Transcript Image enhacement

EE 4780
Image Enhancement
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
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Image Enhancement by Point Processing

Intensity Transformation
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Image Enhancement by Point Processing

Contrast Stretching
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Image Enhancement by Point Processing
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Contrast Stretching
T (r )  c log(1  r )
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Image Enhancement by Point Processing

Intensity Transformation
Matlab exercise
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Image Enhancement by Point Processing
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Intensity Transformation
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Image Enhancement by Point Processing
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Intensity Transformation
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Image Enhancement by Point Processing
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Gray-Level Slicing
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Image Enhancement by Point Processing
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Histogram
 Number of pixels with intensity r 
p(r )  

Total number of pixels


p(r )
0
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r
255
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Histogram Specification

Intensity mapping
s  T (r )


Assume

T(r) is single-valued and monotonically increasing.

0  T (r )  1 and 0  r  1
The original and transformed intensities can be
characterized by their probability density functions (PDFs)
pr (r )
ps ( s )
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Histogram Specification

The relationship between the PDFs is
 p (s)ds   p (r )dr  1
s

r
dr 

ps ( s)   pr (r ) 
ds  r T 1 ( s )

Consider the mapping
r
s  T (r ) 

pr ( w)dw
Cumulative distribution function of r
w 0
r
ds d

pr ( w)dw  pr (r )

dr dr w0

1 
ps ( s )   pr (r )
 1,

p
(
r
)

r
 r T 1 ( s )
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0  s 1
Histogram equalization!
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Image Enhancement by Point Processing

Histogram Equalization

Number of pixels with intensity i  r 
T (r )  round  255

Total number of pixels


r

Number of pixels with intensity i 
 round  255

Total
number
of
pixels
i

0


r


 round  255 p(i) 
i 0


0  r  255
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Image Enhancement by Point Processing

Histogram Equalization Example
Intensity
Number of pixels
0 1 2 3
10 20 12 8
4 5 6
0 0 0
7
0
p(0)  10 / 50  0.2
p(1)  20 / 50  0.4
p(2)  12 / 50  0.24
p(3)  8 / 50  0.16
p(r )  0 / 50  0, r  4,5, 6, 7
 r

T (r )  round  7 p(i) 
 i 0

T (0)  round  7* p(0)   round  7*0.2   1
T (1)  round  7*  p(0)  p(1)    round  7*0.6   4
T (2)  round  7*  p(0)  p(1)  p(2)    round  7*0.84   6
T (3)  round  7*  p(0)  p(1)  p(2)  p(3)    7
T (r )  7, r  4,5, 6, 7
Intensity
Number of pixels
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0 1 2
0 10 0
3 4 5 6
0 20 0 12
7
8
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Image Enhancement by Point Processing
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Histogram Equalization
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Local Histogram Processing

Histogram processing can be applied locally.
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Image Subtraction
g ( x , y )  f ( x , y )  h ( x, y )
The background is subtracted out, the arteries appear bright.
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Image Averaging
g ( x , y )  f ( x , y )  n ( x, y )
Corrupted
image
Original
image
Noise
Assume n(x,y) a white noise with mean=0, and variance  2
E n 2 ( x, y )
If we have a set of noisy images gi ( x, y)
1
g
(
x
,
y
)

The noise variance in the average image ave
M

 1
E 
 M

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
n
(
x
,
y
)

i

i 1

M
2

1



2
M


2
E
n

 i ( x, y) 
M
i 1
M
 g ( x, y )
i 1
i
is
1 2

M
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Image Averaging
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Spatial Filtering
1 1 1
1

1
1
1

9
1 1 1
1 1 1
1 8 1


1 1 1
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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)
Example
Original signal: 100 100 100 100 10 10 10 10 10
Noisy signal: 100 103 100 100 10
9 10 11 10
Filter by [ 1 1 1]/3:
101 101 70 40 10 10 10
Filter by 1x3
median filter:
100 100 100 10 10 10 10
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Spatial Filtering
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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-andpepper noise.)
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Spatial Filtering
Original
3x3
averaging
filter
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Salt&Pepper
noise added
3x3
median
filter
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Spatial Filtering
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Wiener Filter
Y  X W
Noisy
image
Original
image
Wiener Filter
Noise
2

x
Xˆ  2
Y
2
 x w
Signal variance
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Noise variance
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Wiener Filter
 x2
is estimated by
ˆ x2  y 2   w2
Since variance is nonnegative, it is modified as
ˆ x2  max[ 0, y 2   w2 ]
Estimate signal variance locally:
ˆ x2  max[0,
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N2
2
2
y


 i w]
i
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
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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
 1 1 1
 1 9 1


 1 1 1
A high-pass filter
A high-boost filter
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Spatial Filtering

High-boost or high-frequency-emphasis filter
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Spatial Filtering
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