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E. Fatemizadeh, Sharif University of Technology, 20111
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Image Enhancement:– No Explicit definition
• Methods– Spatial Domain:
• Linear• Nonlinear
– Frequency Domain:• Linear• Nonlinear
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20112
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Spatial Domain Process
, ,g x y T f x y
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20113
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• For 11 neighborhood: – Contrast Enhancement/Stretching/Point process
• For w w neighborhood:– Filtering/Mask/Kernel/Window/Template Processing
s T r
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20114
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20115
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Image Negatives: 1s L r
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20116
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Log Transform: log 1s c r
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20117
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Power-Law Transform: s c r
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20118
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Original =0.6
=0.4 =0.3
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 20119
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Original =3
=4 =5
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201110
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Another Medical Example:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201111
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Contrast StretchingOriginal
C. S. THR.
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201112
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Gray Level Slicing
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201113
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• 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 Nnp r nn M N
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201114
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Histogram Example:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201115
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Histogram Visual Meaning:– Dark– Bright– Low Contrast– High Contrast
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201116
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
(0) 0(1) 1
:( ) 0( ) 0
TT
s T rT rT r
• Histogram Equalization:– First assume continuous case.– Seek for a suitable transform (Except for negative):
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201117
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
0
( ) 0,1r
r Ss T r p w dw P s U
0 0
min
min
, 0,1, , 1
ˆ 1 0.51
k kk
k k r JJ J
k kk
k
nS T r P r k Ln
S SS Int LS
Histogram Equalization
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201118
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Transformation Function:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201119
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Medical Examples:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201120
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Example (Mars Image and its Histogram):
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201121
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Histogram Equalization:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201122
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Desired
Initial CDF Modified CDF
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201123
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Local Enhancement:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201124
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Histogram Statistics For Image Enhancement:– Uses of Statistical Parameters
1
00
11
20
10variance
Ln
n i ii
L
i ii
r r m p r
m r p r
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201125
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Histogram Statistics For Image Enhancement:– Global mean and global variance:
• Gross adj. of overall intensity and contrast
– Local mean and local variance:• Changes dependents on predefined region about pixels• Local Definitions:
, ,
22
, ,
, , ,
, , , ,
Ss t S x y
Ss t S x y
m x y r s t p r s t
x y r s t m x y p r s t
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201126
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Measure of relative darkness/lightness:– Compare local mean vs. global mean.
• Measure of relative contrast:– Local variance vs. global variance.
• Rules:
0 1 2. , , ,,
, .S G G S GE f x y m x y K M and k D x y k D
g x yf x y OW
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201127
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• A SEM sample images:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201128
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Local Mean Local Var E or one
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201129
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Enhanced Images:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201130
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Image Subtraction:
• Application in medical imaging:– Angiography– DSA
, , ,g x y f x y h x y
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201131
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Contrast Agent Enhancement:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201132
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
, , ,a b
s a t b
g x y w s t f x s y t
• Windows Processing
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201133
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Smoothing Linear Filter:
, ,,
,
a b
s a t ba b
s a t b
w s t f x s y tg x y
w s t
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201134
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Blurring vs. Denoising
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201135
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Order Statistic filters:– Median– Max– min– Good for Salt-Pepper/impulse noise.
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201136
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Median and LPF Comparison:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201137
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Sharpening Spatial Filter:– First Derivative:
• Discrete Implementation:
– Second Derivative:• Discrete Implementation:
1, ,f f x y f x yx
2
2 1, 2 , 1,f f x y f x y f x yx
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201138
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201139
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• 1st and 2nd 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.
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201140
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Laplacian as an isotropic Edge Enhancer:
• Discrete Implementation:
2 22
2 2
f ffx 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 01 4 1 900 1 0
isotropic
1 1 11 8 1 451 1 1
isotropic
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201141
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Practically use:
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201142
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• Background Recovering:
2
2
, ,,
, ,f x y f x y sign
g x yf x y f x y sign
0 1 01 5 1 90
0 1 0isotropic
1 1 11 9 1 451 1 1
isotropic
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201143
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
2
2
, ,,
, ,f x y f x y sign
g x yf x y f x y sign
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201144
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Two L. MaskSEM image
a. Mask Result b. Mask Result
(Sharper)
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201145
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• First Derivative-Gradient:
1 222
x
x
fG xf
fGy
f f f ffx y x y
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201146
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• First Derivative-Gradient:– Discrete Implementation:
9 5 8 6
1 22 29 5 8 6
9 5 8 6 :
x yG z z G z z
f z z z z
f z z z z Roberts Cross Gradient
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201147
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Roberts Cross Gradient
Sobel
(2 1 for prewitt)
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201148
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• An Example (Contact Lens) of Sobel:
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E. Fatemizadeh, Sharif University of Technology, 201149
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Bone Scan Laplacian
Original +Laplacian
• Combination
Soble of
Original
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201150
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
Smoothed Sobel (Orig. + L.)*S.Sobel
Orig.+
(Orig. + L.)*S.SobelApply Power-Law
ee.sharif.edu/~miap
E. Fatemizadeh, Sharif University of Technology, 201151
Medical Image Analysis and Processing
Image Enhancement in Spatial Domain
• 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,
