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