PERBAIKAN
CITRA
Introduction

Apa itu perbaikan citra?


Proses peningkatan kualitas visual dari citra
karena proses pengambilan gambar yang tidak
ideal. (Tidak fokus, gerakan blurring, illumminasi
yang jelek, dll)
Menilai kualitas visual citra
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A Plague in Image Processing: Blur

Dari mana blur itu berasal?



Mengapa perlu deblurring?




Optical blur: kamera out-of-focus
Motion blur: Kamera bergerak
Mengganggu secara visual
Target yang salah untuk kompressi
Jelek untuk dianalisa
Numerous applications in astronomical
imaging, biomedical imaging, biometrics ...
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Processing
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Restoration Images
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Processing
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Another Example
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Processing
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The Real (Optical) Solution
Before the repair
After the repair
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Application (II): Medical Image
Deblurring (Deconvolution)
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Application (III): Law Enforcement
Motion-blurred license plate image
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Restoration Example
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A Grand Challenge in Iris Recognition
out-of-focus iris image
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Modeling Blurring Process
• Linear degradation model
x(m,n)
h(m,n)
+
y(m,n)
w(m, n)
h(m, n)
blurring filter
w(m, n) ~ N (0, )
2
w
additive white Gaussian noise
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The Curse of Noise
x(m,n)
h(m,n)
z(m,n)
+
y(m,n)
w(m, n) ~ N (0, w2 )
Blurring SNR
 z2
BSNR  10log10 2
w
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Image Example
x(m,n)
BSNR=10dB
BSNR=40dB
h(m,n): 1D horizontal motion blurring [1 1 1 1 1 1 1]/7
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Mengapa butuh metode non linier ?


Proses pemodelan degradasi citra dengan
linear system muncul terutama karena dapat
dinyatakan secara matematis
Tetapi ada fenomena dalam visualisasi dan
pencitraan secara fisik sulit dijelaskan degna
persamaan sederhana secara linier

Examples: relationship between illumination and
luminance on a complex surface, quantization of
intensity values, Gamma-correction in display
devices
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Point Operations Overview
Point operations are zero-memory operations where
a given gray level x[0,L] is mapped to another
gray level y[0,L] according to a transformation
y  f (x)
y
L
L
x
L=255: for grayscale images
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Lazy Man Operation
yx
y
L
L
x
No influence on visual quality at all
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Digital Negative
L
y  Lx
0
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Processing
L
x
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Contrast Stretching
x


y    ( x  a )  ya
  ( x  b)  y
b

0 xa
a xb
bxL
yb
ya
0
a b
L
x
a  50, b  150,  0.2,   2,   1, ya  30, yb  200
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Clipping
0 xa
 0

y   ( x  a) a  x  b
  (b  a) b  x  L

0
a b
L
x
a  50, b  150,   2
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Range Compression
y  c log10 (1  x)
0
L
x
c=100
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Kesimpulan operasi titik



Pemetaan f(x) mengahasilkan hasil
perbaikan yang berbeda beda
Bagaimana memilih fungsi f(x) yang sesuai
untuk sembarang citra?
One systematic solution is based on the
histogram information of an image

Histogram equalization and specification
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Histogram based Enhancement
Histogram of an image represents the relative frequency
of occurrence of various gray levels in the image
3000
2500
2000
1500
1000
500
0
0
50
100
150
200
MATLAB function >imhist(x)
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Why Histogram?
4
x 10
4
3.5
3
2.5
2
1.5
1
0.5
0
0
50
100
150
200
250
It is a baby in the cradle!
Histogram information reveals that image is under-exposed
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Another Example
7000
6000
5000
4000
3000
2000
1000
0
0
50
100
150
200
250
Over-exposed image
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How to Adjust the Image?

Histogram equalization


Basic idea: find a map f(x) such that the histogram
of the modified (equalized) image is flat (uniform).
Key motivation: cumulative probability function
(cdf) of a random variable approximates a uniform
distribution
x
Suppose h(t) is the histogram (pdf)
s( x)   h(t )
t 0
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Histogram Equalization
x
y  L   h(t )
t 0
Uniform
Quantization
L
x
y s   h(t )
t 0
L
0
1
Note:
 h(t )  1
t 0
cumulative probability function
L
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MATLAB Implementation
function y=hist_eq(x)
[M,N]=size(x);
for i=1:256
h(i)=sum(sum(x= =i-1));
End
y=x;s=sum(h);
for i=1:256
I=find(x= =i-1);
y(I)=sum(h(1:i))/s*255;
end
Calculate the histogram
of the input image
Perform histogram
equalization
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Ic. Histogram Equalization


Histogram: diagram yang menunjukkan jumlah
kemunculan grey level (0-255) pada suatu citra
Histogram processing:
Gambar gelap: histogram cenderung ke sebelah kiri
 Gambar terang: histogram cenderung ke sebelah
kanan
 Gambar low contrast: histogram mengumpul di suatu
tempat
 Gambar high contrast: histogram merata di semua
tempat
 Histogram processing: mengubah bentuk histogram
agar pemetaan gray level pada citra juga berubah

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Ic. Histogram Equalization
in all grey level and all area (1)


Ide: mengubah pemetaan
greylevel agar sebarannya
(kontrasnya) lebih menyebar
pada kisaran 0-255
Sifat:



Grey level yang sering
muncul lebih dijarangkan
jaraknya dengan grey level
sebelumnya
Grey level yang jarang
muncul bisa lebih
dirapatkan jaraknya dengan
grey level sebelumnya
Histogram baru pasti
mencapai nilai maksimal
keabuan (contoh: 255)
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Ic. Histogram Equalization
in all grey level and all area (2)
- mengubah pemetaan grey level pada
citra, dengan rumus:
k
nj
j 0
n
sk  T (rk )  
k
  p(rj )
j 0
0  rk  1 dan k  0,1,.....,L  1
L adalah grey levelmaksimalyangada pada citra
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Ic. Histogram Equalization
in all grey level and all area (3)

Citra Akhir:
19 9 95
95 9 55
91 5 55
5 9 10 10 1
Citra awal:
35554
54544
53444
45663


Contoh : citra
dengan derajat
keabuan hanya
berkisar 0-10
Derajat Keabuan
0
1
2
3
4
5
6
7
8
9
10
Kemunculan
0
0
0
3
8
7
2
0
0
0
0
Probabilitas Kemunculan
0
0
0
0.15
0.40
0.35
0.1
0
0
0
0
Sk
0
0
0
0.15
0.55
0.90
1
1
1
1
1
SK * 10
0
0
0
1.5
5.5
9
10
10
10
10
10
Derajat keabuan baru
0
0
0
1
5
9
10
10
10
10
10
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Ic. Histogram Equalization
specific grey level (hist. specification)

Histogram
equalization
tidak dilakukan
pada seluruh
bagian dari
histrogram tapi
hanya pada
bagian tertentu
saja
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Image Example
after
before
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Histogram Comparison
3000
3000
2500
2500
2000
2000
1500
1500
1000
1000
500
0
500
0
50
100
150
200
before equalization
0
0
50
100
150
200
250
300
after equalization
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Application (I): Digital Photography
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Processing
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Application (II): Iris Recognition
after
before
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Processing
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Application (III): Microarray Techniques
after
before
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Frequency-Domain Techniques (I):
Unsharp Masking
y(m, n)  x(m, n)  g (m, n),   0
g(m,n) is a high-pass filtered version of x(m,n)
• Example (Laplacian operator)
1
g (m, n)  x(m, n)  [ x(m  1, n)  x(m  1, n) 
4
x(m, n  1)  x(m, n  1)]
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MATLAB Implementation
% Implementation of Unsharp masking
function y=unsharp_masking(x,lambda)
% Laplacian operation
h=[0 -1 0;-1 4 -1;0 -1 0]/4;
dx=filter2(h,x);
y=x+lambda*dx;
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1D Example
250
250
200
200
150
150
100
100
50
50
0
0
0
50
100
150
200
250
0
50
100
150
200
250
xlp(n)
x(n)
220
8
200
6
4
180
2
160
0
140
-2
120
-4
100
-6
80
-8
0
50
100
150
200
250
0
50
100
150
200
250
300
300
g(n)=x(n)-xlp(n)
y(n)  x(n)  g (n)
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2D Example
MATLAB command
>roidemo
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Frequency-Domain Techniques (II):
Homomorphic
filtering
Basic idea:
f ( x, y )  i ( x , y ) r ( x, y )
Illumination
(low freq.)
reflectance
(high freq.)
ln f ( x, y )  ln i( x, y )  ln r( x, y )
freq. domain enhancement
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Image Example
after
before
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Summary of Nonlinear Image
Enhancement

Understand how image degradation occurs first



Play detective: look at histogram distribution, noise
statistics, frequency-domain coefficients…
Model image degradation mathematically and try inverseengineering
Visual quality is often the simplest way of evaluating
the effectiveness, but it will be more desirable to
measure the performance at a system level


Iris recognition: ROC curve of overall system
Microarray: ground-truth of microarray image segmentation
result provided by biologists
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