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13
13.1
• 1
• 400nm 700nm
• → → → → ( (2))
•
– 650
– 1.2
•
•(R) (G) (B)
1:2:
13.2 (color specification)
CIE()
13.2.1 CIE RGB
•1900 CIE R(Red) B(Blue)G(Green) RBG RGB
R,G,B 600.0nm 546.1nm
1
435.8nm F RGB3
3F RGB
FR,G,B R, G, B
F
550nm
F R FR
•λ F R, G, B
4 r(λ), g(λ), b(λ) r(λ)RGB F R
3:
4: RGB
•RGB
FF R, G, B
R =∫
P (λ)r(λ)dλ
G =∫
P (λ)g(λ)dλ
2
5: CIE
B =∫
P (λ)b(λ)dλ
P (λ) F CIE RGB
13.2.2 XYZ
• XYZCIE RGB RGB
RGBRGB
XYZ1931 CIE RGB
XYZ
XYZ Y
– X
– Y
– Z
• XYZXYZ x(λ), y(λ), z(λ) 5 RGB
XYZy(λ) ( )
3
• RGBXY Z XYZ x(λ), y(λ), z(λ)
RGB RGB r(λ), g(λ), b(λ)
(XYZ
)=
(2.7689 1.7517 1.1302
1 4.5907 0.06010 0.0565 5.5943
)(RGB
)
(x(λ)y(λ)z(λ)
)=
(2.7689 1.7517 1.1302
1 4.5907 0.06010 0.0565 5.5943
)(r(λ)g(λ)b(λ)
)
13.2.3 Yxy
• YxyXYZ Y (x, y)
XYZ XY Z S = X + Y + Z
x = X/S y = Y/S XY Z Y xy
Y xy XY Z S = Y/y S x + y + z = 1z = 1 − x − y X = Sx, Z = Sz X, Z
•6 (x, y) CIE
CIE
CIE RGB 600.0nm 546.1nm 435.8nm 3
6: CIE
4
13.3
13.3.1 RGB
• ( 7 )CRT RGB
RGBRGB
• RGBRGB RGB CIERGB RGBRGB RGB
7: (RGB ) (CMY )
M=R+BRGB
8: M( ) G
13.3.2 CMY
• ( 7 )C( ), M( ), Y( ) CMY
C R M G Y B 8M R+G+B GRB M
CMY R+G+B CMYRGB RGB
RGB
• CMY(CMYK)CMY CMY
K( )CMY(CMYK)
CMY(CMYK) 9 CMYK
CMY RGB
5
9: CMYK
10:
11:
•CRT
10
– CMYK ( )
– RGB ( )
13.3.3 YCC
NTSC
• Y
11 1
RGB Y
Y = 0.299R + 0.587G + 0.114B
6
RGB (R 610nm G: 560nm B: 480nm1
1 R = G = B
Y = 0.298R + 0.587R + 0.114R = R(= G = B)
• CR, CB
Y, R, G
CR = R − Y = 0.701R − 0.587G − 0.114B
CB = B − Y = −0.299R − 0.587G + 0.886B
CR = CB = 0
(Y, CR, CB) YCC
13.4
13.4.1
•A/D
1.
2.
• ( )( 12)(pixel)
2
( )
• ( )( )
( )
•8
0( 255 256
7
12:
– 2 ( 13)1 2
– ( 13)256 8 13
•
141
–
–
( 15)
1
8
2 4 ( 8
16 64 256
13:
7
6
5
4
3
2
1
0
14:
15:
9
20ppi
50ppi 100ppi
16:
13.4.2
1( )
• ppi(pixel per inch)
× 200×320 4inch×8inch 200/4 =50ppi 320/8 = 40ppi
• 16
13.4.3
M N M = 2N
13.5
13.5.1
• 17RGB R,G,B
R,G,B
• RGBRGB
RGB 256 (8 )224 1677 1
24
10
(R,G,B)
(0,0,0)(255,255,255)
(255,0,0)
18
R
G
B
17:
RGB 2 RGB 4 RGB 256
18: RGB
•24 RGB
11
8 16,777,216 256 (8 )
RGB
0 255, 255, 2551 235, 255, 2062 220, 245, 156...
......
...255 0, 0, 0
13.6
JPEG GIFJPEG
19 JPEGJPEG
1.
2.
3.
4. DCT(Discrete Cosine Transform, )
5. DCT
13.6.1
• YJPEG
19 RGB YCCY CR, CB 20
1Y, CR, CB
Y CR
CB
•JPEG 21 CR, CB XY
1/4
13.6.2
YCC22 8 × 8
12
19: JPEG
Y
CR ( CB (
20: JPEG
� ��
�
� � � � � � � � �
21: JPEG
13
13.6.3
YCC 8 0255 ( 23) DCT
128 -128 127 ( 24)
22:23: 24:
13.6.4 DCT
DCT( )
• N φj , (j = 0, 1, 2, . . . , N − 1)
φj =
√1N
kj
cos j·(0+ 12 )·π
N
cos j·(1+ 12 )·π
N
cos j·(2+ 12 )·π
N...
cos j·(i+ 12 )·π
N...
cos j·(N−1+ 12 )·π
N
kj =
{1√2
(j = 0)
1 (j = 1, 2, . . . , N − 1)
C(2)N =
φT0
φT1
φT2
...φT
N−1
C(2)N (2) 2 DCT
1 3 4 JPEG 2 C(2)N
(j, i) √2N
kj cosj · (i + 1
2 ) · πN
j, i = 0, 1, 2, . . . , N − 1
14
) N = 4
�(2)4 =
12
12
12
12
1√2
cos π8
1√2
cos 3π8
1√2
cos 5π8
1√2
cos 7π8
1√2
cos 2π8
1√2
cos 6π8
1√2
cos 10π8
1√2
cos 14π8
1√2
cos 3π8
1√2
cos 9π8
1√2
cos 15π8
1√2
cos 21π8
(1)
) N = 8 25 φj
1(DC)
25: N = 8
•φj
2
– |φj |2 = 1
– φj · φk = δjk
{φj} N
N x = (x0, x1, . . . , xN−1)
x = X0φ0 + X1φ1 + · · · + XN−1φN−1
X = {X0, X1, . . . , XN−1} φi
φi φi · x = Xiφi · φi = Xi|φj |2 = Xi
Xi = φi · x = φTi x
2 2http://epubs.siam.org/sam-bin/dbq/article/33674
15
i = 0, 1, . . . , N − 1
X =
φT0
φT1
...φT
i
...φT
N−1
x = C(2)N x (2)
(x0, x1, . . . , xN−1) 25
• DCTX x DCT (2) C
(2)N
(2) DCT
x = {C(2)N }T X (3)
• 2 DCTDCT 2 2
262 DCT 27
26: 2
27: 8 × 8
Nx ×Ny xij Nx ×Ny DCT Xmn
Xmn = 2√
1Nx
√1
Nykmkn
Nx−1∑i=0
Ny−1∑j=0
xij cosm(i + 1
2 )πNx
cosn(j + 1
2 )πNy
(4)
x, y 1 DCT 2
16
• DCT24 8× 8 2 DCT DCT 28
28: DCT
• DCT
0JPEG
29
28 30
29: 30: DCT
13.6.5 DCT
8× 8 DCT
•DCT
31
17
DCPM
31:32:
•” ” 32
30 00 0
13.6.6
•
JPEG
13.7
•
•2
13.7.1
• 33 34
• 3 3f(i, j) g(i, j)
g(i, j) =19(f(i − 1, j − 1) + f(i − 1, j) + f(i − 1, j + 1)
+f(i, j − 1) + f(i, j) + f(i, j + 1)
+f(i + 1, j − 1) + f(i + 1, j) + f(i + 1, j + 1))
35
•3 × 3
18
33: 34: 35:
g(i, j) =1∑
a,b=−1
c(a, b)f(i + a, j + b)
c(a, b) (kernel)
c(a, b)
c(−1, 1) c(0, 1) c(1, 1)
c(−1, 0) c(0, 0) c(1, 0)
c(−1,−1) c(0,−1) c(1,−1)
19
19
19
19
19
19
19
19
19
3×3 n×n , 3×3 5×5 7×7.
3 × 3
13.7.2
•
f(i, j) 2 f(x, y)
∆f =∂2f
∂x2+
∂2f
∂y2
∂2f
∂x2≈ f(i − 1, j) − 2f(i, j) + f(i + 1, j)
19
36: 2 1 22
∂2f
∂y2≈ f(i, j − 1) − 2f(i, j) + f(i, j + 1)
∆f ≈ −4f(i, j) + f(i − 1, j) + f(i + 1, j) + f(i, j − 1) + f(i, j + 1)
0 1 0
1 -4 1
0 1 0
3
x(i, j)
0 -1 0
-1 5 -1
0 -1 0
3738
37: 38:
1. JPEG&MPEGISBN4-534-02884-9
3 4 8
20