Computer Vision –
Enhancement(Part II)
Hanyang University
Jong-Il Park
Local Enhancement
 Global enhancement
 The same operation for all pixels
 Local enhancement
 Different operation for each pixel
 According to the statistics of local support
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Local Histogram Equalization
 Using a fixed window at each point
 Computationally expensive
 Histogram equalization at each point
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Use of statistics of local support
 Eg.
E  f ( x, y)
g ( x, y)  
 f ( x, y)
m
Original
image
if m  k0 M G AND k1DG    k2 DG
otherwise

E
Enhanced
image
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Spatial Operations
 Spatial averaging and spatial LPF for noise
smoothing
Input
image
output
*
Spatial mask
( 33, 55, )
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Spatial Mask
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Spatial Averaging
 Mean-filtering
v(m, n)   a (k , l ) y (m  k , n  l )
( k .l ) W
ak , l  : filtercoefficients
equal weight filter: ak , l  

1
, N w  2M  1 2 N  1
Nw
Noise reduction
v(m, n)  u(m, n)  (m, n)
(m, n) ~ N (0, )
2
a(k , l ) 
1
Nw
1
v(m, n) 
 u (m  k , n  l )   (m, n)
N w ( k ,l ) W
 (m, n) ~ N (0,   ), where   
2
2
 2
Nw
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Spatial Averaging Mask

Spatial averaging masks a(k,l)

Disadvantage : blurring
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Effect of window size
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Eg. Spatial Averaging(1)
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Eg. Spatial Averaging(2)
Original image
Averaging 후의 image
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Cf. Multi-image averaging
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Spatial Operations - Filtering
 Parametric Low Pass Filter
1 b
 1  
2
H 
b
b

b  2  
1 b
2

but
 h
ij
i
1
1

b
1 
to preserve the mean
j
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Spatial LPF, BPF, HPF
hHP (m, n)   (m, n)  hLP (m, n)
hBP (m, n)  hL (m, n)  hL (m, n)
1
u (m, n)
Spatial
averaging
2
u (m, n)
VLP (m, n)
LPF
+
(a) Spatial low-pass filter
u (m, n)
VHP (m, n)
(b) Spatial high-pass filter
LPF
+
VBP (m, n)
hL (m, n)
1
LPF
hL (m, n)
2
(c) Spatial band-pass filter
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Eg. Spatial LPF
Original image
Lowpass Filter된 후의 image
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Spatial High-Pass Filtering
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Eg. Spatial HPF
Original image
Highpass filtered image
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Spatial Band-Pass Filtering
Original image
Lowpass Filter(Short Term) =A
Bandpass Filter된
후의 Image =B-A
Lowpass Filter(Long Term) =B
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Denoising by LPF
Noisy!
Blurred!
Trade-off?
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Directional Smoothing
 Directional Smoothing
 to protect the edges from blurring while smoothing
spatialaveragesvm, n,  are calculatedin severaldirection
1
v(m, n :  ) 
N
W
 y(m  k , n  l )
( k ,l ) W
 v(m, n)  v(m, n :   )
Find out  
such that min | y(m, n)  v(m, n :   ) |

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

















l
k
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Eg. Directional Smoothing
Original image
Lowpass Filter(Long Term)
Direc. Smoothing (대각선)
Direc. Smoothing (수 직)
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Median Filtering
 Median Filter
v(m, n)  median { y(m  k , n  l ), (k , l ) W }
filter length should be odd number

Properties
 nonlinear filter
median {x( m)  y ( m)}  median {x(m)}  median { y ( m)}

Example
 y  m   2,3,8, 4, 2 , 3 1 median filter
v  0   2  boundary value  , v 1  median 2,3,8  3
v  2   median 3,8, 4  4, v  3  median 8, 4, 2  4
v  5  2  boundary value 
v  m   2,3, 4, 4, 2
Numberof operations 3( NW2 1) / 8 comparisons
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Eg. 1D Median Filtering
L  5 1
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Discussion – Median filter
1) median filter preserve discontinuities in a step function
2) smooth a few pixels whose values differ significantly
from the surrounding, without affecting the other pixels.
3) pulse function, whose width is less than one half the
filter length, are suppressed
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2D Median Filtering
Filter
Filtered Image
Original Image
Filter
Filtered Image
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Eg. Median Filtering
Salt-and-pepper noise(=impulsive noise)
Original
7x7 Median filtered image
 Excellent performance!
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Eg. Median Filter – Impulsive Noise
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Eg. Median Filter – Impulsive Noise
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Eg. Median Filter – Gaussian Noise
Moderate
performance
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Various patterns for median filter
Neighborhood patterns used for median filtering
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Eg. Median filter – Square pattern
Original image
10% black, 10% white
Median filtering using
3 by 3 square region
Median filtering using
5 by 5 square region
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Eg. Median filter – Octagon pattern
Original image
5 by 5 octagonal median filter
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Eg. Median filter – Reconstruction
Original image
Median filtering and color compensation
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Sharpening Images
 Emphasis of high-frequency components
 Usually exploiting 1st order derivative and 2nd order
derivatives
 1D derivatives
f
st
 f ( x  1)  f ( x)
 1 order derivative:
x

2

f
nd
 f ( x  1)  f ( x  1)  2 f ( x)
2 order derivative:
2
x
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Eg. 1st & 2nd order derivatives
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Observation on derivatives
 2nd order derivative
 Thinner edges
 Stronger response to fine details
 Weaker response to a gray-level step
 Double response at step changes
 Intensity of response: point > line > step
 The 2nd order derivative is better suited than the 1st
order derivative for image enhancement.
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Laplacian Operator – Derivation
 The simplest isotropic derivative operator
2
2

f

f
2 f 

x 2
y 2
 x f (i, j )   x f (i  1, j )   x f (i, j )
2
 [ f (i  1, j )  f (i, j )]  [ f (i, j )  f (i  1, j )]
 f (i  1, j )  f (i  1, j )  2 f (i, j )
 y f (i, j )  f (i, j  1)  f (i, j  1)  2 f (i, j )
2
  2 f (i, j )   x f (i, j )   y f (i, j )
2
2
 [ f (i  1, j )  f (i  1, j )  f (i, j  1)  f (i, j  1)]  4 f (i, j )
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Laplacian Operator
 0 1 0 
H1   1 4  1
 0  1 0 
 1  1  1
H 2   1 8  1
 1  1  1
Eg)
0
0
0
1 2 3 4
x f
0
0
1
0 0 0 0 1 0 0 0
2
f  x f
2
0 0 1 1 2 3 4
5
 1 2 1 
H 3   2 4  2
 1  2 1 
5 5 5
6 5 5
5
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Sharpening by Laplacian operator
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Eg. Sharpening
Original SEM image
Laplacian operator
Original image
Laplacian operator
Subtraction of the
Laplacian from the original
Subtraction of the
Laplacian from the original
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Composite Laplacian mask
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Unsharp masking and Crispening
v(m, n)  u (m, n)  g (m, n),   0
where g (m, n) : Laplacianoutput (high pass filtered )
1
g (m, n)  u (m, n)  (u (m  1, n)  u (m, n  1)  u (m  1, n)  u (m, n  1))
4
(1)
Signal
(2)
Low-pass
(3)
High-pass
(1)+(3)
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Unsharp mask application
Original image
Processed image
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High-boost filtering
Let g(n1, n2) = u(n1, n2) - uL(n1, n2)
v(n1, n2) = u(n1, n2) + k g(n1, n2)
 k=1: Unsharp Masking
 Crispening an image
 k>1: High-boost filtering
 edge or line details to be emphasized
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Eg. High-boost filtering
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Zoom(1:2 magnification) revisited
 Nearest neighbor=Replication = zero - order hold
1
0
1
3
2



4 5 6  4



0
0
0
0
0
3
0
5
0
0
0
0
0
2
0
6
0
0
0

0

0
1
1
1
1
1
1
 
4

4
1
1
4
4
3
3
5
5
3
3
5
5
2
2
6
6
2
2
6

6
column, row zero-padding
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Zoom revisited(cont.)
 Linear Interpolation : first - order hold
1
0
1 7

3 1   3



0
0 7 0
1 4
0 0
0 0 0 
 
3 2
0 1 0


0 0 0
0 0



H  




1
4
1
2
1
4
1
2
1
1
2
1
4
1
2
1
4
7 3.5 
 1
 2
0 0 
 
 3
1 0.5 


0 0 
 1.5
3.5 
3 4
2 
2 1 0.5 

1 0.5 0.25 
4
7








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