AREA PROCESS. Area processes use the input pixel as well as the pixels around it to generate a new ouput pixel

AREA PROCESS Area processes use the input pixel as well as the pixels around it to generate a new ouput pixel Topik Bahasan – Konvolusi (convolution) – Filtering (nonmask convolution) – Filter Morfologis

Pengolahan Citra Dijital

3.1

Setiawan Hadi

KONVOLUSI

• Konvolusi diskrit

banyak digunakan dalam pengolahan citra untuk image smoothing, edge detection dan efek-efek lainnya

• Konvolusi dilakukan tetangga

berdasarkan jumlah bobot dari piksel-piksel

• Bobot ditentukan

berdasarkan ukuran window berupa matriks berukuran kecil yang biasa disebut convolution mask atau convolution kernel

• Orde matriks

biasanya ganjil sehingga hasil konvolusi tepat berada di tengah-tengah

• Window atau disebut juga sliding window bergerak sepanjang piksel yang ada pada citra

• Perlu diperhatikan

bahwa nilai piksel hasil konvolusi JANGAN disertakan pada perhitungan konvolusi piksel berikutnya.

• Semakin

besar ukuran window, beban komputasi akan semakin meningkat Pengolahan Citra Dijital

3.2

Setiawan Hadi

Formulasi Matematika I ' ( x, y )  I ( x, y ) * W ( x, y ) 





  I (u, v)W (u  x, v  y)

u   v  


3.3

Setiawan Hadi

Image Filtering

1

6

3

2

9

1/9

1/9

1/9

2

11

3

10

0

1/9

1/9

1/9

5

10

6

9

7

1/9

1/9

1/9

3

1

0

2

8

4

4

2

9

Filter/mask/ operator

New value: 6/9 + 9/9 + 7/9 + 0/9 + 2/9 + 8/9 + 2/9 + 9/9 + 10/9 = 5.889

10

Image

Pengolahan 03Citra Dijital

3.5

Setiawan Hadi

Image Filtering Original Image:

Filtered Image:

11/9 61/9 31/9 2

9

0

0

0

0

21/9 11 1/9 31/9 10

0

0

51/9 10 1/9 61/9 9

7

0

0

3

1

0

2

8

0

0

4

4

2

9

10

0

0

5

0

0

0

value = 1x1/9 + 6x1/9 + 3x1/9 + 2x1/9 + 11x1/9 + 3x1/9 + 5x1/9 + 10x1/9 + 6x1/9 = 47/9 = 5.222


3.6

0

Setiawan Hadi

0


Filtered Image:

1

6 3 2 9 1/9 1/9 1/9

0

0

2

11 3 10 0 1/9 1/9 1/9

0

5

10 1/9 61/9 91/9 7

0

0

3

1

0

2

8

0

0

4

4

2

9

10

0

5

0

0

0

0

7

0

0

value = 6x1/9 + 3x1/9 + 2x1/9 + 11x1/9 + 3x1/9 + 10x1/9 + 10x1/9 + 6x1/9 + 9x1/9 = 60/9 = 6.667


3.7

0

Setiawan Hadi

0


Filtered Image:

1

6

3

2

9

0

2

11

3

10

0

0

5

10

6

9

7

3

1

0

2

4

4

2

9


0

0

0

5

7

5

0

0

5

6

5

0

8

0

4

5

6

0

10

0

0

0

3.8

0

0

0

Setiawan Hadi

PROBLEM PADA KONVOLUSI

•

Bagaimana untuk menentukan piksel-piksel yang berada pada batas citra

•

Solusi: 1. Zero padding –

Treat the empty cells in the convolution window as zero

2. Fit-Position –

Start convolving at the first position where the window doesn’t overlap the image

3. Enlarging –

Enlarging the original image before convolving by duplicating the edges

4. Wrapping –

Wrap the image.


3.9

Setiawan Hadi

EFEK-EFEK HASIL KONVOLUSI

• Embossing • Blurring – – – –

low-pass spatial filtering Simulasi out-of-focus Mengaburkan latar belakang Mengurangi Gaussian noise

• Sharpening – High-pass spatial filtering – Crispening, mempertajam – Metode lain:  unsharp masking, high-boost filtering

HighBoost   Original  Lowpass


3.10

Setiawan Hadi

Ilustrasi

original


3x3

9x9

3.11

15x15

Setiawan Hadi

CONVOLUTION MASKS

• Embossing

•

Blurring

1 0 0 0 0 0 0 0 1

•

1 16 1 8 1 16

Sharpening

0 1 0 1 5 1 0 1 0

1 1 1 1 9 1 1 1 1

1 1 8 16 1 1 4 8 1 1 8 16 1 2 1 2 5 2 1 2 1 W=9a-1


3.12

1 9 1  9 1  9 

Setiawan Hadi

1 9 W 9 1  9 

1 9 1  9 1  9 

EDGE DETECTION

• Jenis-jenis edge

• Non-convolution methods – Homogeneity operator  Subtracts each 8 surrounding pixels from the center pixel of

3 x 3 window. The output is the maximum of the absolute value of each difference

– Difference operator  Upperleft-lowerright, middleleft-middleright, lowerleft-

upperright, topmiddle-bottommiddle

• Convolution methods – First order derivative operator – Second order derivative operator – Compass Gradient operator Pengolahan Citra Dijital

3.13

Setiawan Hadi

Ilustrasi Edge Detection (Deteksi Tepi)


3.14

Setiawan Hadi

Laplacian Filters

33 Laplacian


5x5 Laplacian

3.15

7x7 Laplacian

Setiawan Hadi

Mask/Operator/Filter • First Order Operator: Roberts

Prewitt

Sobel

Frei-Chen

Hr 0  0 0 1  1 1 1  2 1

Hc

0 1 1 0  0 0 

 1 0 0     0 1 0  0 0 0 

0 1 0 1 0 1 0 1 0 2 0 1

 1 0 1     2 0  2  1 0 1   

• Second Order Operator – Laplacian


 1 1  0 0  1 1  1 2  0 0  1 2  1  2  0 0  2 1

 0 1 0   1 4 1    0 1 0  3.16

1 0  1  1 0  1  1  0 1 

 1 1 1  1 8 1    1 1 1 Setiawan Hadi

FILTERING

• Median Filtering

– Menghilangkan impulse noise (bedakan dengan Gaussian Noise yang dapat dihilangkan dengan Low-pass filter) – Impulse noise has a number of pixels that have conspicuosly wrong intensities like 0 or 255

• Averaging Filter

– Mengganti nilai piksel fokus dengan rata-rata jumlah piksel dalam window

• Minimum/Maksimum Filter – Mengganti nilai piksel fokus dengan nilai piksel minimum/maksimum piksel sekitar


3.17

Setiawan Hadi

Ilustrasi Median Filter

3x3 median


3.18

7x7 median

Setiawan Hadi

Filter Morfologis • Kasus Khusus Filtering • Dua operasi dasar: – erosi : menipiskan – Dilasi : menebalkan

• Operasi gabungan: – opening : an erosion followed by a dilation – closing: a dilation followed by an erosion

• Menggunakan mask/operator yang disebut structuring element • Jenis Structuring element: Block, Plus, Cross, Ring, Square • Definisi:


3.19

Setiawan Hadi

Proses Filtering Morfologis

Erosi


3.20

Setiawan Hadi

Proses Filtering Morfologis

Dilasi


3.21

Setiawan Hadi

Ilustrasi


3.22

Setiawan Hadi

Ilustrasi Filter Morfologis


3.23

Setiawan Hadi



3.24

Setiawan Hadi



3.25

Setiawan Hadi



3.26

Setiawan Hadi

BLOB Separation


3.27

Setiawan Hadi

Small Hole Removal


3.28

Setiawan Hadi

Morphological Edge Detector


3.29

Setiawan Hadi

Morphological Edge Detector


3.30

Setiawan Hadi

Morphological Noise FIlter


3.31

Setiawan Hadi

“Salt & Pepper” Noise Generator


3.32

Setiawan Hadi

Noise Removal Using Morphological Filter


3.33

Setiawan Hadi

Cointing Coins


3.34

Setiawan Hadi

Demo Program

•MorfMath •ConnComp


3.35

Setiawan Hadi

AREA PROCESS. Area processes use the input pixel as well as the pixels around it to generate a new ouput pixel

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