Halaman 0
Teknik Komputasi
Ujian Akhir Semester (UAS)
Dosen : Dr. Ir. Nazori Az, MT.
Nama : Yoga Prihastomo
NIM : 1011601026
Kelas : XB
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Halaman 1
∑
= − = N i i i x x N 1 2 ) ( 1σ
∑
==
N iX
N
1 11
μ
A. Soal
Diketahui sebuah citra tekstur yang akan diuji kemiripannya dengan metode
jarak Euclidean. Tentukan besar jarak antar citra X yang akan diuji dengan
citra lainnya dan urutkan hasilnya dengan citra yang paling mirip (nilai jarak
yang paling kecil) berdasarkan ciri‐ciri:
a. Intensitas warna
b. Energi
c. Entropi
d. Standard deviasi
e. Rata‐rata
f. Homogeniti
g. Kontras
Catatan:
Ke‐10 citra yang diuji berukuran sama dan diambil dari database online:
brodatz textures
B. Jawaban
1. Terminologi
Sebuah citra mempunyai beberapa ciri yang digunakan untuk mengenali
citra tersebut, antara lain:
Intensitas warna (σ)
Nilai rata‐rata (μ)
Entropi (e)
Energi (E)
Homogeniti (H)
Kontras (C)
Rumusan:
Ciri‐Ciri
Rumusan
Standard deviasi
Intensitas warna
Nilai rata‐rata
Halaman 2
∑
=−
=
n i i ix
P
x
p
e
1)
(
log
)
(
∑ ∑
= = = M x N y j j M xN P x y E 1 1 2 )] , ( [ 1∑∑
+
−
=
i j dj
i
j
i
P
H
1
)
,
(
∑∑
−
=
i j
d
j
i
P
j
i
C
(
)
2
(
,
)
]
..,
...
,
,
,
[
]
,
...
,
,
,
[
3 2 1 3 2 1 n nb
b
b
b
b
dan
a
a
a
a
a
=
=
2 2 3 3 2 2 2 2 1 1 ) ( ) ( ) ...( ) (a b a b a b an bn ab = − + − + − + −Entropi
Energi
Homogeniti
Kontras
Jarak Euclidean, jika
diketahui dua buah
Jika n buah citra, masing‐masing mempunyai ciri‐ciri yang dibentuk oleh
vektor‐vektor adalah sebagai berikut:
Misal sebuah citra x yang akan diuji, citra mana yang paling mirip dengan
citra x, dengan metode Euclidean dapat ditentukan besarnya jarak antar
citra tsb. Citra yang paling mirip adalah citra yang mempunyai nilai jarak
Euclidean paling kecil.
]
[
...
...
...
...
...
]
[
]
[
2 2 2 2 2 2 2 1 1 1 1 1 1 1 n n n n n n ne
p
c
h
C
h
c
p
e
C
h
c
p
e
C
μ
σ
μ
σ
μ
σ
=
=
=
Halaman 3
2. Jawaban
Sumbef gambar adalah: http://www.ux.uis.no/~tranden/brodatz.html
Diakses tanggal: 25 Desember 2011.
Nama Citra
Nama Citra
Nama Citra
D81.gif
D82.gif
D83.gif
D84gif
D85.gif
D86.gif
D87.gif
D88.gif
D89.gif
D90.gif
Halaman 4
Script Matlab:
%UAS Image Analysis %Yoga Prihastomo clear all clc format longG %Image Reading I1 = imread('c:\gambar\D81.gif'); I2 = imread('c:\gambar\D82.gif'); I3 = imread('c:\gambar\D83.gif'); I4 = imread('c:\gambar\D84.gif'); I5 = imread('c:\gambar\D85.gif'); I6 = imread('c:\gambar\D86.gif'); I7 = imread('c:\gambar\D87.gif'); I8 = imread('c:\gambar\D88.gif'); I9 = imread('c:\gambar\D89.gif'); I10 = imread('c:\gambar\D90.gif'); %Analisa Image 1 av_1 = mean2(I1); ent_1 = entropy(I1); std_1 = std2(I1); stats1 = graycoprops(I1); A1 = [stats1(1,1).Contrast]; cont_1 = A1(1,1); B1 = [stats1(1,1).Correlation]; corr_1 = B1(1,1); C1 = [stats1(1,1).Energy]; ener_1 = C1(1,1); D1 = [stats1(1,1).Homogeneity]; homo_1 = D1(1,1); %Analisa Image 2 av_2 = mean2(I2); ent_2 = entropy(I2); std_2 = std2(I2); stats2 = graycoprops(I2); A2 = [stats2(1,1).Contrast]; cont_2 = A2(1,1); B2 = [stats2(1,1).Correlation]; corr_2 = B2(1,1); C2 = [stats2(1,1).Energy]; ener_2 = C2(1,1); D2 = [stats2(1,1).Homogeneity]; homo_2 = D2(1,1); %Analisa Image 3 av_3 = mean2(I3); ent_3 = entropy(I3); std_3 = std2(I3); stats3 = graycoprops(I3); A3 = [stats3(1,1).Contrast]; cont_3 = A3(1,1);
Halaman 5 B3 = [stats3(1,1).Correlation]; corr_3 = B3(1,1); C3 = [stats3(1,1).Energy]; ener_3 = C3(1,1); D3 = [stats3(1,1).Homogeneity]; homo_3 = D3(1,1); %Analisa Image 4 av_4 = mean2(I4); ent_4 = entropy(I4); std_4 = std2(I4); stats4 = graycoprops(I4); A4 = [stats4(1,1).Contrast]; cont_4 = A4(1,1); B4 = [stats4(1,1).Correlation]; corr_4 = B4(1,1); C4 = [stats4(1,1).Energy]; ener_4 = C4(1,1); D4 = [stats4(1,1).Homogeneity]; homo_4 = D4(1,1); %Analisa Image 5 av_5 = mean2(I5); ent_5 = entropy(I5); std_5 = std2(I5); stats5 = graycoprops(I5); A5 = [stats5(1,1).Contrast]; cont_5 = A5(1,1); B5 = [stats5(1,1).Correlation]; corr_5 = B5(1,1); C5 = [stats5(1,1).Energy]; ener_5 = C5(1,1); D5 = [stats5(1,1).Homogeneity]; homo_5 = D5(1,1); %Analisa Image 6 av_6 = mean2(I6); ent_6 = entropy(I6); std_6 = std2(I6); stats6 = graycoprops(I6); A6 = [stats6(1,1).Contrast]; cont_6 = A6(1,1); B6 = [stats6(1,1).Correlation]; corr_6 = B6(1,1); C6 = [stats6(1,1).Energy]; ener_6 = C6(1,1); D6 = [stats6(1,1).Homogeneity]; homo_6 = D6(1,1); %Analisa Image 7 av_7 = mean2(I7); ent_7 = entropy(I7); std_7 = std2(I7); stats7 = graycoprops(I7); A7 = [stats7(1,1).Contrast];
Halaman 6 cont_7 = A7(1,1); B7 = [stats7(1,1).Correlation]; corr_7 = B7(1,1); C7 = [stats7(1,1).Energy]; ener_7 = C7(1,1); D7 = [stats7(1,1).Homogeneity]; homo_7 = D7(1,1); %Analisa Image 8 av_8 = mean2(I8); ent_8 = entropy(I8); std_8 = std2(I8); stats8 = graycoprops(I8); A8 = [stats8(1,1).Contrast]; cont_8 = A8(1,1); B8 = [stats8(1,1).Correlation]; corr_8 = B8(1,1); C8 = [stats8(1,1).Energy]; ener_8 = C8(1,1); D8 = [stats8(1,1).Homogeneity]; homo_8 = D8(1,1); %Analisa Image 9 av_9 = mean2(I9); ent_9 = entropy(I9); std_9 = std2(I9); stats9 = graycoprops(I9); A9 = [stats9(1,1).Contrast]; cont_9 = A9(1,1); B9 = [stats9(1,1).Correlation]; corr_9 = B9(1,1); C9 = [stats9(1,1).Energy]; ener_9 = C9(1,1); D9 = [stats9(1,1).Homogeneity]; homo_9 = D9(1,1); %Analisa Image 10 av_10 = mean2(I10); ent_10 = entropy(I10); std_10 = std2(I10); stats10 = graycoprops(I10); A10 = [stats10(1,1).Contrast]; cont_10 = A10(1,1); B10 = [stats10(1,1).Correlation]; corr_10 = B10(1,1); C10 = [stats10(1,1).Energy]; ener_10 = C10(1,1); D10 = [stats10(1,1).Homogeneity]; homo_10 = D10(1,1);
%Menghitung Jarak Euclidean Antara Masing-masing Image
euc_1 = sqrt((av_1-av_2)^2+(ent_1-ent_2)^2+(std_1- std_2)^2+(cont_1-cont_2)^2+(corr_1-corr_2)^2+(ener_1-ener_2)^2+(homo_1-homo_2)^2);
Halaman 7 euc_2 = sqrt((av_1-av_3)^2+(ent_1-ent_3)^2+(std_1- std_3)^2+(cont_1-cont_3)^2+(corr_1-corr_3)^2+(ener_1-ener_3)^2+(homo_1-homo_3)^2); euc_3 = sqrt((av_1-av_4)^2+(ent_1-ent_4)^2+(std_1- std_4)^2+(cont_1-cont_4)^2+(corr_1-corr_4)^2+(ener_1-ener_4)^2+(homo_1-homo_4)^2); euc_4 = sqrt((av_1-av_5)^2+(ent_1-ent_5)^2+(std_1- std_5)^2+(cont_1-cont_5)^2+(corr_1-corr_5)^2+(ener_1-ener_5)^2+(homo_1-homo_5)^2); euc_5 = sqrt((av_1-av_6)^2+(ent_1-ent_6)^2+(std_1- std_6)^2+(cont_1-cont_6)^2+(corr_1-corr_6)^2+(ener_1-ener_6)^2+(homo_1-homo_6)^2); euc_6 = sqrt((av_1-av_7)^2+(ent_1-ent_7)^2+(std_1- std_7)^2+(cont_1-cont_7)^2+(corr_1-corr_7)^2+(ener_1-ener_7)^2+(homo_1-homo_7)^2); euc_7 = sqrt((av_1-av_8)^2+(ent_1-ent_8)^2+(std_1- std_8)^2+(cont_1-cont_8)^2+(corr_1-corr_8)^2+(ener_1-ener_8)^2+(homo_1-homo_8)^2); euc_8 = sqrt((av_1-av_9)^2+(ent_1-ent_9)^2+(std_1- std_9)^2+(cont_1-cont_9)^2+(corr_1-corr_9)^2+(ener_1-ener_9)^2+(homo_1-homo_9)^2); euc_9 = sqrt((av_1-av_10)^2+(ent_1-ent_10)^2+(std_1- std_10)^2+(cont_1-cont_10)^2+(corr_1-corr_10)^2+(ener_1-ener_10)^2+(homo_1-homo_10)^2); euc_total = [euc_1,euc_2,euc_3,euc_4,euc_5,euc_6,euc_7,euc_8,euc_9]
%Menampilkan Nilai Euclidean Minimum dari Matriks euc_total
Halaman 8
C. Analisa Hasil
Dari kompilasi script Matlab di atas didapatkan hasil sebagai berikut:
Variables
Images
Average
Entropy
Deviation
Standard
Contrast
Correlation
Energy
Homogenity
D81.gif
105.6751
6.4237
58.0112
66602.4970
0.0426
3.1772e‐06
0.0174
D82.gif
146.7404
5.3969
47.8563
69489.1057
‐0.0015
2.7011e‐06
0.0172
D83.gif
121.1981
5.8093
46.5325
69177.6566
‐0.0099
2.8013e‐06
0.0171
D84.gif
110.0462
6.3917
58.8784
68401.4870
0.0080
3.1403e‐06
0.0173
D85.gif
149.9369
5.8610
49.3649
69879.6769
‐0.0106
2.7061e‐06
0.0171
D86.gif
90.4777
6.2262
58.7261
69357.2689
0.0098
3.4699e‐06
0.0167
D87.gif
107.9567
6.0511
78.2380
68716.5655
‐0.0011
3.7237e‐06
0.0172
D88.gif
141.1719
5.4952
83.8849
70097.1224
‐0.0119
3.3035e‐06
0.0139
D89.gif
173.6082
5.4681
62.8249
68115.1505
‐0.0093
2.7612e‐06
0.0139
D90.gif
133.5599
6.2804
68.2945
64824.7912
0.1121
3.0798e‐06
0.0195
Halaman 9
