Unit IV

Computer Graphics

Color Theory
 Topics

Colors
CIE Color Model
RGB Color Model
CMY Color Model
YIQ Color Model
Intuitive Color Concepts
HSV Color Model
HLS Color Model
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 Colors
Colors
A narrow frequency band within the
electromagnetic spectrum

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 Colors
Visible band
Each frequency corresponds to a distinct color
Low-frequency end (4.3 x 1014 Hz): Red
High-frequency end (7.5 x 1014 Hz): Violet
Wavelength = c/f, where c=300,000km/sec
Low frequency High frequency
red orange yellow green blue violet
Long wavelength Short wavelength
700nm 400nm

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 Colors
Colors of an object
Light source emits white light (all
frequencies of light)
Object reflects/absorbs some frequencies
Color = combination of frequencies
reflected
Dominant wavelength (or frequency)
Hue or color of the light
S(): spectrum (luminance/intensity of light)
E.g., red

400 620 700 5

 CIE Color Model
Color models
Use three primary colors to produce other colors
Primary colors
Colors used in a color model to produce all the other
colors in that model.
Cannot be made from the other (two) colors defining
the model.
CIE color model
X, Y, and Z: nonexistent, super saturated colors
Vectors in 3-D additive color space
Any color S = AX + BY + CZ

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 CIE Color Model

S = AX + BY + CZ can be
normalized to
x = A/(A+B+C)
y = B/(A+B+C)
z = C/(A+B+C)
s = xX + yY + zZ, where x + y + z =
1 y

s lies in the plane x + y + z = 1 in

3D =670

x =400 z 7
 CIE Color Model
CIE chromaticity diagram
s'() = (x(), y())
By viewing the 3D
curve in an
orthographic
projection, looking
along the z-axis
horseshoe shape
y

=670

x =400 z 8
 Uses of CIE Chromaticity
Diagram
Any colors on the line l between two colors a
and b
Is a convex combination of a and b
Is a legitimate color
can be generated by shining various amounts of
a and b onto a screen (like tweening)
Complementary colors
Any two colors on a line passing through white
and added up to be white are complementary
e.g., e and f
redcyan greenmagenta blueyellow

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 RGB Color Model

Used in light emitting devices

Color CRT monitors
Additive
Result = individual contributions of
each primary color added together
C = rR + gG + bB, where r, g, b [0, 1]
R = (1, 0, 0)
G = (0, 1, 0)
B = (0, 0, 1)
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RGB Color Model

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 RGB Color Model
Color Cube
R + G = (1, 0, 0) + (0, 1, 0) = (1, 1, 0) =
Y
R + B = (1, 0, 0) + (0, 0, 1) = (1, 0, 1) =
M
B + G = (0, 0, 1) + (0, 1, 0) = (0, 1, 1) =
C
R + G + B = (1, 1, 1) = W
1 W = (0, 0, 0) = BLK
Grays = (x, x, x), where x (0, 1)
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Color Cube

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 CMY Color Model

CMY: Complements of RGB

Used in light absorbing devices
Hardcopy output devices
Subtractive
Color specified by what is subtracted
from white light
Cyan absorbs red, magenta absorbs
green, and yellow absorbs blue

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CMY Color Model

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 CMY Color Model
W = (0, 0, 0) B = (1, 1, 1)
Conversion from RGB to CMY
C R
M 1 G

Y B
Conversion from CMY to RGB
R C
G 1 M

B Y
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 CMYK Color Model
Motivations
Do we get black if paint cyan, magenta and
yellow on a white paper?
Which cartridge is more expensive?
CMYK model
K = greatest gray that can be extracted
Given C, M, and Y
K = min(C, M, Y)
C=CK
M=MK
Y=YK

Try some examples

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 YIQ Color Model

Used in U.S. commercial color-TV

broadcasting
Recoding of RGB for transmission
efficiency
Backward compatible with black-and-
white TV
Transmitted using NTSC (National
Television System Committee) standard

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 YIQ Color Model

YIQ
Y: luminance
I, Q: chromaticity
Only Y shown in black-and-white TV
RGB YIQ
Y 0.299 0.587 0.114 R

I 0.596 0.275 0.321 G
Q 0.212 0.528 0.311 B

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 YIQ Color Model
Humans visual properties
More sensitive to changes in luminance
than in hue or saturation
more bits should be used to represent Y
than I and Q
Limited color sensation to objects covering
extremely small part of our field of view
One, rather than two color dimensions
would be adequate
I or Q can have a lower bandwidth than
the others

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 YIQ Color Model

NTSC encoding of YIQ into

broadcast signal
Uses humans visual system
properties to maximize information
transmitted in a fixed bandwidth
Y: 4MHz
I: 1.5MHz
Q: 0.6MHz

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 Intuitive Color Concepts
Terminology
Perceptual Term Colorimetr Comments
y
hue dominate to
d distinguish
wavelengt colors
h
saturation excitation e.g., red and
purity pink
Lightness luminance
(reflecting
objects) 22
 Intuitive Color Concepts
tints
white pure color
tones
grays shades

black
Tint: white pigment added to pure pigment
saturation reduced
Shade: black pigment added to pure pigment
lightness reduced
Tone: consequence of adding both white and
black pigments to pure pigments
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 Intuitive Color Concepts

Tints, shades, and tones different

colors of same hue are produced
Grays

= black pigments + white pigments

Graphics packages that provide
color palettes to users often
employ two or more color models

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 HSV Color Model
HSV = Hue, Saturation, and Value
A.k.a. HSB, where B is Brightness
RGB, CMY, and YIQ: hardware-oriented
HSV and HLS: user-oriented
Cylinder coordinate system
Space: hexcone
hexagon is obtained from the color cube in isometric
projection
(h, s, v), where h [0, 360) and s, v [0, 1]
hue: angle round the hexagon
saturation: distance from the center
value: axis through the center

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 HSV Color Model

Color Cube Hexcone

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 HSV Color Model
W = (-, 0, 1)
B = (-, 0, 0)
R = (0, 1, 1)

Y = (60, 1, 1)
:
M = (300, 1, 1)
Adding white pigments S
Adding black pigments V
Creating tones S and V

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 HSV Color Model

True color system: 16 million colors

Q: Do we need that many?
Human eyes can distinguish
128 hues
130 tints (saturation levels)
23 shades of yellow colors, 16 of blue
colors
128 x 130 x 23 = 82720 colors

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 HLS Color Model
HLS: Hue, Lightness, and Saturation
Cylinder coordinate system
Space: double cone
base is from the hexagon as in HSV
(h, l, s), where h [0, 360) and s, v [0, 1]
hue: angle round the base
lightness: axis through the center
saturation: distance from the center
W = (-, 0, 1)
B = (-, 0, 0)
R = (0, 0.5, 1), Y = (60, 0.5, 1),

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 HLS Color Model

Double cones
white

pure h
color

black
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