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Colorimetryy

ColorimetryColorimetry

– Psychophysical Perception of Color AppearancePsychophysical Perception of Color Appearance

– Quantitative DescriptionCIE (Commission Internationale de l’Eclairage) ( g )

Basic Concepts– Trichromatic Generalization : empirical lawTrichromatic Generalization : empirical law

Young-Helmholtz : Trichromatic color thoery

Color ← additive mixture of three different colors

Trichromacy : three independent colors

– Tristimulus SpacepPrimary tristimulus : R, G, B

Color = RQR+GQG+BQB (RQ, GQ, BQ :tristimulus values)Q Q Q Q Q Q

– Chromaticity CoordinatesColor is represented on 3D coordinates of RQ, GQ, BQ

DISPLAY DEVICE Lab., Dong-A UNIVERSITY1

Basic Colorimetric Concepts IBasic Colorimetric Concepts I

Trichromatic GeneralizationTrichromatic Generalization– Additive mixture of trichromacy– Matching lawsg

Symmetry law– A ≡ B ⇒ B ≡ A

Transitivity law– A ≡ B & B ≡ C ⇒ A ≡ C

Proportionality lawProportionality law– A ≡ B ⇒ αA ≡ αB

α : radiant power coefficient (no spectrum change)(no spectrum change)

Additivity law– A ≡ B, C ≡ D

⇒ A + D ≡ B + C


Basic Colorimetric Concepts IIBasic Colorimetric Concepts II

Tristimulus SpaceTristimulus Space– Specific color stimulus Q = {Pλdλ}Q

– Primary tristimulus R Q BPrimary tristimulus R, Q, BR = {ρPλdλ}R

G = {γPλdλ}GG {γPλdλ}G

B = {βPλdλ}B

ρ, γ, β : pisitive constants

– Q is represented as additive mixture of R, G, B

Q Q QR G B= + +Q R G B RQ, GQ, BQ : tristimulus values of QQ Q QR G B+ +Q R G B RQ, GQ, BQ : tristimulus values of Q


Basic Colorimetric Concepts III

Chromaticity Coordinates

Basic Colorimetric Concepts III

By

k RQ+GQ+BQ = kQ Q QR G Bk

r g b= = =

BQ

g

1Q Q Q Q Q QR G B R G B

kr g b+ + + +

= =+ +

Gk

1

1

Q

b

Q = RQR+GQG+BQBg

Q

Q Q Q

Rr

R G B=

+ +1

GBGQ

b

g p = rR+gG+bB

Q Q Q

Q

Q Q Q

Gg

R G B=

+ +

RRQ

r

g

b 1

p rR+gG+bBQ Q Q

Q

Q Q Q

R G B

Bb

R G B

+ +

=+ +

– Only (r, g) represents Q(b = 1–r–g) Rk

1RQ r+g+b = 1Q Q QR G B+ +

DISPLAY DEVICE Lab., Dong-A UNIVERSITY

(b = 1 r g)

4

Rk

Conversion between Two Systems of Primaries

Conversion between Two Primary Tristimulus SetsConversion between Two Primary Tristimulus Sets– One primary tristimulus R’, G’, B’ are represented as

another primary tristimulus R, G, B

11 21 31

12 22 32

a a aa a a

′ = + +′ = + +

R R G BG R G B

11 21 31

12 22 32

a a aa a a

′⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥′ = =⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

R R RG G A G

– C = R’R’+G’G’+B’B’ in R’G’B’ system13 23 33a a a′ = + +B R G B 13 23 33a a a

⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥′⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦B B B

y

( ) ( ) ( )( ) ( ) ( )

11 21 31 12 22 32 13 23 33

11 12 13 21 22 23 31 32 33

R a a a G a a a B a a aa R a G a B a R a G a B a R a G a B′ ′ ′= + + + + + + + +

′ ′ ′ ′ ′ ′ ′ ′ ′= + + + + + + + +C R G B R G B R G B

R G B

– C = RR+GG+BB in RGB system

( ) ( ) ( )11 12 13 21 22 23 31 32 33

= R = G = B

11 12 13

21 22 23T

R a a a R RG a a a G G⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥′ ′= =⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥A


31 32 33B a a a B B⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥

′ ′⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

Monochromatic StimuliMonochromatic Stimuli

CIE 1931 Color Matching FunctionCIE 1931 Color Matching Function– Commission Internationale de l’Eclairage에서 1931에 표준

( ) ( ) ( ) ( )r g bλ λ λ λ= + +E R G B : monochromatic stimuli of unit radiant power

– R (700 nm), G (546.1 nm), B (435.8 nm)

( ) ( ) ( ) ( )r g bλ λ λ λ= + +E R G B( ) ( ) ( ), ,r g bλ λ λ : color matching function

: monochromatic stimuli of unit radiant power

R (700 nm), G (546.1 nm), B (435.8 nm)

CIE 1931CIE 1931

CIE 1964


CIE 1931 Color Matching FunctionCIE 1931 Color Matching Function

Negative MatchingNegative Matching– r(λ) is negative between 435 nm and 546 nm– λ = 475 nm + rR ⇒ color matchingg

Ex) E475 + 0.045R = 0.032G + 0.186B⇒ E475 = – 0.045R + 0.032G + 0.186B


(r, g) Chromaticity Diagram(r, g) Chromaticity Diagram

( )r λ( )( ) ( ) ( )

( )

rr

r g bλ

λ λ λ

λ

=+ +

( )( ) ( ) ( )

( )

gg

r g bλ

λ λ λ=

+ +

( )( ) ( ) ( )

bb

r g bλ

λ λ λ=

+ +


Complex Color Stimulus in (r, g, b)Complex Color Stimulus in (r, g, b)

Complex Color StimulusComplex Color Stimulus: complex spectrum

( ) { } ( )Q P d Eλλ λ λ=( ) { } ( ){ } ( ) ( ) ( ){ } ( ) { } ( ) { } ( )P d r g b

P d r P d g P d bλ

λ λ λ

λ λ λ λ

λ λ λ λ λ λ

⎡ ⎤= + +⎣ ⎦= + +

R G B

R G B{ } ( ) { } ( ) { } ( )P d r P d g P d bλ λ λλ λ λ λ λ λ+ +R G B

( )bR P r dλ

λλλ λ= ∫

RrR G B

=+ +( )

( )a

b

a

G P g d

λλ

λ

λλλ λ=

∫

∫R G B

GgR G B

+ +

=+ +

( )b

a

B P b dλ

λλλ λ= ∫ Bb

R G B=

+ +

– Negative region → complicated⇒ virtual tristimulus → novel color matching functions


g

9

XYZ CoordinatesXYZ Coordinates

Virtual Color Matching FunctionsVirtual Color Matching Functions– Non-negative function, r(λ) → x(λ)– y(λ) ⇔ V(λ) : relative photopic luminous efficiency functiony( ) ( ) p p y

Monochromatic Light

X Y Z in RGB coordinates( ) ( )2 7689 1 7528 1 1302x rλ λ⎡ ⎤ ⎡ ⎤⎡ ⎤ X, Y, Z in RGB coordinates( )( )( )

( )( )( )

2.7689 1.7528 1.13021.000 4.5907 0.06010 000 0 0565 5 5943

x ry gz b

λ λλ λλ λ

⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥=⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦ ⎣ ⎦( ) ( )0.000 0.0565 5.5943z bλ λ⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦ ⎣ ⎦

( )( ) ( ) ( )

xx

λλ λ λ

=( ) ( ) ( )

( )( ) ( ) ( )

x y z

yy

λ λ λ

λ

+ +

=( ) ( ) ( )

( )

yx y z

zz

λ λ λ

λ

+ +

=


( ) ( ) ( )z

x y zλ λ λ+ +

Tristimulus in XYZ Coordinates (CIE 1931)Tristimulus in XYZ Coordinates (CIE 1931)


Complex Color Stimulus XYZ CoordinatesComplex Color Stimulus XYZ Coordinates

Complex Color StimulusComplex Color Stimulus: complex spectrum

( ) ( ){ } ( )F d Eλ φ λ λ λ=( ) ( ){ } ( )( ){ } ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )

F d E

d x y z

d d d

λ φ λ λ λ

φ λ λ λ λ λ

φ λ λ λ φ λ λ λ φ λ λ λ

⎡ ⎤= + +⎣ ⎦+ +

X Y Z

X Y Z( ) ( ) ( ) ( ) ( ) ( )d x d y d zφ λ λ λ φ λ λ λ φ λ λ λ= + +X Y Z

( ) ( )bX k dλφ λ λ λ∫ k li ti( )X x λ⎡ ⎤⎡ ⎤( ) ( )

( ) ( )a

b

X k x d

Y k y d

λ

λ

φ λ λ λ

φ λ λ λ

=

=

∫

∫

k : normalizationλa = 380 nm λb = 780 nm

( )( )( )( )

b

a

X xY k y dZ z

λ

λ

λφ λ λ λ

λ

⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥ = ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦

∫( ) ( )

( ) ( )a

b

a

y

Z k z d

λ

λ

λ

φ

φ λ λ λ=

∫

∫ , ,X Y Zx y z= = =

( )Z z λ⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦

, ,yX Y Z X Y Z X Y Z+ + + + + +


Chromaticity Diagram of CIE 1931Chromaticity Diagram of CIE 1931


CIE 1964 Supplementary Standard Coordinate System

CIE 1964 Supplementary StandardCIE 1964 Supplementary Standard– Field of View : 10° for television application– cf. CIE 1936, 2°,


CIE 1964 Supplementary StandardCIE 1964 Supplementary Standard


Color Differences in CIE 1931Color Differences in CIE 1931

Equally Perceptible Color DifferencesEqually Perceptible Color Differences– 10 times their actual area


Uniform Color Space (UCS)Uniform Color Space (UCS)

CIE 1960 UCS Diagram (u, v)CIE 1960 UCS Diagram (u, v)4 4 6 6,

2 12 3 15 3 2 12 3 15 3x X y Yu v

x y X Y Z x y X Y Z= = = =− + + + + − + + + +y y

66 16 12

uxu v

=− +6 16 12

46 16 12

u vvy

u v

+

=− +


U*V*W* Coordinate (1964)U V W Coordinate (1964)

3D Coordinate3D Coordinate– Expanded CIE 1960 UCS (u, v)– Color rendering : effect of light source on object colorg g j

( )( )

* *

* *

1313

nU W u uV W v v

= −= −( )

( )

* 1 3

1325 171 100

nV W v vW Y

Y

=

= −

≤ ≤( )1 100Y≤ ≤

un : u (standard white)v : v (standard white)

– W* : lightness index– U*, V* : chromaticness index

vn : v (standard white)

– 자극치 사이의 감지 크기

( ) ( ) ( )2 2 2* * *E U V WΔ Δ + Δ + Δ ⇔ W* = 50

Munsell Value = 5


( ) ( ) ( )64CIEE U V WΔ = Δ + Δ + Δ

CIE 1976 UCS Diagram (u’, v’)CIE 1976 UCS Diagram (u , v )

– u’ = u, v’ = 1.5×v in CIE 1960 UCSu u, v 1.5 v in CIE 1960 UCS

415 3

XuX Y Z

′ =+ +15 3

915 3

X Y ZYv

X Y Z

+ +

′ =+ +


CIE 1976 L*u*v* (CIELUV) CIE 1976 L u v (CIELUV)

Expand V* in U*V*W* Coordinate by 50 %Expand V in U V W Coordinate by 50 %

( )1 3* 116 16nL Y Y= − 4xu′ = Yn : Y (standard white) ( t d d hit )( )

( )* *

* *

1313

n

n

u L u uv L v v

′= −′= −

2 12 39

2 12 3

xyv

x

− + +

′ =− + +

un : u (standard white)vn : v (standard white)

( )2 12 3

, 1.5x

u u v v− + +′ ′= =

– Yn = 100 : L* ≈ W*– If Y/Yn ≤ 0.008856 ⇒ L* = 903.3(Y/Yn)– CIE 1976 L*u*v* Color Difference

( ) ( ) ( )2 2 2* * *E L u vΔ = Δ + Δ + Δ

– In additive mixture, mixed color = center of gravity law between two colors

( ) ( ) ( )uvE L u vΔ Δ + Δ + Δ


mixed color = center of gravity law between two colors20

CIE 1976 L*u*v* Color SpaceCIE 1976 L u v Color Space


CIE 1976 L*u*v* UCS (L* = 50)CIE 1976 L u v UCS (L = 50)

MacAdam’s Ellipse (L* = 50)MacAdam s Ellipse (L 50)

DISPLAY DEVICE Lab., Dong-A UNIVERSITY22NTSC (national television system committee

CIE 1976 L*a*b* Coordinate (CIELAB) I

From CIE 1964 Supplementary Standard

CIE 1976 L a b Coordinate (CIELAB) I

From CIE 1964 Supplementary Standard – If X/Xn, Y/Yn, Z/Zn > 0.01

( )1 3* 116 16L Y Y= X : X (standard white)( )( ) ( )1 3 1 3*

116 16

500n

n n

L Y Y

a X X Y Y

= −

⎡ ⎤= −⎣ ⎦

Xn : X (standard white)Yn : Y (standard white)Zn : Z (standard white)

If X/X Y/Y Z/Z < 0 01

( ) ( )1 3 1 3* 200 n nb Y Y Z Z⎡ ⎤= −⎣ ⎦

– If X/Xn, Y/Yn, Z/Zn < 0.01

( )( ) ( )

*

*

903.3 for 0.008856m n nL Y Y Y Y= ≤

⎡ ⎤( ) ( )( ) ( )

*

*

500

200m n n

m n n

a f X X f Y Y

b f Y Y f Z Z

⎡ ⎤= −⎣ ⎦⎡ ⎤= −⎣ ⎦

( )

( )

1 3 0.008856167 787 0 008856

f q q q

f

= >

+ ≤


( ) 7.787 0.008856116

f q q q= + ≤

CIE 1976 L*a*b* Coordinate (CIELAB) IICIE 1976 L a b Coordinate (CIELAB) II

– L* in CIELAB ⇔ L* in CIELUVL in CIELAB ⇔ L in CIELUV

– CIE 1976 L*a*b* Color Difference2 2 2


( ) ( ) ( )2 2 2* * *abE L a bΔ = Δ + Δ + Δ

Perceived Values in CIELUV IPerceived Values in CIELUV I

Hue, Perceived Chroma, Saturation, LightnessHue, Perceived Chroma, Saturation, Lightness– CIE 1976 u, v : hue angle

*1 vh

– CIE 1976 u, v : chroma

1*tanuv

vhu

−=

,

( ) ( )2 2* * *uvC u v= +

– CIE 1976 u, v : hue difference

( ) ( ) ( )2 2 2* * * *H E L CΔ = Δ − Δ − Δ

– Total color difference

( ) ( ) ( )uv uv uvH E L CΔ Δ Δ Δ

( ) ( ) ( )2 2 2* * * *uv uv uvE L C HΔ = Δ + Δ + Δ


Perceived Values in CIELUV IIPerceived Values in CIELUV II

– CIE 1976 u, v : saturationCIE 1976 u, v : saturation

( ) ( )2 213uv n ns u u v v′ ′ ′ ′= − + −

In color television – 0.25 × L* (lightness)( g )

( ) ( ) ( ) ( )2 2 2* * * *0.25uvE L u v′Δ = Δ + Δ + Δ

( ) ( ) ( ) ( )2 2 2* * * *0.25uv uv uvE L C H′Δ = Δ + Δ + Δ

In CIE 1976 UCS u’, v’ – Two adjacent color samples : ΔEu’v’ ≥ 0.004 distinguishable– Two separated color samples : ΔEu’v’ ≥ 0.04 distinguishable


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