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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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