Embed Size (px)
Citation preview
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
Bahadir K. Gunturk 6
Image Enhancement by Point Processing
Intensity Transformation
Matlab exercise
Bahadir K. Gunturk 7
Image Enhancement by Point Processing Intensity Transformation
Bahadir K. Gunturk 8
Image Enhancement by Point Processing Intensity Transformation
Bahadir K. Gunturk 9
Image Enhancement by Point Processing Gray-Level Slicing
Bahadir K. Gunturk 10
Image Enhancement by Point Processing Histogram
0 255
Number of pixels with intensity ( )
Total number of pixels
rp r
( )p r
r
Bahadir K. Gunturk 11
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
Bahadir K. Gunturk 12
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
Bahadir K. Gunturk 13
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
Bahadir K. Gunturk 14
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
Bahadir K. Gunturk 15
Image Enhancement by Point Processing Histogram Equalization
Bahadir K. Gunturk 20
Local Histogram Processing
Histogram processing can be applied locally.
Bahadir K. Gunturk 21
Image Subtraction
The background is subtracted out, the arteries appear bright.
( , ) ( , ) ( , )g x y f x y h x y
Bahadir K. Gunturk 22
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
Bahadir K. Gunturk 23
Image Averaging
Bahadir K. Gunturk 24
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
Bahadir K. Gunturk 25
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:
Bahadir K. Gunturk 26
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.)
Bahadir K. Gunturk 27
Spatial Filtering
Original
3x3 averaging
filter
Salt&Pepper noise added
3x3 median filter
Bahadir K. Gunturk 28
Spatial Filtering
Bahadir K. Gunturk 29
Wiener Filter
WXY
YXwx
x22
2
ˆ
Wiener Filter
Original
imageNoiseNoisy
image
Noise varianceSignal variance
Bahadir K. Gunturk 30
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
Bahadir K. Gunturk 31
Wiener Filter
Noisy, =10 Denoised (3x3neighborhood)Mean Squared Error is 56
wiener2 in Matlab
Bahadir K. Gunturk 35
Spatial Filtering
1 1 1
1 8 1
1 1 1
Bahadir K. Gunturk 36
Spatial Filtering
High-boost or high-frequency-emphasis filter Sharpens the image but does not remove the low-frequency
components unlike high-pass filtering
Bahadir K. Gunturk 37
Spatial Filtering
High-boost or high-frequency-emphasis filter
High pass = Original – Low pass
High boost = (Original) + K*(High pass)
Bahadir K. Gunturk 38
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
Bahadir K. Gunturk 39
Spatial Filtering
High-boost or high-frequency-emphasis filter
Bahadir K. Gunturk 40
Spatial Filtering
