IF-UTAMA 1

IF-UTAMA 1

Point Operation

Dosen Pembina Sriyani Violina

Danang Junaedi

IF-UTAMA 2

Review• Data image dinyatakan sebagai matrik dengan ukuran matrik

adalah resolusi (ukuran image) dan nilai tiap elemennya adalah nilai warna dari setiap pixel pada image tersebut.

• Kuantisasi pada image adalah banyaknya level warna yang digunakan untuk menyatakan dari warna yang paling gelap (hitam) sampai warna yang paling terang sesuai satuan atau format warna yang digunakan.

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Digital Image Processing

• Function of Image Processing: to change

– perceived / viewed image contrast

– perceived / viewed image colour

– perceived spatial information

– reduce image noise

– change viewing conditions

– segmentation / pattern recognition

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General Areas of Image Processing

• 3 general areas of digital image processing

– Point Operations

• Pixel Point Processing

– Local Operations

• Pixel Group Processing

– Global Operations

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Basics of Digital Images (review)

• Digital images are a 2D array of values in rows and columns

given by I(x,y) (or some by I(c,r))

0 1 2 3 4 4 6

0 152 120 22 215 34 1 0 117

1 3 114 199 134 88 20 60 199

2 234 72 65 17 145 185 235 181

3 141 214 169 134 85 234 237 68

4 241 154 141 231 145 236 35 27

5 45 95 65 127 123 94 47 166

6 127 98 137 149 67 45 52 29

7 162 81 83 189 69 195 94 171

8 64 123 130 100 58 226 214 34

102 189 174 35 169 203 243 135

213 235 219 137 22 195 168 208

227 103 192 243 102 220 187 21

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Point Operations / Intensity Transform

input gray level u

ou

tpu

t g

ray

leve

l

v

• Basic idea– “Zero memory” operation

• each output only depend on the input intensity at the point

– Map a given gray or color level u to a new level v, i.e. v = f ( u )

– Doesn’t bring in new info.

– But can improve visual appearance or make features easier to detect

• Example-1: Color coordinate transformations

– RGB of each pixel � luminance + chrominance components �etc.

• Example-2: Scalar quantization

– quantize pixel luminance/color with fewer bits

Operasi-operasi Dasar Pengolahan CitraOperasi Aljabar : Aritmatika & BooleanOperasi Geometri

Operasi Aljabar

• X opr Y = Z

– X: citra

– Y: citra atau besaran skalar

– Z: citra

• Level komputasi:

– Berbasis titik (pointwise): dilakukan antara tiap elemen X dan Y

– Berbasis matriks: melibatkan matriks ketetanggaan

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Operasi Aritmatika

• Beberapa operasi aritmatika:

– Penjumlahan

– Pengurangan

– Perkalian

– Pembagian

Untuk citra RGB,

operasi dilakukan per plane

Efek Penjumlahan pada Citra

• Y citra:

– Z adalah jumlah nilai brightness dari tiap pixel pada X dan Y

• Y besaran skalar:

– Z adalah versi yang lebih terang dari citra X

– nilai kenaikan brightness sama dengan Y

• Y citra:

– Z adalah perbedaan nilai brightness antar X dan Y

• Y besaran skalar:

– Z adalah versi yang lebih gelap daripada X

– nilai penurunan brightness sama dengan Y

Efek Pengurangan pada CitraEfek Perkalian & Pembagian

pada Citra• Perkalian

– Y citra:

• Z adalah hasil product antara nilai brightness citra X

dan Y

– Y besaran skalar:

• nilai brightness Z proporsional terhadap X pada nilai Y

• Pembagian

– Y citra:

• Z adalah nilai skala brightness pada tiap pixel di X

terhadap tiap pixel di Y

– Y besaran skalar:

• nilai brightness Z akan proportional terbalik terhadap X

dengan nilai Y

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Operasi Boolean

• Operasi boolean � AND, OR, NOT

• Kombinasinya : NAND, NOR, XOR

Operasi Geometri

• Proses yang memanipulasi posisi spatial dari pixel

• Contoh:

– Zoom (in & out)

– Rotasi

– Flipping

– Cut & paste

– Warping

Zoom

• Proses-proses yang melibatkan penaikan atau penurunan ukuran citra

• Teknik yang paling sederhana dalam zooming � menduplikasikan nilai pixel pada arah X atau Y.

• Jika citra tidak di zoom dengan nilai yang sama, maka “aspect ratio” dari citra akan berubah.

Aspect Ratio

• Rasio antara jumlah titik vertikal dan horizontal untuk mendapatkan panjang yang sama di kedua arah tersebut

IF-UTAMA 5

Zoom in

• Resolusi tidak bertambah

• Perubahan pada besar

pixelnya

– titik kecil dapat terlihat lebih besar

Zoom 3x

AR = 1

Zoom 3x

AR ≠ 1

Contoh algoritma zoom 2x, AR = 1

int i,j,m,n;

m=0;

n=0;

for (i=0;i<=jmlbaris-1;i++)

{

for(j=0;j<=jmlkolom-1;j++)

{

Z[m,n] = X[i,j];

Z[m,n+1] = X[i,j];

Z[m+1,n] = X[i,j];

Z[m+1,n+1] = X[i,j];

n=n+2;

}

m=m+2;

n=0;

}

Zoom out

• Ada informasi pada citra yang harus dihilangkan.

• Salah satu metode sederhana � ambil rata-rata dari n pixel bertetangga pada X sebagai nilai dari satu pixel pada Z

– Contoh: hasil rata-ratanya 4 pixel pada X menjadi 1 pixel pada Z

Zoom in � reversible

Zoom 2x Zoom 0.5x

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Zoom out � not reversible

Zoom 0.25x Zoom 4x

Rotasi

Rotate 900

Rotate 900

• Rotasi sederhana: kelipatan 900

– salin pixel-pixel baris ke pixel-pixel kolom sesuai

arah rotasi

Algoritma rotasi 900

int i,j,k;

k=jmlkolom-1;

for (i=0;i<=jmlbaris-1;i++)

{

for(j=0;j<=jmlkolom-1;j++)

{

Z[j,k] = X[i,j];

}

k=k-1;

}

Rotasi β0

Titik (a,b)����(c,d), dimana :

a = r.cos α

b = r.sin α

c = r.cos(α+β)= r.cos α.cos β–r.sin α.sin β

= a.cos β – b.sin β

d = r.sin(α+β)= r.sin α.cos β+r.cos α.sin β

= b.cos β + a.sin β

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Rotasi X0 (cont’d)

• Di titik mana sebaiknya sumbu putaran?

• Bagaimana rumus umum mencari ukuran citra yang

dirotasikan X0?

243

254

352

352

Rotasi

450

Flipping

horizontal

vertikal

Algoritma flipping vertikal

int i,j,k;

k=jmlbaris-1;

for (i=0;i<=jmlbaris-1;i++)

{

for(j=0;j<=jmlkolom-1;j++)

{

Z[k,j] = X[i,j];

}

k=k-1;

}

Cut & Paste

• Pemilihan (mulai paling mudah):

– Segiempat

– Bentuk geometri lain: lingkaran, elips, poligon

– Freeform

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Warping

Warp

• Citra diubah dengan cara mengatur kembali

hubungan spatial antara objek dengan suatu template spatial � menimbulkan efek-efek khusus

Contoh warping

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Point Operations

• Point Operations are primarily used to change the

perceived or viewed optical densities or colours and the perceived or viewed image contrast

• A point operation operates on individual pixels and does not take into account any neighbouring pixel values

• The same operation occurs on all of the pixels in the image

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Point Operation Process

• The process of the Point Operation is, starting at the top left

of the image, to calculate the new (output) pixel value and

place this at the same spatial location in a new (output)

matrix of the same dimension as the original image.

• The process then moves to the pixel to the right and

perform the operation until all pixels in the row have an output.

• The process then moves to the next row and continues until the entire image has an output.

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0 1 2 3 4 4 6

0 152 120 22 215 34 1 0 117

1 3 114 199 134 88 20 60 199

2 234 72 65 17 145 185 235 181

3 141 214 169 134 85 234 237 68

4 241 154 141 231 145 236 35 27

5 45 95 65 127 123 94 47 166

6 127 98 137 149 67 45 52 29

7 162 81 83 189 69 195 94 171

8 64 123 130 100 58 226 214 34

102 189 174 35 169 203 243 135

213 235 219 137 22 195 168 208

227 103 192 243 102 220 187 21

0 1 2 3 4 4 6

0 255 180

1

2

3

4

5

6

7

8

Operation

x 1.5

I(x,y)

O(x,y)

Point Operation Process

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Point Operation Process

The Point Operation process is denoted by:

O(x,y) = M . I(x,y)

where M is the mapping function or operation

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Point Operations

• The output of a point operations can be:

– a new image

• the new image O(x,y) will be the same size,

rows and columns, and have the same bit depth, as the original image I(x,y)

– the displaying on stored image

• displayed contrast or brightness may or may not be altered compared to the original image values

• LUTs will typically be used to do this operation

(some discussion earlier)

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Gambaran Transformasi Citra

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IF-UTAMA 37

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Typical Types of Gray-level Transformation

Figure is from slides at Gonzalez/ Woods DIP book website (Chapter 3)

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Transformasi Citra

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Mengubah Format kuantisasi

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Konversi RGB ke Gray Scale

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Konversi Gray Scale ke Biner

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Konversi Gray Scale ke m Bit

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Pengaturan Brightness

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Pengaturan Contrast

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Inversi

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Negative Image

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Example: Negative Transformation

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Figure is from slides at Gonzalez/ Woods DIP book website (Chapter 3)

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Transformasi Logaritmik

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Contoh

• Tranformasi Logaritmik

• Transformasi Inverse Logaritmik

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Example: Log Transformation

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Figure is from slides at Gonzalez/ Woods DIP book website (Chapter 3)

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Transformasi Power Law

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Contoh Hasil Transformasi power Law

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IF-UTAMA 53

Gamma Characteristics & Gamma Correction

• Non-linearity in CRT display

– Voltage U vs. Displayed luminance L’

• L’ ~ U γ

where γ = 2.0 ~ 2.5

• Use preprocessing to compensate γ-

distortion

– U ~ L 1/ γ

– log(L) gives similar compensation

curve to γ-correction

• good for many practical

applications

– Camera may have L1/γc

capturing

distortion

with γc = 1.0-1.7

• Power-law transformations are also useful for general purpose contrast manipulation

U

L’

L’ = a Uγ

L

U ~ logL

~ L1/γ

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Example: Effects of Different Gammas

( “vectors” sample image

from Matlab )

L02.2 L0

1/2.2

L0

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Figure is from slides at Gonzalez/ Woods DIP book website (Chapter 3)

IF-UTAMA 56

Look-Up Table (LUT)

• The LUT is a point operation that can have any mathematical calculation as its basis.

• Used for both display of the image and for creation of a new stored image

• LUTs are still constrained by the bit depth of the image ie, clipping and the output value must be an integer

• LUT’s are used to improve performance of the operation.

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IF-UTAMA 57

Look-Up Table (LUT)

• Each operation is performed on each possible value within the image ie. in an 8 bit depth image, on the values 0, 1, 2, ………, 255.

• If the image has a spatial resolution of 1000 rows and columns, then the operation, without the use of LUT’s, would have to be performed 1,000,000 times, rather than 256 times

• With LUT’s, values still need to be “looked-up” but overall operation performance is improved.

IF-UTAMA 58

Input Operation Output

Value Value

0 x 1.5 0

1 x 1.5 2

2 x 1.5 3

3 x 1.5 5

4 x 1.5 6

5 x 1.5 8

6 x 1.5 9

7 x 1.5 11

8 x 1.5 12

9 x 1.5 14

10 x 1.5 15

11 x 1.5 17

12 x 1.5 18

250 x 1.5 255

251 x 1.5 255

252 x 1.5 255

253 x 1.5 255

254 x 1.5 255

255 x 1.5 255

Note:

Output values are

integers & between

0 and 255

Example of a LUT

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Referensi

1. Achmad Basuki, Pelatihan Image Processing

dan Aplikasinya, Politeknik Elektronika Negeri Surabaya, 2005

2. Min Wu, Point Operations, ECE Department, Univ. of Maryland, College Park, 2004

3. http://csusap.csu.edu.au/~xzheng/lectures/mis303/MIS303_5.ppt, Tanggal Akses : 29 April 2009