Tugas 1b. Pemfilteran Citra sederhana

Diberikan citra sederhana seperti dibawah ini.12 2 7

10 4

6 413

14

10

1 7 8 410

4 814

10 1

Lakukan pemfilteran dengan teknik:

1. Median, mask 3×32. Min, mask 3×33. Max, mask 3×34. Mid-point, mask 3×35. Contraharmonic, order (Q) = 26. Laplacian dengan filter berikut: 

7. Sobel8. Geometrik Mean Filter, m=3, n=3

JAWABAN:

1. Median, mask 3x3

Hasil perhitungan dengan Matlab:

Matriks Awal

Setelah Filter

2. Min, mask 3x3

Matriks Awal

Setelah Filter

Hasil perhitungan dengan Matlab:

Matriks Awal

Setelah filter:

3. Max, mask 3x3

Matriks Awal:

Setelah Filter:

Hasil perhitungan dengan Matlab:

Matriks Awal

Setelah Filter

4. Mid Point, mask 3x3

Matriks Awal:

We count:

a=12(min+max)

a=12

(0+12 )a=6

a=12(min+max)

a=12

(0+13 )a=6,5

a=7

a=12(min+max)

a=12

(0+14 )a=7

a=12(min+max)

a=12

(0+14 )a=7

a=12(min+max)

a=12

(0+14 )a=7

a=12(min+max)

a=12

(0+12 )a=6a=12(min+max)

a=12

(1+13 )a=7a=12(min+max)

a=12

(2+14 )a=8

a=12(min+max)

a=12

(4+14 )a=9

a=12(min+max)

a=12

(0+14 )a=7a=12(min+max)

a=12

(0+8 )a=4a=12(min+max)

a=12

(1+14 )a=7,5a=8

a=12(min+max)

a=12

(4+14 )a=9

a=12(min+max)

a=12

(1+14 )a=7,5

a=8

a=12(min+max)

a=12

(0+14 )a=7

a=12(min+max)

a=12

(0+8 )a=4

a=12(min+max)

a=12

(1+14 )a=7,5

a=8

a=12(min+max)

a=12

(0+14 )a=7

a=12(min+max)

a=12

(0+14 )a=7a=12(min+max)

a=12

(0+15 )a=7.5a=8

Hasil setelah filter:

5. Contraharmonic, order (Q) = 26. Laplacian dengan filter berikut:

Matriks Awal:

0 0 0 1 1 1 0 0 0 -840 12 2 x 1 -8 1 0 -96 20 6 4 1 1 1 0 6 4

0 0 0 1 1 1 0 0 0 2612 2 7 x 1 -8 1 12 -16 76 4 13 1 1 1 6 4 13

0 0 0 1 1 1 0 0 0 -132 7 10 x 1 -8 1 2 -56 104 13 14 1 1 1 4 13 14

0 0 0 1 1 1 0 0 0 -327 10 4 x 1 -8 1 7 -80 413 14 10 1 1 1 13 14 10

0 0 0 1 1 1 0 0 0 210 4 0 x 1 -8 1 10 -32 014 10 0 1 1 1 14 10 0

0 12 2 1 1 1 0 12 2 -220 6 4 x 1 -8 1 0 -48 40 1 7 1 1 1 0 1 7

12 2 7 1 1 1 12 2 7 246 4 13 x 1 -8 1 6 -32 131 7 8 1 1 1 1 7 8

2 7 10 1 1 1 2 7 10 -484 13 14 x 1 -8 1 4 -104 147 8 4 1 1 1 7 8 4

7 10 4 1 1 1 7 10 4 -1413 14 10 x 1 -8 1 13 -80 108 4 10 1 1 1 8 4 10

10 4 0 1 1 1 10 4 0 -3814 10 0 x 1 -8 1 14 -80 04 10 0 1 1 1 4 10 0

0 6 4 1 1 1 0 6 4 210 1 7 x 1 -8 1 0 -8 70 4 8 1 1 1 0 4 8

6 4 13 1 1 1 6 4 13 21 7 8 x 1 -8 1 1 -56 84 8 14 1 1 1 4 8 14

4 13 14 1 1 1 4 13 14 107 8 4 x 1 -8 1 7 -64 48 14 10 1 1 1 8 14 10

13 14 10 1 1 1 13 14 10 488 4 10 x 1 -8 1 8 -32 1014 10 1 1 1 1 14 10 1

14 10 0 1 1 1 14 10 0 -414 10 0 x 1 -8 1 4 -80 010 1 0 1 1 1 10 1 0

0 1 7 1 1 1 0 1 7 -160 4 8 x 1 -8 1 0 -32 80 0 0 1 1 1 0 0 0

13 12 12 1 1 1 13 1212 -30

6 11 14 x 1 -8 1 6 -8814

0 0 0 1 1 1 0 0 0

1 7 8 1 1 1 1 7 8 -75

4 8 14 x 1 -8 1 4 -6414

0 0 0 1 1 1 0 0 0

7 8 10 1 1 1 7 810 -43

14 10 1 x 1 -8 1 14 -80 10 0 0 1 1 1 0 0 0

4 10 0 1 1 1 4 10 0 -1610 1 0 x 1 -8 1 10 -8 00 0 0 1 1 1 0 0 0

Setelah Filter:

Hasil perhitungan dengan Matlab:

Matriks Awal:

Setelah Filter:

7. Sobel

Matriks Awal

We count:

0 0 0 -1 -2 -1 0 0 00 12 2 x 0 0 0 0 0 0 240 6 4 1 2 1 0 6 4

gx24

0 0 0 -1 0 1 0 0 00 12 2 x -2 0 2 0 0 4 160 6 4 -1 0 1 0 0 4

gy

g=gx+gyg=18+30g=24

0 0 0 -1 -2 -1 0 0 012 2 7 x 0 0 0 0 0 0 216 4 13 1 2 1 6 12 3

gx24

0 0 0 -1 0 1 0 0 012 2 7 x -2 0 2 -24 0 12 -156 4 13 -1 0 1 -6 0 3

gy

g=gx+gyg=21+(−15)g=24

0 0 0 -1 -2 -1 0 0 02 7 10 x 0 0 0 0 0 0 224 13 14 1 2 1 6 6 10

gx70

0 0 0 -1 0 1 0 0 02 7 10 x -2 0 2 -24 0 10 -104 13 14 -1 0 1 -6 0 10

gy

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

g=gx+gyg=22+(−10)g=70

0 0 0 -1 -2 -1 0 0 07 10 4 0 0 0 0 0 0 2613 14 10 1 2 1 3 20 3

gx42

0 0 0 -1 0 1 0 0 07 10 4 -2 0 2 -12 0 24 1213 14 10 -1 0 1 -3 0 3

gy

g=gx+gyg=26+12g=42

0 0 0 -1 -2 -1 0 0 010 4 0 0 0 0 0 0 0 1614 10 0 1 2 1 10 6 0

gx0

0 0 0 -1 0 1 0 0 010 4 0 -2 0 2 -10 0 0 -2014 10 0 -1 0 1 -10 0 0

gy

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

g=gx+gyg=16+(−20)g=0

0 12 2 -1 -2 -1 0 -24 -120 6 4 x 0 0 0 0 0 0 20 1 7 1 2 1 0 26 12

gx0

0 12 2 -1 0 1 0 0 120 6 4 x -2 0 2 0 0 12 360 1 7 -1 0 1 0 0 12

gy

g=gx+gyg=2+36g=0

12 2 7 -1 -2 -1 -12 -24 -66 4 13 x 0 0 0 0 0 0 71 7 8 1 2 1 13 24 12

gx 16

12 2 7 -1 0 1 -12 0 66 4 13 x -2 0 2 -12 0 6 -31 7 8 -1 0 1 -13 0 12

gy

g=gx+gyg=7+(−13)g=16

2 7 10 -1 -2 -1 -12 -12 -5

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

4 13 14 x 0 0 0 0 0 0 147 8 4 1 2 1 12 24 7

gx 26

2 7 10 -1 0 1 -12 0 54 13 14 x -2 0 2 -12 0 20 -47 8 4 -1 0 1 -12 0 7

gy

g=gx+gyg=14+(−4)g=26

7 10 4 -1 -2 -1 -6 -10 -1213 14 10 x 0 0 0 0 0 0 118 4 10 1 2 1 12 14 13

gx -12

7 10 4 -1 0 1 -6 0 1213 14 10 x -2 0 2 -6 0 6 78 4 10 -1 0 1 -12 0 13

gy

g=gx+gyg=11+7g=−12

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

10 4 0 -1 -2 -1 -5 -24 014 10 0 x 0 0 0 0 0 0 44 10 0 1 2 1 7 26 0

gx-36

10 4 0 -1 0 1 -5 0 014 10 0 x -2 0 2 -20 0 0 -324 10 0 -1 0 1 -7 0 0

gy

g=gx+gyg=4+(−32)g=−36

0 6 4 -1 -2 -1 0 -12 -60 1 7 x 0 0 0 0 0 0 50 4 8 1 2 1 0 12 11

gx 26

0 6 4 -1 0 1 0 0 60 1 7 x -2 0 2 0 0 24 410 4 8 -1 0 1 0 0 11

gy

g=gx+gyg=5+41g=26

6 4 13 -1 -2 -1 -6 -12 -31 7 8 x 0 0 0 0 0 0 21

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

4 8 14 1 2 1 6 22 14gx 38

6 4 13 -1 0 1 -6 0 31 7 8 x -2 0 2 -26 0 24 34 8 14 -1 0 1 -6 0 14

gy

g=gx+gyg=21+3g=38

4 13 14 -1 -2 -1 -6 -6 -107 8 4 x 0 0 0 0 0 0 308 14 10 1 2 1 11 28 13

gx8

4 13 14 x -1 0 1 -6 0 107 8 4 -2 0 2 -24 0 14 -48 14 10 -1 0 1 -11 0 13

gy

g=gx+gyg=30+(−4)g=8

13 14 10 -1 -2 -1 -3 -20 -38 4 10 x 0 0 0 0 0 0 2914 10 1 1 2 1 14 26 15

gx -28

13 14 10 -1 0 1 -3 0 38 4 10 x -2 0 2 -24 0 26 314 10 1 -1 0 1 -14 0 15

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

gy

g=gx+gyg=29+3g=−28

14 10 0 -1 -2 -1 -1 -6 0

4 10 0 x 0 0 0 0 0 0 27

10 1 0 1 2 1 13 30 0

gx -54

14 10 0 -1 0 1 -10 0 04 10 0 x -2 0 2 -14 0 0 -3710 1 0 -1 0 1 -13 0 0

gy

g=gx+gyg=27+(−37)g=−54

0 1 7 -1 -2 -1 0 -26 -120 4 8 x 0 0 0 0 0 0 -380 0 0 1 2 1 0 0 0

gx 14

0 1 7 -1 0 1 0 0 120 4 8 x -2 0 2 0 0 22 34

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

0 0 0 -1 0 1 0 0 0gy

g=gx+gyg=−38+34g=14

13 12 12 -1 -2 -1 -13 -24 -126 11 14 x 0 0 0 0 0 0 -490 0 0 1 2 1 0 0 0

gx 4

13 12 12 -1 0 1 -13 0 126 11 14 x -2 0 2 -12 0 28 150 0 0 -1 0 1 0 0 0

gy

g=gx+gyg=−49+15g=4

1 7 8 -1 -2 -1 -12 -24 -74 8 14 x 0 0 0 0 0 0 -430 0 0 1 2 1 0 0 0

gx-26

1 7 8 x -1 0 1 -12 0 74 8 14 -2 0 2 -22 0 26 -10 0 0 -1 0 1 0 0 0

gy

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

g=gx+gyg=−43+(−1)g=−26

7 8 10 -1 -2 -1 -13 -24 -1214 10 1 x 0 0 0 0 0 0 -490 0 0 1 2 1 0 0 0

gx -50

7 8 10 -1 0 1 -13 0 1214 10 1 x -2 0 2 -12 0 28 150 0 0 -1 0 1 0 0 0

gy

g=gx+gyg=−49+15g=−50

4 10 0 -1 -2 -1 -12 -24 -710 1 0 x 0 0 0 0 0 0 -430 0 0 1 2 1 0 0 0

gx-48

4 10 0 x -1 0 1 -12 0 710 1 0 -2 0 2 -22 0 26 -10 0 0 -1 0 1 0 0 0

gy

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

gx=d fdx

=( z7+2 z8+z9 )− ( z1+2 z2+ z3 )

gx=(0+2×6+4 )−(0+2×0+0 )

gx=(0+12+4 )− (0+0+0 )gx=16−0gx=16

gy=d fd y

=( z3+2 z6+ z9)−( z1+2 z4+ z7 )

gy= (0+2×12+6 )−(0+2×0+0 )

gy= (0+24+6 )−(0+0+0 )gy 30−0gy=30

g=gx+gyg=−43+(−1)g=−48

Hasil Filter:

24 24 70 42 0

0 16 26 -12 -36

26 38 8 -28 -54

14 4 -26 -50 -48

Hasil perhitungan dengan Matlab:

8. Geometric Filter, m=3, n=3

Matriks Awal:

0 0 0 0 12 2 0 6 4 0 1 70 12 2 0 0 6 4 0 0 1 7 0 0 4 8 00 6 4 0 1 7 0 4 8 0 0 0

0 0 0 12 2 7 6 4 13 1 7 812 2 7 0 6 4 13 8.22 1 7 8 8.28 4 8 14 06 4 13 1 7 8 4 8 14 0 0 0

0 0 0 2 7 10 4 13 14 7 8 42 7 10 0 4 13 14 7.37 7 8 4 8.92 8 14 10 04 13 14 7 8 4 8 14 10 0 0 0

0 0 0 7 10 4 13 14 10 7 8 107 10 4 0 13 14 10 6.89 8 4 10 8.62 14 10 1 013 14 10 8 4 10 14 10 1 0 0 0

0 0 0 10 4 0 14 10 0 4 10 010 4 0 0 14 10 0 0 4 10 0 0 10 1 0 014 10 0 4 10 0 10 1 0 0 0 0

We count:

0 0 00 12 2 00 6 4

a=(0×0×0×0×12×2×0×6×4 )1

3×3a=(0 )19a=0

0 0 012 2 7 06 4 13

a=(0×0×0×12×2×7×6×4×13 )1

3×3a=(0 )19a=0

0 0 02 7 10 04 13 14

a=(0×0×0×2×7×10×4×13×14 )1

3×3a=(0 )19a=0

0 0 07 10 4 013 14 10

a=(0×0×0×7×10×4×13×14×10 )1

3×3a=(0 )19a=0

0 0 010 4 0 014 10 0

a=(0×0×0×10×4×0×14×10×0 )1

3× 3a=(0 )19a=0

0 12 20 6 4 00 1 7

a=(0×12×2×0×6×4×0×1×7 )1

3× 3a=(0 )19a=0

12 2 76 4 13 8.221 7 8

a=(12×2×7×6×4×13×1×7×8 )1

3×3a=(4402944 )19a=8.22

2 7 104 13 14 7.377 8 4

a=(2×7×10×4×13×14×7×8×4 )1

3×3a=(22830080 )19a=7.37

7 10 413 14 10 6.898 4 10

a=(7×10×4×13×14×10×8×4×10 )1

3× 3a=(35380800 )19a=6.89

10 4 014 10 0 04 10 0

a=(10×4×0×14×10×0×4×10×0 )1

3×3a=(35380800 )19a=6.89

0 6 40 1 7 00 4 8

a=(0×6×4×0×1×7×0×4×8 )1

3×3a=(0 )19a=0

6 4 131 7 8 8.284 8 14

a=(6×4×13×1×7×8×4×8×14 )1

3×3a=(186810624 )19a=8.28

4 13 147 8 4 8.928 14 10

a=(4×13×14×7×8×4×8×14×10 )1

3×3a=(363242880 )19a=8.92

13 14 108 4 10 8.6214 10 1

a=(3×1 4×10×8×4×10×14×10×1 )1

3× 3a=(268304400 )19a=8.62

14 10 04 10 0 010 1 0

a=(14×10×0×4×10×0×10×1×0 )1

3×3a=(0 )19a=0

0 1 70 4 8 00 0 0

a=(0×1×7×0×4×8×0×0×0 )1

3×3a=(0 )19a=0

13 12 126 11 14 00 0 0

a=(13×12×12×6×11×14×0×0×0 )1

3×3a=(0 )19a=0

1 7 84 8 14 00 0 0

a=(1×7×8×4×8×14×0×0×0 )1

3× 3a=(0 )19a=0

7 8 1014 10 1 00 0 0

a=(7×8×10×14×10×1×0×0×0 )1

3× 3a=(0 )19a=0

4 10 010 1 0 00 0 0

a=(4×10×0×10×1×0×0×0×0 )1

3×3a=(0 )19a=0

Setelah Filter:

0 0 0 0 00 8 7 7 00 8 9 9 00 0 0 0 0