Color RepresentationFoley & Van Dam, Chapter 13

Color Representation

• Visible Light Spectrum• Color Matching• Trichromatic Color Theory• Psychophysics• CIE standard• RGB and CMYK Color Spaces• HLS Color Model• YIQ Color Model

Visible Light Spectrum and ColorsLight is an electro-magnetic radiation

• Hue: distinguished among colors• Saturation: how far is color from a gray of equal intensity• Lightness: perceived intensity of a reflective surface• Brightness: perceived intensity of emitting surface

Gamma X rays Infrared Radar FM TV AMUltra-violet

10 -12 10 -8 10 -4 10 41 10 8

electricityACShort-

wave

400 nm 500 nm 600 nm 700 nmWavelength in nanometers (1nm=10-9 m)

Wavelength in meters (m)

Visible light

Spectral Power Distribution• The Spectral Power Distribution of a light is a function f(λ) defining the energy at each wavelength

Blue Skylight Tungsten bulb

Red monitor phosphor Monochromatic light

400 500 600 7000

0.5

1

400 500 600 7000

0.5

1

400 500 600 7000

0.5

1

400 500 600 7000

0.5

1

Color Matching Experiment• Three primary lights are set to match a test light• Metamer: two lights visually undistinguishable (they might have different spectral power distributions)

+ -

+ -

+ -

test match

=~Test light(tungsten light)

Match light(monitor emission)

400 500 600 7000400 500 600 7000

Pow

er

Trichromatic Color Theory• Trichromatic: “tri”=three “chroma”=color also tristimulus

color vision is based on three primaries (three dimensional)

•Thomas Young • A few different retinal receptors operating with differentwavelength sensitivities allow humans to perceive colors

• Suggested 3 receptors

• Helmholtz & Maxwell• Color matching with 3 primaries

The Human Eye

conesOptic NerveFovea

Vitreous

Optic Disc

Lens

Pupil

Cornea

Ocular MuscleRetina

HumorIris

light

rods

amacrinebipolar

ganglion

horizontal

Retinal Photoreceptors• Cones: Sensitive to high illumination levels (Photopic vision)

Less sensitive than rods5 million cones in each eyeOnly cones in fovea (approx. 50,000)Density decreases with distance from fovea3 types differing in their spectral sensitivity: L , M, and S

Wavelength (nm)

Rel

ativ

e se

nsiti

vity

400 500 600 7000

0.25

0.5

0.75

1 LMS

Retinal Photoreceptors

Linear Color Spaces• Colors in 3D color space can be described as linear

combinations of 3 basis colors called primaries

A • + B • + C •=

The representation of the color having spectrum:

Is given by (A, B, C)

Choosing The Primaries• Stiles & Burch (1959) used 3 monochromatic primaries of wavelengths 444.4, 525.3 and 645.2

Color Matching Diagram

Problem: Subtractive components

r(λ)

g(λ)b(λ)

400 500 600 700

0

1

2

3

Wavelength (nm)

Prim

ary

Inte

nsity

CIE Color Standard

Wavelength (nm)

Tris

timul

usva

lues

400 500 600 7000.2

0.6

1

1.4

1.8z(λ)

y(λ)x(λ)

• CIE: Commision Internationale d’Eclairage (1931) defined a standard system (CIE- XYZ) for color representation

• Weights are non negative over the visible wavelengths• The 3 primaries associated with x y z color matching

functions cannot be easily realized in hardware• y was chosen to equal luminance of monochromatic lights

CIE Color Standard

650610

590

550

570

600

580

560

540

505

500

510520 530

490

495

485480

470450

1.00.50.0

0.5

0.9

y

0.0x

X

Z

Y

If X, Y and Z are the weights used to define a color C, then the chromaticity values x, y, z (independent from the luminosity) are given by:x= X/(X+Y+Z) y=Y/(X+Y+Z) z=Z/(X+Y+Z)(x,y,z) is a point on the plane X+Y+Z=1

CIE Chromaticity Diagram

CIE Color Standard• Color Gamut: A convex sum of several colors

RGB Color RepresentationCathode

(electron gun)

deflection yoke

focusing anode

shadow mask and phosphor coated screen

Cathode(electron gun)

deflection yoke

focusing anode

shadow mask and phosphor coated screen

phosphors on glass screen

shadow mask

electron guns

phosphors on glass screen

shadow mask

electron guns

• In a CRT each color can be defined by the required powerof each electron gun:

• The intensity is defined as:

•The chroma(ticy) is defined as:

C r R g G b B= + +

bgrI ++=

r R g G b BCr g b+ +

=+ +

RGB Color Images126141113636 111

36111

36 1212 17

17 11114

12617

36

12111

3636200 1214

126 1736 36

1111214

3636200 12

14126 1736 36

11136200

2001214111

14126

12617

36

36

36

361214

111

111

361261736

36200

11172

7212

12 17

10 1283617

200 1111214

126

126126

126

17 1717

17

36

36

36

3636

200200

20012

12

12

1414

111

111

72

7272 106 155

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

72 106 155

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

black

redgreen

blue

white

RGB to CIE-XYZ Conversion• RGB to CIE-XYZ is a linear transformation:

• R = monochromatic primary 700nm• G = monochromatic primary 546.1nm• B = monochromatic primary 435.8nm

2 .3 6 5 0 .5 1 5 0 .0 0 50 .8 9 7 1 .4 2 6 0 .0 1 40 .4 6 8 0 .0 8 9 1 .0 0 9

R XG YB Z

− − − = −

RGB vs. CMY(K) Color Scheme• RGB and CMYK (Cyan, Magenta, Yellow andblacK) are hardware-oriented representations

• CMY is used in color photography and (with K) inmost color printers

RGB is Additive CMY is Subtractive

111

C RM GY B

= −

The HLS Color Model

Hue (red, green, yellow, blue ...)Saturation (pink, bright red, ....)Lightness (black, grey, white ....)

Munsell Book of Colors

• HLS: Hue Lightness, Saturation similar toHSV: Hue Saturation Value

The YIQ Color Model• Based on the concept of opponent colors• Used in NTSC Television (National Television Systems Committee)

• Similar method (YCbCr) used in JPEG and MPEG

• Y = Luminance• I = Red-Green• Q = Blue-Yellow

+

+--

0 .2 9 9 0 .5 8 7 0 .1 1 40 .5 9 6 0 .2 7 5 0 .3 2 10 .2 1 2 0 .5 2 3 0 .3 1 1

R YG IB Q

− − = −

The YIQ Color Model• The human eye is more sensitive to luminosity than to colors, so it ispossible to save space by encoding colors more coarsely

• Preferred by the NTSC because of backward compatibility with B/W TV

Original Y - Blur

I - Blur Q - Blur

Summary• CIE-XYZ

• Tristimulus Coordinates• Device Independent• Universal standard

• CIE-Lab• Perceptual Space, used to assess image quality

• RGB and CMY• Hardware oriented• Additive spaces used for CRT, printers, photography

• YIQ and YCbCr• Opponent Space• Used for color television broadcast and image compression

• HLS• Perceptual Digitized Space• Used for Human Interactive Painting