PENGOLAHAN CITRA DIGITAL

STMIK AMIKOM PURWOKERTO

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. 5

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

Hi s togr a m dar i i ma ge di g i ta l dengan gray levels dari 0 sampai L-1 adalah fungsi diskrit h(rk)=nk, i m a a : d n 







rk adalah nilai gray level ke k nk adalah jumlah pixels dalam image yang memiliki gray level k n adalah jumlah keselirihan pixel pada image k = 0, 1, 2, …, L-1

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

Histogram dari image digital dengan gray level [0, L-1] adalah sebuah yang berada dalam range f u n g s i d i s k r i t h(rk) = nk dimana rk adalah nilai gray level ke k dan nk adalah jumlah pixel yang memiliki nilai gray level rk . Number of Occurrences 0

255 Pixel Value

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Image colors

red

green

blue 11

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Sifat – Sifat Histogram  

Histogram adalah pemetaan Many-to-One Image yang berbeda dimungkinkan untuk memiliki histogram yang sama.

A

1 3

2

4

Images B Histograms 12

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

Histogram sebuah image tidak berubah bila image dikenakan operasi tertentu seperti : Rotation, scaling, flip. Rotate Clockwise Flip Scale 13

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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] Tu j u a n : mencari transformasi contrast stretching T(k) sedemikian sehingga I2 = T(I) and p2 = 1(uniform)

p(k)

p2 15

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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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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) = nk /n. Normalisasi Histogram berguna untuk melihat statistika dari i m a g e . 17

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

Diberikan sebuah image 8-level berukuran 64 x 64 dengan nilai gray value (0, 1, …, 7). Nilai normalisasi dari gray value adalah (0, 1/7, 2/ 7, …, …, ….,…., 1).

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

Hanya ada 5 nilai gray level yang berbeda yang berpengaruh dalam image tsb.

Hasil ekualisasi adalah pendekatan terhadap bentuk histogram yang u n i f o r m 21

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Spatial Filtering



2D FIR filtering

Mask filtering: operasi konvolusi image dengan 2 D masking Applikasinya antara lain untuk image enhancement:  Smoothing: low pass  Sharpening: high pass



Data-dependent nonlinear filters Local histogram Order statistic filters  Medium filter

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Spatial filtering adalah operasi y a n g d i l a k u k a n Terhadap intensitas pixel dari s u a t u i m a g e Dan bukan terhadap komponen frekuensi dari image

a

b

g(x, y)

w(s, t) f (x s, y t) s

at

a = (m - 1) / 2

b

b = (n - 1) / 2 27

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Konvolusi Image

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Smoothing Spatial Filters _ Linear averaging (lowpass) filters Smoothing filters are used - Noise reduction - Smoothing of false contours - Reduction of irrelevant detail Undesirable side effect of smoothing filters - Blur edges

Weighted average filter reduces blurring in the smoothing process. Box filter

Weighted average

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Smoothing Linear Filters

I

J

w(i, j) f (m i, n g(m, n)

i

I j

j)

J 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 n = 15

Thrsh = 25% of highest intensity

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Sharpening Linear Filters 

High boosting filter:

Laplacian operator:



2 2





A≥1

f (x, y)

f (x 1, y)

f (x, y) x2 f (x 1, y)

2

f (x, y) y2 f (x, y 1)

f (x, y 1) 4 f (x, y)

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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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 by the filter, and then replacing the value of the center pixel with the value determined by the ranking result. 3 3 3

3 Median filter [10 125 125 135 141 141 144 230 240] = 141 3 Max filter [10 125 125 135 141 141 144 230 240] = 240 3 Min filter [10 125 125 135 141 141 144 230 240] = 10

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. 33

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Order Statistics Filters

n=3 Average filter

n=3 Median filter

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2-D, 2ndPURWOKERTO Order Derivatives STMIK AMIKOM for Image Enhancement

 

Isotropic filters: rotation invariant Laplacian (linear operator): 2 2



f

f

x2 Discrete version:

2

f

y2

2

f 2 2 x 2 f 2 2 y

f (x 1, y)

f (x 1, y) 2 f (x, y)

f (x, y 1)

f (x, y 1) 2 f (x, y) 35

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Laplacian

 2





Digital implementation: f

[ f (x 1, y)

f (x 1, y)

f (x, y 1)

f (x, y 1)] 4 f (x, y)

Two definitions of Laplacian: one is the negative of the other Accordingly, to recover background features:

g(x, y)

f ( x,y )

{ f ( x,y )

2 f ( x,y )( I ) 2 f ( x,y )( II )

I: if the center of the mask is negative II: if the center of the mask is positive 36

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Simplification

Filter and recover original part in one step: g(x,y) f (x,y) [f (x 1,y) f (x 1,y) f (x,y 1) f (x,y 1)] 4f (x,y) g(x, y) 5 f (x, y) [ f (x 1, y) f (x 1, y) f (x, y 1) f (x, y 1)]

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H igh-boost Filtering 

Unsharp masking: f s (x, y) f (x, y) f (x, y) 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 : the high-boost image looks more like 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 is the gradient: f F

Gx Gy

x f y

at (x,y)

• The magnitude of this vector is: 1

f

mag( f ) [G

2 x

2 2 y

G ]

f x

2

f y

2 1/ 2

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The Gradient

 







Non-isotropic Its magnitude (often call the gradient) is rotation invariant Computations: f Gx Gy Roberts uses:

Gx Gy

(z9 (z8

z5 ) z6 )

Approximation (Roberts Cross-Gradient Operators): f z9 z5 z8 z6 45

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Derivative Filters

At z5, the magnitude can be approximated as:

f

[(z5 z8 ) 2 (z5 f | z5

z8 | | z 5

z6 )2 ]1/ 2 z6 | 47

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Derivative Filters 

Another approach is: f

[(z5 f | z5

z9 ) 2 (z6 z9 | | z 6

z8 ) 2 ]1/ 2 z8 |

• 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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PENGOLAHAN CITRA DIGITAL

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