ee 4780 image enhancement. bahadir k. gunturk2 image enhancement the objective of image enhancement...
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EE 4780
Image Enhancement
Bahadir K. Gunturk 2
Image Enhancement The objective of image enhancement is to process an
image so that the result is more suitable than the original image for a specific application.
There are two main approaches: Image enhancement in spatial domain: Direct
manipulation of pixels in an image Point processing: Change pixel intensities Spatial filtering
Image enhancement in frequency domain: Modifying the Fourier transform of an image
Bahadir K. Gunturk 3
Image Enhancement by Point Processing
Intensity Transformation
Bahadir K. Gunturk 4
Image Enhancement by Point Processing Contrast Stretching
Bahadir K. Gunturk 5
Image Enhancement by Point Processing Contrast Stretching
( ) log(1 )T r c r
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Image Enhancement by Point Processing
Intensity Transformation
Matlab exercise
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Image Enhancement by Point Processing Intensity Transformation
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Image Enhancement by Point Processing Intensity Transformation
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Image Enhancement by Point Processing Gray-Level Slicing
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Image Enhancement by Point Processing Histogram
0 255
Number of pixels with intensity ( )
Total number of pixels
rp r
( )p r
r
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Histogram Specification
( )s T r
Intensity mapping
Assume T(r) is single-valued and monotonically increasing.
The original and transformed intensities can be characterized by their probability density functions (PDFs)
0 ( ) 1 and 0 1T r r
( )rp r
( )sp s
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Histogram Specification
1 ( )
( ) ( )s rr T s
drp s p r
ds
The relationship between the PDFs is
0
( ) ( )r
r
w
s T r p w dw
0
( ) ( )r
r r
w
ds dp w dw p r
dr dr
Consider the mapping
Cumulative distribution function of r
1 ( )
1( ) ( ) 1, 0 1
( )s rr r T s
p s p r sp r
Histogram equalization!
( ) ( ) 1s rp s ds p r dr
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Image Enhancement by Point Processing Histogram Equalization
Number of pixels with intensity ( ) 255
Total number of pixels
i rT r round
0 255r
0
255 ( )r
i
round p i
0
Number of pixels with intensity 255
Total number of pixels
r
i
iround
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Image Enhancement by Point Processing Histogram Equalization Example
Intensity 0 1 2 3 4 5 6 7
Number of pixels 10 20 12 8 0 0 0 0
Intensity 0 1 2 3 4 5 6 7
Number of pixels 0 10 0 0 20 0 12 8
(0) 10 / 50 0.2p (1) 20 / 50 0.4p (2) 12 / 50 0.24p (3) 8 / 50 0.16p
( ) 0 / 50 0, 4,5,6,7p r r
0
( ) 7 ( )r
i
T r round p i
(0) 7* (0) 7*0.2 1T round p round (1) 7* (0) (1) 7*0.6 4T round p p round (2) 7* (0) (1) (2) 7*0.84 6T round p p p round (3) 7* (0) (1) (2) (3) 7T round p p p p
( ) 7, 4,5,6,7T r r
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Image Enhancement by Point Processing Histogram Equalization
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Local Histogram Processing
Histogram processing can be applied locally.
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Image Subtraction
The background is subtracted out, the arteries appear bright.
( , ) ( , ) ( , )g x y f x y h x y
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Image Averaging
( , ) ( , ) ( , )g x y f x y n x y
Original
imageNoiseCorrupted
image
Assume n(x,y) a white noise with mean=0, and variance 2 2 ( , )E n x y
If we have a set of noisy images ( , )ig x y
The noise variance in the average image is1
1( , ) ( , )
M
ave ii
g x y g x yM
2
2 22
1 1
1 1 1( , ) ( , )
M M
i ii i
E n x y E n x yM M M
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Image Averaging
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Spatial Filtering
1 1 11
1 1 19
1 1 1
1 1 1
1 8 1
1 1 1
A low-pass filter
A high-pass filter
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Spatial Filtering
Median Filter
10 20 10
25 10 75
90 85 100
Sort: (10 10 10 20 25 75 85 90 100)
100 100 100 100 10 10 10 10 10
Example
Original signal:
100 103 100 100 10 9 10 11 10Noisy signal:
101 101 70 40 10 10 10Filter by [ 1 1 1]/3:
100 100 100 10 10 10 10Filter by 1x3 median filter:
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Spatial Filtering
Median filters are nonlinear. Median filtering reduces noise without blurring edges and
other sharp details. Median filtering is particularly effective when the noise
pattern consists of strong, spike-like components. (Salt-and-pepper noise.)
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Spatial Filtering
Original
3x3 averaging
filter
Salt&Pepper noise added
3x3 median filter
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Spatial Filtering
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Wiener Filter
WXY
YXwx
x22
2
ˆ
Wiener Filter
Original
imageNoiseNoisy
image
Noise varianceSignal variance
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Wiener Filter
222ˆ wx y
2x is estimated by
Since variance is nonnegative, it is modified as
],0max[ˆ 222wx y
2 2 22
1ˆ max[0, ]x i w
i
yN
Estimate signal variance locally:
N
N
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Wiener Filter
Noisy, =10 Denoised (3x3neighborhood)Mean Squared Error is 56
wiener2 in Matlab
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Spatial Filtering
1 1 1
1 8 1
1 1 1
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Spatial Filtering
High-boost or high-frequency-emphasis filter Sharpens the image but does not remove the low-frequency
components unlike high-pass filtering
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Spatial Filtering
High-boost or high-frequency-emphasis filter
High pass = Original – Low pass
High boost = (Original) + K*(High pass)
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Spatial Filtering
1 1 1
1 8 1
1 1 1
A high-pass filter A high-boost filter
1 1 1
1 9 1
1 1 1
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Spatial Filtering
High-boost or high-frequency-emphasis filter
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Spatial Filtering