STMIK AMIKOM PURWOKERTO
ABDUL AZIS, M.KOM
PENGOLAHAN CITRA DIGITAL
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Representasi Image
1 bit 8 bits
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24 bits 4
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Apakah itu histogram?
(3, 8, 5)
Histogram memberikan deskripsi global dari penampakan sebuah image.
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rk adalah nilai gray level ke k nk adalah jumlah pixels dalam image
Hi s togr a m dar i levels
i ma ge di g i ta l
dengan gray dari 0 sampai L-1 d
adalah fungsi diskrit n
h(rk)=nk, i m a a :
yang memiliki gray level k n adalah jumlah keselirihan pada image k = 0, 1, 2, …, L-1
pixel
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Histogram dari image digital dengan gray level
[0, L-1] yang berada dalam range adalah sebuah f u n g s i d i s k r i t
h(rk) adalah nilai
= nk gray rk nk adalah dimana
jumlah level ke k dan
rk. pixel yang memiliki nilai gray level
Number of
Occurrences
0 255
Pixel Value
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Image colors
red green blue
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Sifat – Sifat Histogram
Histogram adalah pemetaan Many-to-One
Image yang berbeda dimungkinkan untuk
m e m i l i k i h i s t o g r a m y a n g s a m a .
A 1
2 4 3
Images
B
Histograms
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Histogram sebuah image tidak
berubah o p e r a s i
bila image dikenakan t e r t e n t u s e p e r t i :
. R o t a t i o n , s c a l i n g , f l i p
Rotate
Clockwise
Flip
Scale
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Ekualisasi Histogram
Adalah proses Mapping dari Grey Levels
”p” menjadi Grey Levels “q” sedemikian sehingga distribusi dari Grey Levels pada “q” mendekati bentuk Uniform
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Bila p(k) = image histogram pada
k = [0..1] T u j u a n : contrast sehingga
m e n c a r i stretching
t r a n s f o r m a s i
T(k) sedemikian I2 = T(I) and p2 = 1(uniform)
p2 p(k)
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Dengan Histogram informasi spasial dari image diabaikan
dan hanya mempertimbangkan frekuensi relatif
p e n a m p i l a n g r a y l e v e l .
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untuk melihat statistika dari i m a g e .
Normalisasi Histogram
Normalized histogram: p(rk)=nk/n
Jumlah keseluruhan komponen = 1
Adalah membagi setiap nilai dari
histogram dengan jumlah pixel d a r i i m a g e ( n ) ,
p(rk) Normalisasi
= nk /n. Histogram berguna
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Diberikan sebuah image
8-level berukuran 64 x 64 dengan nilai gray
Nilai gray 1/7,
1).
value (0, 1, …, 7). normalisasi dari
(0, value 2/ 7,
adalah …, …, … . ,… . ,
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Hanya ada 5 nilai gray level yang berbeda
yang berpengaruh dalam image tsb.
H a s i l e k u a l i s a s i a d a l a h p e n d e k a t a n t e r h a d a p b e n t u k h i s t o g r a m y a n g u n i f o r m
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Spatial Filtering
2D FIR filtering Mask filtering: operasi konvolusi image
2 D masking Applikasinya antara lain untuk image
enhancement: Smoothing: low pass Sharpening: high pass
dengan
Data-dependent nonlinear Local histogram Order statistic filters Medium filter
filters
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Spatial filtering adalah operasi
y a n g d i l a k u k a n
dari Terhadap intensitas pixel
s u a t u i m a g e
Dan bukan terhadap komponen
f r e k u e n s i d a r i i m a g e
a b
g(x, y) w(s, t) f (x s, y t) s a t b
a = (m - 1) / 2 b = (n - 1) / 2 27
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Konvolusi Image
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Smoothing Spatial Filters _ averaging (lowpass) filters
Linear
Smoothing filters are used
-
-
-
Noise reduction
Smoothing of false contours
Reduction of irrelevant detail
Undesirable side effect of
- Blur edges
smoothing filters
Weighted average filter
reduces blurring in the
smoothing process.
Box
filter Weighted
average 29
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Smoothing Linear Filters
I J
w(i, j) f (m i, n j) i I j J
g(m, n) I J
w(i, j) i I j J
Normalization of coefficient to
ensure 0 ≤ g(m,n) ≤ L-1
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Averaging dan Threshold
filter size Thrsh = 25% of
n = 15 highest intensity
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Sharpening Linear Filters
High boosting filter: Laplacian operator:
2 2 f (x, y) f (x, y) 2 f (x, y) x2
f (x
y 2
f (x, y f (x 1, y) 1, y) 1) f (x, y 1) 4 f (x, y)
A ≥ 1
Derivative filter:
Use derivatives to
approximate high pass filters. Usually 2nd
derivatives are preferred. The most common one is the Laplacian operator.
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3 3 Median filter [10 125 125 135 141 141 144 230 240] = 141
3 3 Max filter [10 125 125 135 141 141 144 230 240] = 240
3 3 Min filter [10 125 125 135 141 141 144 230 240] = 10
Order Statistics Filters
Order-statistics filters are nonlinear spatial filters whose
response is based on ordering (ranking) the pixels
contained in the image area encompassed
and then replacing the value of the center
by the filter,
pixel with the
value determined by the ranking result.
Median filter eliminates isolated clusters of pixels that are light or
dark with respect to their neighbors, and whose area is less than n2/2.
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Order Statistics Filters
n = 3
Median
filter
n = 3
Average
filter
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2-D, 2nd Order Derivatives for Image Enhancement
Isotropic filters: rotation invariant
Laplacian (linear 2
operator):
2 f f 2 f x2 y2
Discrete 2 f
version:
f (x 1, y) f (x 1, y) 2 f (x, y) 2 x 2
2 f f (x, y 1) f (x, y 1) 2 f (x, y)
2 y 2
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Laplacian Digital implementation:
2 f [ f (x 1, y) f (x 1, y) f (x, y 1) f (x, y 1)] 4 f (x, y)
Two definitions negative of the Accordingly, to features:
of Laplacian: one is the other recover background
2 f f ( x,y ) ( x,y )( I )
g(x, y) { 2 f ( x,y ) f ( x,y )( II )
I: if the center of the mask is negative II: if the center of the mask is positive
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Simplification
Filter and step:
recover original part in one
g(x,y)
g(x, y)
f (x,y) [ f (x 1,y) f (x 1, y)
1,y) f (x
f (x,y 1, y)
1) f (x,y 1)] 4 f (x,y)
5 f (x, y) [ f (x f (x, y 1) f (x, y 1)]
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H igh-boost Filtering
fs(x, y) f (x, y) f (x, y) Unsharp masking:
Highpass filtered image = Original – lowpass filtered image.
If A is an amplification factor then:
High-boost = A · original – lowpass (blurred) = (A-1) · original + original – lowpass = (A-1) · original + highpass
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High-boost Filtering
A=1 : standard highpass result
A>1 like
: the high-boost image looks more the original with a degree of edge
enhancement, depending on the value of A.
w=9A-1, A≥1
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1st Derivatives
The most common method of
differentiation in Image Processing f
is the gradient:
F Gx
Gy
x f at (x,y)
y
• The magnitude of this vector is: 1/ 2
2 2 1 f f 2 2 f mag( f ) [Gx Gy ]
2
x y
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The Gradient Non-isotropic Its magnitude (often rotation invariant
call the gradient) is
Computations: f Gx Gy
Gx
Gy
(z9
(z8
z5 ) z6 )
Roberts uses:
Approximation Operators):
(Roberts Cross-Gradient
f z9 z5 z8 z6 45
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Derivative Filters
At z5, the magnitude can be approximated as:
2 2 1/ 2 f [(z5
| z5
z8 ) (z5
| z5
z6 ) ] z6 | f z8 |
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Derivative Filters
Another approach is:
2 2 1/ 2 f [(z5
| z5
z9 ) (z6
| z6
z8 ) ] z8 | f z9 |
• One last approach is (Sobel Operators):
f (z7 2z8 z9 ) (z1 2z2 z3) (z3 2z6 z9 ) (z1 2z4 z7)
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Robert operator
Sobel operators 49
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(b)
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