Color

Representation

Electromagnetic Radiation - Spectrum

400 nm 500 nm 600 nm 700 nm

Wavelength in nanometers (nm)

Gamma X rays Infrared Radar FM TV AMUltra-violet

10-12

10-8

10-4

104

1 108

electricityACShort-

wave

Wavelength in meters (m)

Visible light

What is a Color?

The Spectral Power Distribution (SPD) of a light is

a function V(l) which defines the power in the light

at each wavelength.

Wavelength (l)

400 500 600 7000

0.5

1

Re

lative

Po

we

r

12614111

3636 111

36

111

36 12

12 17

17 111

14

126

17

36

12

111

3636200 12

14

126 17

36 36

111

12

14

3636200 12

14

126 17

36 36

111

36200

200

12

14111

14

126

126

17

36

36

36

36

12

14

111

111

36

12617

36

36200

111

72

72

12

12 17

10 128

3617

200 11112

14

126

126

126

126

17 17

17

17

36

36

36

36

36

200

200

200

12

12

12

14

14

111

111

72

72

72 106 15510 128

3617

200 11112

14

126

126

126

126

17 17

17

17

36

36

36

36

36

200

200

200

12

12

12

14

14

111

111

72

72

72 106 155

14

126 17

36 36

111

36200

200

12

14111

14

126

126

17

36

36

36

36

12

14

111

111

36

12617

36

36200

111

72

72

12

12 17

12614111

3636 111

36

111

36 12

12 17

17 111

14

126

17

36

12

111

3636200 12

14

126 17

36 36

111

12

14

3636200 12

Rgb Image

Trichromatic Color Theory

Thomas Young (1773-1829) -A few different retinal receptors operating with different

wavelength sensitivities will allow humans to perceive

the number of colors that they do.

Suggested 3 receptors.

Helmholtz & Maxwell (1850) -Color matching with 3 primaries.

Trichromatic: “tri”=three “chroma”=color

color vision is based on three primaries

(i.e., it is 3 dimensional).

Color Matching

Color Matching - behavioral basis for color

representation.

Metamer - two lights that appear the same

visually. They might have different SPDs

(spectral power distributions).

400 500 600 7000

400

800

400 500 600 7000

100

200

Wavelength (nm)

Po

we

r

The phosphors of the monitor were set to match

the tungsten light.

Tungsten light Monitor emission

+ -

+ -

+ -

test match

Color Matching Experiment

Three primary lights are set to match a test light.

=~

400 500 600 7000

0.25

0.5

0.75

1

400 500 600 7000

0.25

0.5

0.75

1

Test light Match light

The Human Eye

Optic NerveFovea

Vitreous

Optic Disc

Lens

Pupil

Cornea

Ocular Muscle

Retina

Humor

Iris

The Human Retina

light

rods cones

horizontal

amacrine

bipolar

ganglion

Cones -

Wavelength (nm)

Re

lative

se

nsitiv

ity

Retinal Photoreceptors

Cone Spectral Sensitivity

400 500 600 7000

0.25

0.5

0.75

1

• High illumination levels (Photopic vision)

• Less sensitive than rods.

• 5 million cones in each eye.

• Only cones in fovea (aprox. 50,000).

• Density decreases with distance from fovea.

• 3 cone types differing in their spectral

sensitivity: L , M, and S cones.

LMS

3D Color Spaces

R

G

B

Brightness

Hue

black-white

red-green

blue-yellow

Cubic Color Spaces

Polar Color Spaces

Opponent Color Spaces

Hue

Saturation

Brightness

Black

White

RG

B

Color Description

Hue (red, green, yelow, blue ...)

Saturation (pink,bright red, ....)

Lightness (black, grey, white ....)

Munsell Color System

Equal perceptual steps in Hue Saturation Value.

Hue: R, YR, Y, GY, G, BG, B, PB, P, RP

(each subdivided into 10)

Value: 0 ... 10 (dark ... pure white)

Chroma: 0 ... 20 (neutral ... saturated)

5R10R

5YR

10YR

5Y

5PB

10PB

5P

10P

5RP

10RP

10B

5B10GB 5GB

10G

5G

10GY

5GY

10Y

/2

/4

/6

/8/10

Example:

5YR 8/4

Val

ue

Chroma

Munsell Book of Colors

Linear Color Spaces

Colors in 3D color space can be described as linear

combinations of 3 basis colors.

a + b + c=

The representation of :

is then given by: (a, b, c)

the color matching functions

Stiles & Burch (1959) Color matching functions.

Primaries are: 444.4 525.3 645.2

10 deg field..

r(l)

g(l)b(l)

400 500 600 700

0

1

2

3

Wavelength (nm)

Prim

ary

In

ten

sity

RGB Space

This is the color model used in color CRT monitors

Given the color matching functions, we can describe

any light with 3 values (CIE-RGB):

(85, 38, 10) (21, 45, 72) (65, 54, 73)

BG

R

Additive primaries

CIE Color Standard - 1931

CIE - Commision Internationale d‟Eclairage

XYZ tristimulus coordinate system.

1931 - defined a standard system for

color representation.

1) Non negative over the visible wavelengths.

2) The 3 primaries associated with x y z color

matching functions are unrealizable (negative

power in some of the wavelengths).

3) y was chosen to equal luminance of

monochromatic lights.

Wavelength (nm)

Tristim

ulu

s v

alu

es

400 500 600 700

0.2

0.6

1

1.4

1.8

z(l)

y(l)

x(l)

.

,

,

ll

ll

ll

l

l

l

dzPkZ

dyPkY

dxPkXz(l)

y(l)

x(l)

k is set so Y is between 0 and 100

RGB to XYZ

RGB to XYZ is a linear transformation

2.365 -0.515 0.005

-0.897 1.426 -0.014

-0.468 0.089 1.009

R

G

B

X

Y

Z

=

R = monochromatic primary 700nm

G = monochromatic primary 546.1nm

B = monochromatic primary 435.8nm

(Primaries are normalized so that equal amounts are

required to match equal energy illuminant E).

xλ, yλ, zλ, are linear combination of rλ, gλ, bλ.

X

Z

Y

X

Y

CIE Chromaticity Diagram

A common representative of color signal: [x,y,Y]

(x,y) – do not contain brightness info.x

650

610

590

550

570

600

580

560

540

505

500

510

520530

490

495

485

480

470450

1.00.50.0

0.5

0.9

y

0.0

All visible colors

Let’s ignore the brightness:

X+Y+Z

Y= y

X+Y+Z

X= x

x+y+z = 1

X+Y+Z

Z= z

y

x

650

610

590

550

570

600

580

560

540

505

500

510

520530

490

495

485

480

470450

1.00.50.0

0.5

0.9

green

yellow-green

yellow

orange

red

magenta

purple

blue

cyan white

pink

Color Naming

x

650

610

590

550

570

600

580

560

540

505

500

510

520530

490

495

485

480

470450

y

C

A

B

Blend of 2 colors lies on the segment between them.

Example: A between B & C.

Chromaticity defined in Polar Coordinates

Dominant Wavelength - wavelength of the

spectral color which added to the reference

white, produces the given color.

Reference white: CIE standard illuminant - C.

x

650

610

590

550

570

600

580

560

540

505

500

510

520530

490

495

485

480

470450

y

100% saturation (Purity)

Reference white

C

A

B

Example: B – dominant wave-length of A.

E is a dominant wavelength of D

Chromaticity defined in Polar Coordinates

D E

Complementary Wavelength - wavelength of the

spectral color which added to the given color,

produces the reference white.

x

650

610

590

550

570

600

580

560

540

505

500

510

520530

490

495

485

480

470450

y

C

Chromaticity defined in Polar Coordinates

Complementary Wavelength of color D is E’.

A does not have a complimentary wavelength.„

A

B

D E

E’

x

650

610

590

550

570

600

580

560

540

505

500

510

520530

490

495

485

480

470450

y

100% saturation (Purity)

C

A

B

Excitation purity of A: AC/BC

Excitation purity of D: DC/EC

Chromaticity defined in Polar Coordinates

Excitation Purity - the ratio of the lengths between

the given color and reference white and between

the dominant wavelength light and reference

white.

Ranges between 0 .. 1.

PurityD E

0 0.2 0.4 0.6 0.80

0.2

0.4

0.6

0.8

G1

R1

B1B2

R2

G2

CE

D65

PALNTSC

Television Primaries and Gamut

R G B - Primaries used for PAL

R G B - Primaries used for NTSC1 1 1

2 2 2

C - reference white for NTSCD65 - reference white for PAL

x

y

Color gamut – color range

HSV/HSB Color Space – perceptual scale

HSV = Hue Saturation Value

HSB = Hue Saturation Brightness

red0°

green120° yellow

Blue240°

cyan

magenta

V

black0.0

1.0

HS

(Smith „78)

Hue

Saturation

Brightness

Relationship between HSV and XYZ

Y vs V :

Luminance (intensity) vs Brightness (Lightness)

Lum

inance

DI1

DI2I2

I1

I1 < I2, DI1 = DI2

Weber‟s Law:

Perceived Brightness = log (I)

Equal intensity steps:

Equal brightness steps:

Munsell lines of constant Hue and Chroma.

MacAdam Ellipses of JND (Just Noticable difference)

x

y

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

Value =1/

0.2

0.4

0.6

0.8

0

y

0.2 0.4 0.60x

(Ellipses

scaled by 10)

The transformation from XYZ space to perceptual

space is Non Linear:

CIE- Luv Coordinates

u =4x

-2x + 12y + 3

v =6y

-2x + 12y + 3

CIE-uv Chromaticity Coordinates:

Munsell lines of constant hue and chroma

plotted in CIE-uv coordinates:

u

v

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

CIE- L*u*v* Coordinates (1964,1976)

u0 v0 Y0 = coordinates of reference white

u„ = u

v„ = 1.5 v

u* = 13 L*(u‟-u0‟)

v* = 13 L*(1.5v‟-v0‟)

{L* =116(Y/Y0)

1/3 - 16 for Y/Y0

903(Y/Y0) otherwise

> 0.01

Munsell lines of constant hue and chroma

plotted in CIE- L*u*v* Coordinates:

u*-150 -100 -50 0 50 100 150

-150

Value =5/

200

100

50

0

-50

-100

v*

MacAdam Ellipses of JND plotted in

CIE- L*u*v* Coordinates:

u*-150 -100 -50 0 50 100 150 200

-150

100

50

0

-50

-100

v*

YIQ - Color Space

NTSC = National Television Systems Committee

Y = luminance – B&W signal

I = red-green

Q = blue-yellow

X

Y

Z

=Y

I

Q

0.299 0.587 0.114

0.569 -0.275 -0.321

0.212 -0.523 0.311

Original Y - Blur

I - Blur Q - Blur

Our visual system is more sensitive to

changes in luminance than to changes in

color (hue, saturation).

CMY - Color Model

Subtractive primaries

cyan – complement of red

magenta – complement of green

Yellow- complement of blue

CMY used for hardcopy devices such as printers.

X

Y

Z

=C

M

Y

1

1

1

-

-

-

CMYK (K – black) – Black ink instade of color ink.

K = min (C,M,Y)

C = C-K

M = M-K

Y = Y-K

Color Spaces - Summary

RGB space - Additive space used for CRT,

Color Image representation

CIE-XYZ Tri-stimulus Coordinates -

Device Independent, Universal standard

YIQ - Opponent Space,

used for color television broadcast.

HSV - Perceptual Digitized Space,

used for Human Interactive Painting.

CMY/CMYK – Subtractive space used for hardcopy

devices.

All these color spaces are 3D.

There are conversions from one space to the other.