtering
28
• Example (Mars image and its histogram):
![Page 29: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/29.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
29
Digital Image Processing
Intensity Transformations and Spatial Filtering
29
• Histogram Matching:
– Washout Gray
![Page 30: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/30.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
30
Digital Image Processing
Intensity Transformations and Spatial Filtering
30
Desired
Transform using
Initial CDF
Transform using
Initial Modified CDF
• Histogram Matching:
![Page 31: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/31.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
31
Digital Image Processing
Intensity Transformations and Spatial Filtering
31
• Local Histogram Enhancement
![Page 32: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/32.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
32
Digital Image Processing
Intensity Transformations and Spatial Filtering
32
• Histogram Statistics For Image Enhancement:
– Use of Global Statistical Measures
– Gross adjustments in overall intensity (m) and contrast (µ2)
1
0 1 1
1
0 1 1
1,
1,
L M Nnn
n i i
i x y
L M N
i i
i x y
r r m p r f x y mMN
m r p r f x yMN
![Page 33: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/33.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
33
Digital Image Processing
Intensity Transformations and Spatial Filtering
33
• Histogram Statistics For Image Enhancement:
– Local mean and local variance:
– Local information intensity and contrast (edges)
1
0 ,
1 2 22
0 ,
1, ,
1, , , ,
: Neighborhood centered on ,
xy xy
xy
xy xy xy xy
xy
L
S i S i
i s t Sxy
L
S i S S i S
i s t Sxy
xy
m x y r p r f s tS
x y r m x y p r f s t m x yS
S x y
![Page 34: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/34.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
34
Digital Image Processing
Intensity Transformations and Spatial Filtering
34
• A simple enhancement algorithm for SEM image:
0 1 2
0 1 2
. , , ,,
, .
4.0, 0.4, 0.02, 0.4
S G G S GE f x y m x y k m and k x y kg x y
f x y OW
E k k k
![Page 35: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/35.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
35
Digital Image Processing
Intensity Transformations and Spatial Filtering
35
• Graphical Illustration:
Local Mean Local Var E or one
![Page 36: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/36.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
36
Digital Image Processing
Intensity Transformations and Spatial Filtering
36
• Enhanced Image
– Global histogram equalization
– Use of statistical moments
Original Local Histogram Local Statistics
![Page 37: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/37.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
37
Digital Image Processing
Intensity Transformations and Spatial Filtering
37
• Fundamentals of Spatial Filtering:
, , ,a b
s a t b
g x y w s t f x s y t
![Page 38: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/38.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
38
Digital Image Processing
Intensity Transformations and Spatial Filtering
38
• Spatial Correlation () and Convolution ()
• Reflection/Rotation in convolution:
, , , ,
, , , ,
a b
s a t b
a b
s a t b
w x y f x y w s t f x s y t
w x y f x y w s t f x s y t
4 6 6 45 5
3 7
7 3
2 8
2
1 9
98 1
![Page 39: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/39.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
39
Digital Image Processing
Intensity Transformations and Spatial Filtering
39
• Smoothing Spatial Filters:
– Linear Filters (averaging, lowpass)
– General Formulation
, ,
,
,
a b
s a t b
a b
s a t b
w s t f x s y t
g x y
w s t
2 2
22,
x y
G x y e
![Page 40: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/40.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
40
Digital Image Processing
Intensity Transformations and Spatial Filtering
40
• Square averaging Filter:
– Denoising/Smoothing
– Blurring (Equal Value Kernel
1 3
5 9
15 35
![Page 41: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/41.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
41
Digital Image Processing
Intensity Transformations and Spatial Filtering
41
• Blurring Usage:
– Delete unwanted (small) subjects.
Original Smoothed Thresholded
![Page 42: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/42.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
42
Digital Image Processing
Intensity Transformations and Spatial Filtering
42
• Order Statistics Filters:
– Impulsive noise: • Mono Level : Salt, Pepper noises
• Bi Level: Salt-Pepper noises
– Filter • Median
• Max
• Min
![Page 43: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/43.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
43
Digital Image Processing
Intensity Transformations and Spatial Filtering
43
• Example:
Salt-Pepper Noise 3×3 Averaging 3×3 Median
![Page 44: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/44.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
44
Digital Image Processing
Intensity Transformations and Spatial Filtering
44
• Sharpening Spatial Filter
– Highlights Intensity Transitions
– First and Second order Derivatives
1, ,
, 1,
0.5 1, 1,
f x y f x yf
f x y f x yx
f x y f x y
2
21, 2 , 1,
ff x y f x y f x y
x
![Page 45: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/45.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
45
Digital Image Processing
Intensity Transformations and Spatial Filtering
45
• First Order Derivative:
– Zero in flat region
– Non-zero at start of step/ramp region
– Non-zero along ramp
![Page 46: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/46.jpg)
ee.sharif.edu/~dip
E. Fatemizadeh, Sharif University of Technology, 2012
46
Digital Image Processing
Intensity Transformations and Spatial Filtering
46
• Second Order Derivative:
– Zero in flat region
– Non-zero at start/end of step/ramp region
– Zero along ramp
![Page 47: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/47.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
47
Digital Image Processing
Intensity Transformations and Spatial Filtering
47
• Comparison:
![Page 48: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/48.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
48
Digital Image Processing
Intensity Transformations and Spatial Filtering
48
• 1st and 2nd Order Derivative Comparison:
– First Derivative: • Thicker Edge;
• Strong Response for step changes;
– Second Derivative: • Strong response for fine details and isolated points;
• Double response at step changes.
![Page 49: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/49.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
49
Digital Image Processing
Intensity Transformations and Spatial Filtering
49
• Laplacian as an isotropic Enhancer:
• Discrete Implementation:
2 22
2 2
f ff
x y
2 1, , 1 1, , 1 4 ,f f x y f x y f x y f x y f x y
0 1 0
1 4 1 90
0 1 0
isotropic
1 1 1
1 8 1 45
1 1 1
isotropic
![Page 50: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/50.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
50
Digital Image Processing
Intensity Transformations and Spatial Filtering
50
Practically use:
• Laplacian Masks
![Page 51: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/51.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
51
Digital Image Processing
Intensity Transformations and Spatial Filtering
51
• Background Recovering:
2
2
, ,,
, ,
f x y f x y signg x y
f x y f x y sign
0 1 0
1 1 90
0 0
5
1
isotropic
1 1 1
1 1 45
1 1
9
1
isotropic
![Page 52: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/52.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
52
Digital Image Processing
Intensity Transformations and Spatial Filtering
52
• Example:
Non-Scaled and scaled Laplacian
Sharpened using 90º and 45º degree isotropic Laplacian
![Page 53: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/53.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
53
Digital Image Processing
Intensity Transformations and Spatial Filtering
53
• Unsharp Masking and High-Boost Filtering:
• k≥0
– k=1: Unsharp Masking
– k>1: High Boost
• Another mask:
– Laplacian and any highpass filter
, , , , , : Blurred image
g , , ,
mask
mask
g x y f x y f x y f x y
x y f x y k g x y
![Page 54: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/54.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
54
Digital Image Processing
Intensity Transformations and Spatial Filtering
54
• One Dimensional Illustration
![Page 55: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/55.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
55
Digital Image Processing
Intensity Transformations and Spatial Filtering
55
• Two Dimensional Example
Blurred, 5×5, σ=3
Unsharp mask
Unsharp masking , k=1
Highboost, k=4.5
![Page 56: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/56.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
56
Digital Image Processing
Intensity Transformations and Spatial Filtering
56
• First Derivative - Gradient:
1 222
TT
x y
f ff G G
x y
f f f ff
x y x y
![Page 57: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/57.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
57
Digital Image Processing
Intensity Transformations and Spatial Filtering
57
Roberts Cross Gradient
9 5 8 6x yG z z G z z
7 8 9 1 2 3
3 6 9 1 4 7
2 2
2 2
x
y
G z z z z z z
G z z z z z z
Sobel Gradient
• Discrete Implementation
![Page 58: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/58.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
58
Digital Image Processing
Intensity Transformations and Spatial Filtering
58
• Example (Sobel Mask):
![Page 59: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/59.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
59
Digital Image Processing
Intensity Transformations and Spatial Filtering
59
• Image Subtraction:
– Physically static object and background
– Intensity changes in object but not in background
, , ,g x y f x y f x y
![Page 60: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/60.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
60
Digital Image Processing
Intensity Transformations and Spatial Filtering
60
• Example:
– Original
– Discard Some bits
– Difference
– Histogram Equalized
![Page 61: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/61.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
61
Digital Image Processing
Intensity Transformations and Spatial Filtering
61
• Image Averaging: – Consider an additive noise condition:
g(x,y)=f(x,y)+η(x,y)
– Conditions: • Noise, η(x,y):
– Uncorrelated
– i.i.d
– Zero Mean
• Subject, f(x,y): – Physical Stationary
– Repeatable Experiments
![Page 62: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/62.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
62
Digital Image Processing
Intensity Transformations and Spatial Filtering
62
• Image Averaging:
– For i.i.d RV’s:
2 2
, ,1
, , , , ,
1 1, ,
i i
N
i g x y x yi
g x y f x y x y E g x y f x y
g x y g x yN N
1
Var1, Var
N
i
i
E EN N
![Page 63: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/63.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
63
Digital Image Processing
Intensity Transformations and Spatial Filtering
63
• Astronomical Application:
– Repeatable Experiments!
Original Noisy
N=8 N=16
N=64 N=128
![Page 64: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/64.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
64
Digital Image Processing
Intensity Transformations and Spatial Filtering
64
• Difference Histogram: N=8
N=16
N=64
N=128
![Page 65: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/65.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
65
Digital Image Processing
Intensity Transformations and Spatial Filtering
65
• Combination:
Bone Scan Laplacian
Original+Laplacian Soble of Original
![Page 66: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/66.jpg)
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66
Digital Image Processing
Intensity Transformations and Spatial Filtering
66
Smoothed Sobel (Orig. + L.)*S.Sobel
Orig.+ (Orig.+L.)*S.Sobel Apply Power-Law
• Combination:
![Page 67: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/67.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
67
Digital Image Processing
Intensity Transformations and Spatial Filtering
67
• Fuzzy Image Enhancement:
– Brief Introduction to Fuzzy set
– Fuzzy Intensity Transformation
– Fuzzy Spatial Filtering
![Page 68: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/68.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
68
Digital Image Processing
Intensity Transformations and Spatial Filtering
68
• Introduction
– Logic of real world
– “He is young man” is true of false?
– Fuzzy and Crisp sets:
• Membership function:
![Page 69: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/69.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
69
Digital Image Processing
Intensity Transformations and Spatial Filtering
69
• Fuzzy Set:
– Definition:
, , :Set of Elements
Empty Set: 0
Equality:
Subset:
Complement: 1
Union (A B, A B): max ,
Intersection (A B, A B): min ,
A
A
A B
A B
AA
C A B
C A B
A z z z Z Z
z
z z
z z
z z
OR z z z
AND z z z
![Page 70: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/70.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
70
Digital Image Processing
Intensity Transformations and Spatial Filtering
70
• Graphical Illustration
![Page 71: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/71.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
71
Digital Image Processing
Intensity Transformations and Spatial Filtering
71
• Some Membership Functions:
![Page 72: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/72.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
72
Digital Image Processing
Intensity Transformations and Spatial Filtering
72
• Using Fuzzy Sets in inferring:
– Example: Using color to categorize fruits
R1: If color is green then the fruit is verdant
OR
R2: If color is yellow then the fruit is half-mature
OR
R3: If color is red then the fruit is mature
![Page 73: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/73.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
73
Digital Image Processing
Intensity Transformations and Spatial Filtering
73
• We should to do:
– Fuzzify antecedent and consequent of each rule
– Evaluate membership function of each rules (R1, R2, R3),
– Rules aggregation,
– Final crisp value (Defuzzification).
![Page 74: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/74.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
74
Digital Image Processing
Intensity Transformations and Spatial Filtering
74
• Fuzzification of antecedents and consequents
![Page 75: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/75.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
75
Digital Image Processing
Intensity Transformations and Spatial Filtering
75
• if-then rule fuzzification:
– Possibility of consequents is less than antecedents • Example: “if x is A then y is D”
– Our Example:
0 01
2 0 0
0 03
, min ,
, min ,
, min ,
green verd
yellow half
red mat
z v z v
z v z v
z v z v
![Page 76: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/76.jpg)
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76
Digital Image Processing
Intensity Transformations and Spatial Filtering
76
• Rule aggregation
R = R1 OR R2 OR … OR Rn
![Page 77: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/77.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
77
Digital Image Processing
Intensity Transformations and Spatial Filtering
77
• Rule aggregation in our Example
– Q = Q1 OR Q2 OR Q3
1 2 030 0 0, max , , , , ,z v z v z v z v
![Page 78: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/78.jpg)
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78
Digital Image Processing
Intensity Transformations and Spatial Filtering
78
• Defuzzification:
– Max Membership
– Center of Gravity
– ….
1
1
,
N
i i
i
N
i
i
x xx x dx
x xx dx
x
: ,x x x x
![Page 79: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/79.jpg)
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79
Digital Image Processing
Intensity Transformations and Spatial Filtering
79
• Complex antecedent:
1 2
1 2
1 2 n
1 2 n
R: IF is AND is AND is THEN is B
: IF is THEN is
min , ,
R: IF is OR is OR is THEN is B
: IF is THEN is
, ,
n
n
A A A A
A A A A
x A x A x A y
R x A y B
x x x x
x A x A x A y
R x A y B
x Max x x x
![Page 80: No Slide Titleee.sharif.edu/~dip/Files/ImageEnhancementInSpatialDomain(ForPrint).pdfIntensity Transformations and Spatial Filtering . 1 • Image Enhancement: ... Intensity Transformations](https://reader033.fdocuments.in/reader033/viewer/2022042712/5f8b117ee531424ec20e537b/html5/thumbnails/80.jpg)
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E. Fatemizadeh, Sharif University of Technology, 2012
80
Digital Image Processing
Intensity Transformations and Spatial Filtering
80
• Fuzzy Intensity Transformation:
R1: If a pixel is Dark then make it Darker
R2: If a pixel is Gray then make it Gray
R3: If a pixel is Bright then make it Brighter
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• Results
Original Histogram Equalization Fuzzy Enhancement
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E. Fatemizadeh, Sharif University of Technology, 2012
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Digital Image Processing
Intensity Transformations and Spatial Filtering
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• Analysis:
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E. Fatemizadeh, Sharif University of Technology, 2012
83
Digital Image Processing
Intensity Transformations and Spatial Filtering
83
• Spatial Filtering Using Fuzzy Sets
– Goal: Boundary Extraction
– General Rule:
– Uniformity: Intensity difference central pixel and its neighbors
– For a 3×3 maks: di = zi - z5
if “a pixel belongs to a uniform region”, then ”make it
white, else make it black”
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E. Fatemizadeh, Sharif University of Technology, 2012
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Digital Image Processing
Intensity Transformations and Spatial Filtering
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• Filtering Rule:
IF d2 is zero AND d6 is zero THEN z5 is white
IF d6 is zero AND d8 is zero THEN z5 is white
IF d8 is zero AND d4 is zero THEN z5 is white
IF d4 is zero AND d2 is zero THEN z5 is white
ELSE z5 is black
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E. Fatemizadeh, Sharif University of Technology, 2012
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Digital Image Processing
Intensity Transformations and Spatial Filtering
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• Membership Function
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E. Fatemizadeh, Sharif University of Technology, 2012
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Digital Image Processing
Intensity Transformations and Spatial Filtering
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• Rules Graphical Interpretation
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Intensity Transformations and Spatial Filtering
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• Example:
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E. Fatemizadeh, Sharif University of Technology, 2012
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Digital Image Processing
Intensity Transformations and Spatial Filtering
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• MATLAB Command:
– Image Statistics:
• means2, std2, corr2, imhist, regionprops
– Image Intensity Adjustment:
• imadjust, histeq, adapthisteq, imnoise
– Linear Filter:
• imfilter, fspecial, conv2, corr2,
– Nonlinear filter:
• medfilt2, ordfilt2,