i
Universitas Kristen MaranathaKOREKSI WARNA PADA FOTO DIGITAL DENGAN
METODA INTERPOLASI BICUBIC
Disusun Oleh:
Albertus Andry Soesilo K
0622021
Jurusan Teknik Elektro, Fakultas Teknik, Universitas Kristen Maranatha,
Jl. Prof.Drg.Suria Sumantri, MPH no.65, Bandung, Indonesia,
email : albert_6399_sk@yahoo.co.id
ABSTRAK
Kamera digital biasanya menggunakan sensor elektronik tunggal (CCD
atau CMOS) yang dilapisi oleh sebuah filter warna sehingga menyebabkan setiap
piksel hanya diambil satu contoh warna, dan warna yang lain diinterpolasi /
ditambahkan menggunakan contoh dari piksel di sampingnya. Proses interpolasi
warna untuk merekontruksi piksel warna yang tidak lengkap dikenal dengan nama
demosaicing / demosaicking.
Tugas akhir ini merealisasikan sebuah sistem untuk memperbaiki warna
gambar (demosaicing) dengan Metode
denoise dan Interpolasi
Bicubic (metode
yang membuat nilai piksel baru dari hasil membandingkan beberapa nilai piksel di
sekitarnya).
Dari hasil pengujian dalam tugas Akhir ini pada lima buah gambar dengan
berbagai tingkat dan model noise menunjukkan bahwa sistem Metode Interpolasi
Bicubic berhasil memperbaiki gambar yang mengalami distorsi warna. Dari hasil
pengamatan memperlihatkan
Demosaicing dengan Metode Interpolasi
Bicubic
dengan
denoise lebih baik dibandingkan dengan
Demosaicing dengan Metode
Interpolasi Bicubic tanpa denoise.
ii
Universitas Kristen MaranathaCOLOR CORRECTION ON THE DIGITAL PHOTO BY BICUBIC
INTERPOLATION METHOD
Composed by:
Albertus Andry Soesilo K
0622021
Electrical Engineering, Maranatha Cristian University,
Jl. Prof.Drg.Suria Sumantri, MPH no.65, Bandung, Indonesia,
email : albert_6399_sk@yahoo.co.id
ABSTRACT
Digital cameras commonly use a single electronic sensor (CCD or
CMOS) which overlaid with a color filter in order to each pixel only taken one
example of color, and other colors interpolated / added using the example of the
pixels on side. This color interpolation process to reconstruct incomplete pixel
color known as demosaicing or demosaicking.
On this final project has been realized a system for improving color
image (demosaicing) with denoising and Bicubic Interpolation Method (The
method makes a new pixel value of the results comparing several values in the
surrounding pixels).
From the result of the final project on five images with various levels and
models of noise shown that the system Bicubic interpolation method is
successfully improves the image which had distorted colors. From the
observation, it shown Demosaicing with Bicubic Interpolation with denoising
Method is better than Bicubic Interpolation without denoising Method.
v
Universitas Kristen MaranathaDAFTAR ISI
ABSTRAK
... i
ABSTRACT
... ii
KATA PENGANTAR
... iii
DAFTAR ISI
... v
DAFTAR LAMPIRAN
... vii
DAFTAR TABEL
... viii
DAFTAR GAMBAR
... ix
BAB I
PENDAHULUAN
... 1
I.1
LATAR BELAKANG ... 1
I.2
PERUMUSAN MASALAH ... 1
I.3
TUJUAN TUGAS AKHIR ... 2
I.4
PEMBATASAN MASALAH ... 2
I.5
METODOLOGI ... 2
I.6
SISTEMATIKA PENULISAN ... 2
BAB II
LANDASAN TEORI
... 4
II.1
PENGOLAHAN CITRA DIGITAL ... 4
II.2
PIKSEL ... 6
II.3
PIKSEL TETANGGA ... 6
II.4
CITRA BERWARNA ... 7
II.5
NOISE PADA CITRA... 9
II.5.1 MEMBANGKITKAN NOISE GAUSSIAN PSF ... 10
II.5.2 MEMBANGKITKAN NOISE Salt & Pepper ... 10
II.6
DENOISE PADA CITRA ... 11
II.6.1 DENOISE MENGGUNAKAN FILTER GAUSSIAN ... 11
II.7
DEMOSAICING ... 12
II.8
INTERPOLASI BICUBIC ... 14
II.9
PENILAIAN CITRA ... 15
vi
Universitas Kristen MaranathaBAB III
PERANCANGAN DAN REALISASI
... 20
III.1
NOISE GAUSSIAN PSF... 22
III.2
NOISE SALT & PEPPER ... 23
III.3
DENOISE ... 26
III.4
DEMOSAICING ... 27
BAB IV
DATA PENGAMATAN DAN ANALISA
... 31
IV.1
DATA PENGAMATAN ... 32
IV.1.1 NOISE GAUSSIAN... 32
IV.1.2 NOISE SALT & PEPPER... 33
IV.2
ANALISA DATA ... 34
BAB V
KESIMPULAN DAN SARAN
... 37
V.1
KESIMPULAN ... 37
V.2
SARAN ... 37
vii
Universitas Kristen MaranathaDAFTAR LAMPIRAN
LAMPIRAN A
LIST PROGRAM VISUAL BASIC ... A-1
LAMPIRAN B
TAMPILAN VISUAL BASIC ... B-1
LAMPIRAN C
HASIL DATA PENGAMATAN ... C-1
LAMPIRAN D
viii
Universitas Kristen MaranathaDAFTAR TABEL
Tabel 2.1
Skala MOS (Mean Opinion Score) ... 15
Tabel 4.1
Data Pengamatan Noise Gaussian ... 32
Tabel 4.2
Data Pengamatan Noise Salt & Pepper... 33
ix
Universitas Kristen MaranathaDAFTAR GAMBAR
Gambar 2.1
Contoh Gambar Pembagian Piksel ... 5
Gambar 2.2
Piksel - Piksel Tetangga ... 7
Gambar 2.3
Visualisasi Ruang Warna RGB ... 8
Gambar 2.4
Visualisasi Ruang Warna YCbCr ... 8
Gambar 2.5
Model Fungsi Gaussian dalam Ruang ... 12
Gambar 2.6
Model Contour dari Filter Gaussian ... 12
Gambar 2.7
Filter Pola Bayer ... 13
Gambar 2.8
Blok Filter Pola Bayer ... 13
Gambar 2.9
Tampilan New Project ... 17
Gambar 2.10 Tampilan Dasar MS Visual Basic 6.0 ... 17
Gambar 3.1
Diagram Blok Sistem Proses Demosaicing yang Direalisasi... 20
Gambar 3.2(a)Diagram Alir Proses Pemberian Noise Gaussian PSF atau Noise
Salt & Pepper pada Gambar ... 21
Gambar 3.2(b) Diagram Alir Proses Denoise dan Proses Demosaicing ... 21
Gambar 3.3
Diagram Alir Noise Gaussian PSF ... 23
Gambar 3.4
Diagram Alir Noise Salt & Pepper ... 25
Gambar 3.5
Diagram Alir Denoise Filter Gaussian ... 26
Gambar 3.6
Diagram Alir Demosaicing dengan Metode Interpolasi Bicubic ... 28
Gambar 4.1(a) BLUESTONE ... 31
Gambar 4.1(b) JELLYFISH ... 31
Gambar 4.1(c) PATTERN TEST ... 31
Gambar 4.1(d) PEGUNUNGAN ... 31
A-0
LAMPIRAN A
A-1
PROGRAM UTAMA
Dim h As Integer, i As Integer, j As Integer Dim r(16) As Integer
Dim g(16) As Integer Dim b(16) As Integer
Private Sub Command1_Click() CommonDialog1.ShowOpen
Picture1.Picture = LoadPicture(CommonDialog1.FileName) Text1.Text = CommonDialog1.FileName
End Sub
'Gaussian Noise
Private Sub Command2_Click() probnoise = Val(HScroll1) / 100 Label5.Caption = Val(HScroll1) Picture1.AutoRedraw = True Picture2.AutoRedraw = True Picture5.AutoRedraw = True ‘Pindai gambar awal
For i = 1 To Picture1.Width Step 1 For j = 1 To Picture1.Height Step 1
warna = Picture1.Point(i, j)
rr = warna And RGB(255, 0, 0)
gg = Int((warna And RGB(0, 255, 0)) / 256)
bb = Int(Int((warna And RGB(0, 0, 255)) / 256) / 256)
' Merubah RGB ke YCrcB
Y = 0.299 * rr + 0.587 * gg + 0.114 * bb
cb = -0.16874 * rr - 0.33126 * gg + 0.5 * bb + 128 cr = 0.5 * rr - 0.41869 * gg - 0.08131 * bb + 128 ‘Noise Gaussian PSF
a = 0 While a = 0
X = 2 * Rnd - 1 yy = Rnd
If yy < Exp(-X ^ 2) Then a = X
End If Wend
‘Pemberian Noise Gaussian PSF Y1 = Y
'Y1 = Abs(Y - A * 127 * probnoise) 'If Y1 > 255 Then Y1 = 255
cb1 = Abs(cb - a * 127 * probnoise) 'If cb1 > 255 Then cb1 = 255 cr1 = Abs(cr - a * 127 * probnoise) 'If cr1 > 255 Then cr1 = 255
'Merubah YCrcB ke RGB
r1 = Abs(Y1 + 1.371 * (cr1 - 128))g1 = Abs(Y1 - 0.698 * (cr1 - 128) - 0.336 * (cb1 - 128)) b1 = Abs(Y1 + 1.732 * (cb1 - 128))
A-2
Picture2.PSet (i, j), RGB(r1, g1, b1) Picture5.PSet (i, j), RGB(r1, g1, b1) Next j
Next i
‘ MENGHITUNG PSNR n = 3
hitung = 1
X = Picture2.ScaleWidth Y = Picture2.ScaleHeight For brs = 1 To Y Step (n + 1) * 1 For klm = 1 To X Step (n + 1) * 1 mseR = 0
mseB = 0 mseG = 0
For m = 0 To n * 1 Step 1 For n1 = 0 To n * 1 Step 1
warna = Picture1.Point(klm + n1, brs + m) rr = warna And RGB(255, 0, 0)
gg = Int((warna And RGB(0, 255, 0)) / 256)
bg = Int(Int((warna And RGB(0, 0, 255)) / 256) / 256)
warna5 = Picture2.Point(klm + n1, brs + m) r1 = warna5 And RGB(255, 0, 0)
g1 = Int((warna5 And RGB(0, 255, 0)) / 256)
b1 = Int(Int((warna5 And RGB(0, 0, 255)) / 256) / 256)
mseR = mseR + (r1 - rr) ^ 2 mseB = mseB + (g1 - gg) ^ 2 mseG = mseG + (b1 - bb) ^ 2
Next n1 Next m
mse = (mseR + mseB + mseG) / (3 * (n * 1) * (n * 1)) If mse = 0 Then mse = 1
' psnr = Abs(20 * (Log(255 / (mse ^ (0.5))) / Log(10))) psnr = psnr + Abs(10 * (Log((255 ^ 2) / mse) / Log(10))) hitung = hitung + 1
Next klm Next brs
psnr = psnr / (hitung - 1)
Label9.Caption = "PSNR =" + Str(psnr) End Sub
Private Sub Command3_Click()
'denoising filter gaussian
Picture3.AutoRedraw = True X = Picture2.ScaleWidth Y = Picture2.ScaleHeight
‘MATRIKS FILTER GAUSSIAN m1 = 0.077
A-3
m6 = 0.077 m7 = 0.077 m8 = 0.077 m9 = 0.077 mulai3= Time
For brs = 2 To Y - 1 Step 1 For klm = 2 To X - 1 Step 1
a1 = Picture2.Point(klm - 1, brs - 1) r1 = a1 And RGB(255, 0, 0)
g1 = (a1 And RGB(0, 255, 0)) \ 256 b1 = (a1 And RGB(0, 0, 255)) \ 256 \ 256
a2 = Picture2.Point(klm, brs - 1) r2 = a2 And RGB(255, 0, 0) g2 = (a2 And RGB(0, 255, 0)) \ 256 b2 = (a2 And RGB(0, 0, 255)) \ 256 \ 256
a3 = Picture2.Point(klm + 1, brs - 1) r3 = a3 And RGB(255, 0, 0)
g3 = (a3 And RGB(0, 255, 0)) \ 256 b3 = (a3 And RGB(0, 0, 255)) \ 256 \ 256
a4 = Picture2.Point(klm - 1, brs) r4 = a4 And RGB(255, 0, 0) g4 = (a4 And RGB(0, 255, 0)) \ 256 b4 = (a4 And RGB(0, 0, 255)) \ 256 \ 256
a5 = Picture2.Point(klm, brs) r5 = a5 And RGB(255, 0, 0) g5 = (a5 And RGB(0, 255, 0)) \ 256 b5 = (a5 And RGB(0, 0, 255)) \ 256 \ 256
a6 = Picture2.Point(klm + 1, brs) r6 = a6 And RGB(255, 0, 0) g6 = (a6 And RGB(0, 255, 0)) \ 256 b6 = (a6 And RGB(0, 0, 255)) \ 256 \ 256
a7 = Picture2.Point(klm - 1, brs + 1) r7 = a7 And RGB(255, 0, 0)
g7 = (a7 And RGB(0, 255, 0)) \ 256 b7 = (a7 And RGB(0, 0, 255)) \ 256 \ 256
a8 = Picture2.Point(klm, brs + 1) r8 = a8 And RGB(255, 0, 0) g8 = (a8 And RGB(0, 255, 0)) \ 256 b8 = (a8 And RGB(0, 0, 255)) \ 256 \ 256
a9 = Picture2.Point(klm + 1, brs + 1) r9 = a9 And RGB(255, 0, 0)
g9 = (a9 And RGB(0, 255, 0)) \ 256 b9 = (a9 And RGB(0, 0, 255)) \ 256 \ 256
A-4
i = Abs(g1 * m9 + g2 * m8 + g3 * m7 + g4 * m6 + g5 * m5 + g6 * m4 + g7 * m3 + g8 * m2 + g9 * m1)
j = Abs(b1 * m9 + b2 * m8 + b3 * m7 + b4 * m6 + b5 * m5 + b6 * m4 + b7 * m3 + b8 * m2 + b9 * m1)
Picture3.PSet (klm, brs), RGB(h, i, j) Picture4.PSet (klm, brs), RGB(h, i, j) Next klm
Next brs selesai3 = Time
selisih3 = selesai3 - mulai3 Form1.Refresh
‘MENGHITUNG PSNR n = 3
hitung = 1
X = Picture3.ScaleWidth Y = Picture3.ScaleHeight For brs = 1 To Y Step (n + 1) * 1 For klm = 1 To X Step (n + 1) * 1 mseR = 0
mseB = 0 mseG = 0
For m = 0 To n * 1 Step 1 For n1 = 0 To n * 1 Step 1
warna = Picture1.Point(klm + n1, brs + m) rr = warna And RGB(255, 0, 0)
gg = Int((warna And RGB(0, 255, 0)) / 256)
bg = Int(Int((warna And RGB(0, 0, 255)) / 256) / 256)
warna5 = Picture3.Point(klm + n1, brs + m) r1 = warna5 And RGB(255, 0, 0)
g1 = Int((warna5 And RGB(0, 255, 0)) / 256)
b1 = Int(Int((warna5 And RGB(0, 0, 255)) / 256) / 256)
mseR = mseR + (r1 - rr) ^ 2 mseB = mseB + (g1 - gg) ^ 2 mseG = mseG + (b1 - bb) ^ 2
Next n1 Next m
mse = (mseR + mseB + mseG) / (3 * (n * 1) * (n * 1)) If mse = 0 Then mse = 1
'psnr = Abs(20 * (Log(255 / (mse ^ (0.5))) / Log(10))) psnr = psnr + Abs(10 * (Log((255 ^ 2) / mse) / Log(10))) hitung = hitung + 1
Next klm Next brs
psnr = psnr / (hitung - 1)
Label6.Caption = "PSNR =" + Str(psnr) End Sub
Private Sub Command4_Click()
'Interpolasi Bicubic dengan denoising
Picture4.AutoRedraw = FalseA-5
mulai = Time
For brs = 2 To Y - 1 Step 1 For klm = 2 To X - 1 Step 1
a1 = Picture3.Point(klm - 1, brs - 1) r1 = a1 And RGB(255, 0, 0)
g1 = (a1 And RGB(0, 255, 0)) \ 256 b1 = (a1 And RGB(0, 0, 255)) \ 256 \ 256
a2 = Picture3.Point(klm, brs - 1) r2 = a2 And RGB(255, 0, 0) g2 = (a2 And RGB(0, 255, 0)) \ 256 b2 = (a2 And RGB(0, 0, 255)) \ 256 \ 256
a3 = Picture3.Point(klm + 1, brs - 1) r3 = a3 And RGB(255, 0, 0)
g3 = (a3 And RGB(0, 255, 0)) \ 256 b3 = (a3 And RGB(0, 0, 255)) \ 256 \ 256
a4 = Picture3.Point(klm + 2, brs - 1) r4 = a4 And RGB(255, 0, 0)
g4 = (a4 And RGB(0, 255, 0)) \ 256 b4 = (a4 And RGB(0, 0, 255)) \ 256 \ 256
a5 = Picture3.Point(klm - 1, brs) r5 = a5 And RGB(255, 0, 0) g5 = (a5 And RGB(0, 255, 0)) \ 256 b5 = (a5 And RGB(0, 0, 255)) \ 256 \ 256
a6 = Picture3.Point(klm, brs) r6 = a6 And RGB(255, 0, 0) g6 = (a6 And RGB(0, 255, 0)) \ 256 b6 = (a6 And RGB(0, 0, 255)) \ 256 \ 256
a7 = Picture3.Point(klm + 1, brs) r7 = a7 And RGB(255, 0, 0) g7 = (a7 And RGB(0, 255, 0)) \ 256 b7 = (a7 And RGB(0, 0, 255)) \ 256 \ 256
a8 = Picture3.Point(klm + 2, brs) r8 = a8 And RGB(255, 0, 0) g8 = (a8 And RGB(0, 255, 0)) \ 256 b8 = (a8 And RGB(0, 0, 255)) \ 256 \ 256
a9 = Picture3.Point(klm - 1, brs + 1) r9 = a9 And RGB(255, 0, 0)
g9 = (a9 And RGB(0, 255, 0)) \ 256 b9 = (a9 And RGB(0, 0, 255)) \ 256 \ 256
A-6
a11 = Picture3.Point(klm + 1, brs + 1) r11 = a11 And RGB(255, 0, 0)
g11 = (a11 And RGB(0, 255, 0)) \ 256 b11 = (a11 And RGB(0, 0, 255)) \ 256 \ 256
a12 = Picture3.Point(klm + 2, brs + 1) r12 = a12 And RGB(255, 0, 0)
g12 = (a12 And RGB(0, 255, 0)) \ 256 b12 = (a12 And RGB(0, 0, 255)) \ 256 \ 256
a13 = Picture3.Point(klm - 1, brs + 2) r13 = a13 And RGB(255, 0, 0) g13 = (a13 And RGB(0, 255, 0)) \ 256 b13 = (a13 And RGB(0, 0, 255)) \ 256 \ 256
a14 = Picture3.Point(klm, brs + 2) r14 = a14 And RGB(255, 0, 0) g14 = (a14 And RGB(0, 255, 0)) \ 256 b14 = (a14 And RGB(0, 0, 255)) \ 256 \ 256
a15 = Picture3.Point(klm + 1, brs + 2) r15 = a15 And RGB(255, 0, 0)
g15 = (a15 And RGB(0, 255, 0)) \ 256 b15 = (a15 And RGB(0, 0, 255)) \ 256 \ 256
a16 = Picture3.Point(klm + 2, brs + 2) r16 = a16 And RGB(255, 0, 0)
g16 = (a16 And RGB(0, 255, 0)) \ 256 b16 = (a16 And RGB(0, 0, 255)) \ 256 \ 256
'Pengisian matrix W(sy) dan W(sx)
sy = 1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
'Perkalian W(sy) dengan matrix 4x4 = matrix h
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13)h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16)
'Perkalian matrix h dengan W(sx) = matrix m
m00 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3)
'Perkalian W(sy) dengan matrix 4x4 = matrix p
p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13)A-7
q00 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3)
'Perkalian W(sy) dengan matrix 4x4 = matrix s
s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13)s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16)
'Perkalian matrix s dengan W(sx) = matrix t
t00 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 0
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m01 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q01 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t01 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
A-8
h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m02 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q02 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t02 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -2 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m03 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q03 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t03 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 0
A-9
f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m10 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q10 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t10 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 0
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 0
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m11 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q11 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t11 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 0
A-10
f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m12 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q12 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t12 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -2 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 0
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m13 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q13 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t13 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 1 / 3
A-11
sx = -1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m20 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q20 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t20 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 0
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m21 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q21 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t21 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -1 / 3
A-12
e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m22 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q22 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t22 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -2 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -1
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m23 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q23 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t23 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
A-13
sy = 1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -2 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m30 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q30 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t30 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 0
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -2 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
A-14
t31 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -2 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m32 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q32 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t32 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -2 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -2 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
A-15
s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t33 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
zr = (q00 + q01 + q02 + q03 + q10 + q11 + q12 + q13 + q20 + q21 + q22 + q23 + q30 + q31 + q32 + q33) / 16
zg = (m00 + m01 + m02 + m03 + m10 + m11 + m12 + m13 + m20 + m21 + m22 + m23 + m30 + m31 + m32 + m33) / 16
zb = (t00 + t01 + t02 + t03 + t10 + t11 + t12 + t13 + t20 + t21 + t22 + t23 + t30 + t31 + t32 + t33) / 16
zr = Int(zr) zg = Int(zg) zb = Int(zb)
If zr < 0 Then zr = r6 If zg < 0 Then zg = g6 If zb < 0 Then zb = b6
'List1.AddItem (Str(klm) + "," + Str(brs) + " = " + Str(zr) + "," + Str(zg) + "," + Str(zb)) Picture4.PSet (klm, brs), RGB(zr, zg, zb)
Next klm Next brs selesai = Time
beda = (selesai - mulai) total = selisih3 + beda
Text2.Text = Format(total, "h:m:s") Form1.Refresh
‘menghitung PSNR
n = 3 hitung = 1
X = Picture4.ScaleWidth Y = Picture4.ScaleHeight For brs = 1 To Y Step (n + 1) * 1 For klm = 1 To X Step (n + 1) * 1 mseR = 0
mseB = 0 mseG = 0
For m = 0 To n * 1 Step 1 For n1 = 0 To n * 1 Step 1
warna = Picture1.Point(klm + n1, brs + m) rr = warna And RGB(255, 0, 0)
gg = Int((warna And RGB(0, 255, 0)) / 256)
bg = Int(Int((warna And RGB(0, 0, 255)) / 256) / 256)
warna5 = Picture4.Point(klm + n1, brs + m) r1 = warna5 And RGB(255, 0, 0)
g1 = Int((warna5 And RGB(0, 255, 0)) / 256)
b1 = Int(Int((warna5 And RGB(0, 0, 255)) / 256) / 256)
mseR = mseR + (r1 - rr) ^ 2 mseB = mseB + (g1 - gg) ^ 2 mseG = mseG + (b1 - bb) ^ 2
A-16
mse = (mseR + mseB + mseG) / (3 * (n * 1) * (n * 1)) If mse = 0 Then mse = 1
'psnr = Abs(20 * (Log(255 / (mse ^ (0.5))) / Log(10))) psnr = psnr + Abs(10 * (Log((255 ^ 2) / mse) / Log(10))) hitung = hitung + 1
Next klm Next brs
psnr = psnr / (hitung - 1)
Label7.Caption = "PSNR =" + Str(psnr) End Sub
‘ SAVE
Private Sub Command5_Click()
CommonDialog2.Filter = "Bitmap (*.BMP)|*.bmp" CommonDialog2.ShowSave
CommonDialog3.Filter = "Bitmap (*.BMP)|*.bmp" CommonDialog3.ShowSave
CommonDialog4.Filter = "Bitmap (*.BMP)|*.bmp" CommonDialog4.ShowSave
CommonDialog5.Filter = "Bitmap (*.BMP)|*.bmp" CommonDialog5.ShowSave
SavePicture Picture2.Image, CommonDialog2.FileName SavePicture Picture3.Image, CommonDialog3.FileName SavePicture Picture4.Image, CommonDialog4.FileName SavePicture Picture5.Image, CommonDialog5.FileName End Sub
'Interpolasi Bicubic tanpa denoising
Private Sub Command6_Click() Picture5.AutoRedraw = False X = Picture2.ScaleWidth Y = Picture2.ScaleHeight List1.Clearmulai = Time
For brs = 2 To Y - 1 Step 1 For klm = 2 To X - 1 Step 1
a1 = Picture2.Point(klm - 1, brs - 1) r1 = a1 And RGB(255, 0, 0)
g1 = (a1 And RGB(0, 255, 0)) \ 256 b1 = (a1 And RGB(0, 0, 255)) \ 256 \ 256
a2 = Picture2.Point(klm, brs - 1) r2 = a2 And RGB(255, 0, 0) g2 = (a2 And RGB(0, 255, 0)) \ 256 b2 = (a2 And RGB(0, 0, 255)) \ 256 \ 256
a3 = Picture2.Point(klm + 1, brs - 1) r3 = a3 And RGB(255, 0, 0)
g3 = (a3 And RGB(0, 255, 0)) \ 256 b3 = (a3 And RGB(0, 0, 255)) \ 256 \ 256
a4 = Picture2.Point(klm + 2, brs - 1) r4 = a4 And RGB(255, 0, 0)
A-17
b4 = (a4 And RGB(0, 0, 255)) \ 256 \ 256
a5 = Picture2.Point(klm - 1, brs) r5 = a5 And RGB(255, 0, 0) g5 = (a5 And RGB(0, 255, 0)) \ 256 b5 = (a5 And RGB(0, 0, 255)) \ 256 \ 256
a6 = Picture2.Point(klm, brs) r6 = a6 And RGB(255, 0, 0) g6 = (a6 And RGB(0, 255, 0)) \ 256 b6 = (a6 And RGB(0, 0, 255)) \ 256 \ 256
a7 = Picture2.Point(klm + 1, brs) r7 = a7 And RGB(255, 0, 0) g7 = (a7 And RGB(0, 255, 0)) \ 256 b7 = (a7 And RGB(0, 0, 255)) \ 256 \ 256
a8 = Picture2.Point(klm + 2, brs) r8 = a8 And RGB(255, 0, 0) g8 = (a8 And RGB(0, 255, 0)) \ 256 b8 = (a8 And RGB(0, 0, 255)) \ 256 \ 256
a9 = Picture2.Point(klm - 1, brs + 1) r9 = a9 And RGB(255, 0, 0)
g9 = (a9 And RGB(0, 255, 0)) \ 256 b9 = (a9 And RGB(0, 0, 255)) \ 256 \ 256
a10 = Picture2.Point(klm, brs + 1) r10 = a10 And RGB(255, 0, 0) g10 = (a10 And RGB(0, 255, 0)) \ 256 b10 = (a10 And RGB(0, 0, 255)) \ 256 \ 256
a11 = Picture2.Point(klm + 1, brs + 1) r11 = a11 And RGB(255, 0, 0)
g11 = (a11 And RGB(0, 255, 0)) \ 256 b11 = (a11 And RGB(0, 0, 255)) \ 256 \ 256
a12 = Picture2.Point(klm + 2, brs + 1) r12 = a12 And RGB(255, 0, 0)
g12 = (a12 And RGB(0, 255, 0)) \ 256 b12 = (a12 And RGB(0, 0, 255)) \ 256 \ 256
a13 = Picture2.Point(klm - 1, brs + 2) r13 = a13 And RGB(255, 0, 0) g13 = (a13 And RGB(0, 255, 0)) \ 256 b13 = (a13 And RGB(0, 0, 255)) \ 256 \ 256
a14 = Picture2.Point(klm, brs + 2) r14 = a14 And RGB(255, 0, 0) g14 = (a14 And RGB(0, 255, 0)) \ 256 b14 = (a14 And RGB(0, 0, 255)) \ 256 \ 256
a15 = Picture2.Point(klm + 1, brs + 2) r15 = a15 And RGB(255, 0, 0)
A-18
b15 = (a15 And RGB(0, 0, 255)) \ 256 \ 256
a16 = Picture2.Point(klm + 2, brs + 2) r16 = a16 And RGB(255, 0, 0)
g16 = (a16 And RGB(0, 255, 0)) \ 256 b16 = (a16 And RGB(0, 0, 255)) \ 256 \ 256
‘Pengisian matrix W(sy) dan W(sx)
sy = 1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
'Perkalian W(sy) dengan matrix 4x4 = matrix h
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13)h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16)
'Perkalian matrix h dengan W(sx) = matrix m
m00 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3)
'Perkalian W(sy) dengan matrix 4x4 = matrix p
p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13)p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16)
'Perkalian matrix p dengan W(sx) = matrix q
q00 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3)
'Perkalian W(sy) dengan matrix 4x4 = matrix s
s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16)'Perkalian matrix s dengan W(sx) = matrix t
t00 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 0
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
A-19
h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m01 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q01 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t01 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3) sy = -1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m02 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q02 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t02 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3) sy = -2 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
A-20
m03 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q03 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t03 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3) sy = 1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 0
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m10 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q10 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t10 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3) sy = 0
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 0
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
A-21
p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q11 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t11 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3) sy = -1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 0
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m12 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q12 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t12 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -2 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = 0
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
A-22
q13 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t13 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m20 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q20 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t20 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 0
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
A-23
p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q21 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t21 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -1 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m22 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q22 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t22 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -2 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -1
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
A-24
h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m23 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q23 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t23 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -2 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m30 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q30 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t30 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = 0
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -2 / 3
A-25
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m31 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q31 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t31 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -1 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -2 / 3
f0 = ((-(sx ^ 3)) + (2 * (sx ^ 2)) - sx) / 2 f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m32 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q32 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t32 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
sy = -2 / 3
e0 = ((-(sy ^ 3)) + (2 * (sy ^ 2)) - sy) / 2 e1 = ((3 * (sy ^ 3)) - (5 * (sy ^ 2)) + 2) / 2 e2 = ((-3 * (sy ^ 3)) + (4 * (sy ^ 2)) + sy) / 2 e3 = ((sy ^ 3) - (sy ^ 2)) / 2
sx = -2 / 3
A-26
f1 = ((3 * (sx ^ 3)) - (5 * (sx ^ 2)) + 2) / 2 f2 = ((-3 * (sx ^ 3)) + (4 * (sx ^ 2)) + sx) / 2 f3 = ((sx ^ 3) - (sx ^ 2)) / 2
h0 = (e0 * g1 + e1 * g5 + e2 * g9 + e3 * g13) h1 = (e0 * g2 + e1 * g6 + e2 * g10 + e3 * g14) h2 = (e0 * g3 + e1 * g7 + e2 * g11 + e3 * g15) h3 = (e0 * g4 + e1 * g8 + e2 * g12 + e3 * g16) m33 = (h0 * f0 + h1 * f1 + h2 * f2 + h3 * f3) p0 = (e0 * r1 + e1 * r5 + e2 * r9 + e3 * r13) p1 = (e0 * r2 + e1 * r6 + e2 * r10 + e3 * r14) p2 = (e0 * r3 + e1 * r7 + e2 * r11 + e3 * r15) p3 = (e0 * r4 + e1 * r8 + e2 * r12 + e3 * r16) q33 = (p0 * f0 + p1 * f1 + p2 * f2 + p3 * f3) s0 = (e0 * b1 + e1 * b5 + e2 * b9 + e3 * b13) s1 = (e0 * b2 + e1 * b6 + e2 * b10 + e3 * b14) s2 = (e0 * b3 + e1 * b7 + e2 * b11 + e3 * b15) s3 = (e0 * b4 + e1 * b8 + e2 * b12 + e3 * b16) t33 = (s0 * f0 + s1 * f1 + s2 * f2 + s3 * f3)
zr = (q00 + q01 + q02 + q03 + q10 + q11 + q12 + q13 + q20 + q21 + q22 + q23 + q30 + q31 + q32 + q33) / 16
zg = (m00 + m01 + m02 + m03 + m10 + m11 + m12 + m13 + m20 + m21 + m22 + m23 + m30 + m31 + m32 + m33) / 16
zb = (t00 + t01 + t02 + t03 + t10 + t11 + t12 + t13 + t20 + t21 + t22 + t23 + t30 + t31 + t32 + t33) / 16
zr = Int(zr) zg = Int(zg) zb = Int(zb)
If zr < 0 Then zr = r6 If zg < 0 Then zg = g6 If zb < 0 Then zb = b6
' List1.AddItem (Str(klm) + "," + Str(brs) + " = " + Str(zr) + "," + Str(zg) + "," + Str(zb)) Picture5.PSet (klm, brs), RGB(zr, zg, zb)
Next klm Next brs selesai = Time beda = selesai - mulai
Text3.Text = Format(beda, "h:m:s") Form1.Refresh
‘Menghitung PSNR
n = 3 hitung = 1
X = Picture5.ScaleWidth Y = Picture5.ScaleHeight For brs = 1 To Y Step (n + 1) * 1 For klm = 1 To X Step (n + 1) * 1 mseR = 0
mseB = 0 mseG = 0
A-27
For n1 = 0 To n * 1 Step 1
warna = Picture1.Point(klm + n1, brs + m) rr = warna And RGB(255, 0, 0)
gg = Int((warna And RGB(0, 255, 0)) / 256)
bg = Int(Int((warna And RGB(0, 0, 255)) / 256) / 256)
warna5 = Picture5.Point(klm + n1, brs + m) r1 = warna5 And RGB(255, 0, 0)
g1 = Int((warna5 And RGB(0, 255, 0)) / 256)
b1 = Int(Int((warna5 And RGB(0, 0, 255)) / 256) / 256)
mseR = mseR + (r1 - rr) ^ 2 mseB = mseB + (g1 - gg) ^ 2 mseG = mseG + (b1 - bb) ^ 2
Next n1 Next m
mse = (mseR + mseB + mseG) / (3 * (n * 1) * (n * 1)) If mse = 0 Then mse = 1
'psnr = Abs(20 * (Log(255 / (mse ^ (0.5))) / Log(10))) psnr = psnr + Abs(10 * (Log((255 ^ 2) / mse) / Log(10))) hitung = hitung + 1
Next klm Next brs
psnr = psnr / (hitung - 1)
Label8.Caption = "PSNR =" + Str(psnr) 'Picture5.Refresh
End Sub
'Noise Salt and Pepper
Private Sub Command7_Click() probnoise = Val(HScroll1) / 100For i = 1 To Picture1.ScaleWidth Step 1 For j = 1 To Picture1.ScaleHeight Step 1 warna = Picture1.Point(i, j)
rr = warna And RGB(255, 0, 0)
gg = Int((warna And RGB(0, 255, 0)) / 256)
bb = Int(Int((warna And RGB(0, 0, 255)) / 256) / 256)
'pembangkitan noise dengan metode Salt dan Papper
sw = RndIf sw < probnoise Then rr = 255
gg = 255 bb = 255 End If
Picture2.PSet (i, j), RGB(rr, gg, bb) Picture5.PSet (i, j), RGB(rr, gg, bb) Next j
Next i
‘menghitung PSNR n = 3
hitung = 1
A-28
For brs = 1 To Y Step (n + 1) * 1 For klm = 1 To X Step (n + 1) * 1 mseR = 0
mseB = 0 mseG = 0
For m = 0 To n * 1 Step 1 For n1 = 0 To n * 1 Step 1
warna = Picture1.Point(klm + n1, brs + m) rr = warna And RGB(255, 0, 0)
gg = Int((warna And RGB(0, 255, 0)) / 256)
bg = Int(Int((warna And RGB(0, 0, 255)) / 256) / 256)
warna5 = Picture2.Point(klm + n1, brs + m) r1 = warna5 And RGB(255, 0, 0)
g1 = Int((warna5 And RGB(0, 255, 0)) / 256)
b1 = Int(Int((warna5 And RGB(0, 0, 255)) / 256) / 256)
mseR = mseR + (r1 - rr) ^ 2 mseB = mseB + (g1 - gg) ^ 2 mseG = mseG + (b1 - bb) ^ 2
Next n1 Next m
mse = (mseR + mseB + mseG) / (3 * (n * 1) * (n * 1)) If mse = 0 Then mse = 1
'psnr = Abs(20 * (Log(255 / (mse ^ (0.5))) / Log(10))) psnr = psnr + Abs(10 * (Log((255 ^ 2) / mse) / Log(10))) hitung = hitung + 1
Next klm Next brs
psnr = psnr / (hitung - 1)
Label9.Caption = "PSNR =" + Str(psnr) End Sub
‘Menampilkan Persentase noise Private Sub Timer1_Timer()
