Lecture 3
Color Representation
CIEXYZ Color Space
CIE Chromaticity Space
HSL,HSV,LUV,CIELab
Y
X
Z
CIEXYZ
Color Coordinate System
1931 – The Commission International de l’Eclairage (CIE)
Defined a standard system for color representation.
The CIE-XYZ Color Coordinate System.
In this system, the XYZ Tristimulus values can describe
any visible color.
The XYZ system is based on the color matching experiments
Trichromatic Color Theory
“tri”=three “chroma”=color
Every color can be represented by 3 values.
80
60
e1
e2
e3
40
20
0
400
500
600
700
Wavelength (nm)
Space of visible colors is 3 Dimensional.
Calculating the CIEXYZ
Color Coordinate System
CIE-RGB
Primary Intensity
3
r(l)
2
1
b(l)
g(l)
0
400
500
600
700
Wavelength (nm)
David Wright 1928-1929, 1929-1930 & John Guild 1931
17 observers responses to Monochromatic lights between 400700nm using viewing field of 2 deg angular subtense.
Primaries are monochromatic : 435.8 546.1 700 nm
2 deg field.
These were defined as CIE-RGB primaries and CMF.
XYZ are a linear transformation away from the observed data.
CIEXYZ
Color Coordinate System
CIE Criteria for choosing Primaries X,Y,Z and
Color Matching Functions x,y,z.
1) CMFs are non-negative over visible wavelengths.
(i.e. any color is represented by 3 positive values).
2) Equal amounts of the Primaries produce white.
(i.e. X=Y=Z for stimulus of equal luminance at
each wavelength).
3) The y color matching function is defined to match
the luminous-efficiency function of the human eye.
4) Primaries are as ‘tight’ as possible around the
set of possible colors (Maxwell triangle Projects
to equilateral in XYZ space).
Luminous Efficiency
Luminous-Efficiency function of
the human eye
1
0.6
0.2
400
500
600
Wavelength (nm)
700
CIEXYZ
Color Coordinate System
Y
X
Z
CIE-RGB to CIE-XYZ
CIE-RGB Chromaticity space (rg).
* Cr, Cg, Cb must enclose the Gamut.
* Line Cb-Cr is defined by Y being Luminance Function.
(the Alychne = line of zero luminance).
* Line Cr-Cg is tangent at 650+ (z is zero beyond 650).
* Thus Cr is defined.
* Equal Energy (x=y=z=1/3) puts constraint on Cb-Cg
* Tight around Gamut -> line Cb-Cg is close to green.
* Cb and Cg are defined.
CIE-RGB to CIE-XYZ
CIE RGB space to XYZ space.
Map Cb Cg Cr to x=(0,0) y=(0,1) z=(1,0)
CIE Color Standard - 1931
Tristimulus values
1.8
1.4
z(l)
y(l)
1
x(l)
0.6
0.2
400
500
600
700
Wavelength (nm)
• y is predefined.
• Non negative over the visible wavelengths.
(X,Z – Several Hundreds, Y – 0..100).
• The 3 primaries associated with x y z color
matching functions are unrealizable
(negative power in some of the wavelengths).
• Integral over the CMF gives equal values.
• CMF are linear transformation away from
CIE-RGB and from LMS.
CIE Color Standard - 1964
Stiles and Birch data (1959):
Color Matching Experiment with:
10 Deg view
Primaries: 444.4 525.3 645.2
CIE-XYZ10
Colorimeters
Color matching functions vs
LMS - cone photoreceptor responses
XYZ Tristimulus System
Cone Spectral Sensitivity
x(l)
y(l)
z(l)
1.4
1
0.6
1
Relative sensitivity
Tristimulus values
1.8
L
M
S
0.75
0.5
0.25
0.2
400
500
600
0
700
Wavelength (nm)
400
500
600
700
Wavelength (nm)
The cone responses form a 3D linear system.
Cone responses are equivalent for metamers.
thus
The cone spectral sensitivities and the XYZ color
matching functions are related by a 3 x 3 linear
transformation.
X
1.9023 -1.4000 0.3544
Y = 0.6371 0.3933 -0.0093
Z
0.0007 0.0033 1.7462
L
M
S
CIE – RGB
Primaries are monochromatic : 435.8 546.1 700 nm
X
0.49 0.31 0.20
Y = 0.17 0.81 0.01
Z
0.00 0.01 0.99
R
G
B
CIEXYZ
Color Coordinate System
x y z Color Matching Functions
Tristimulus values
1.8
1.4
z(l)
y(l)
1
x(l)
0.6
0.2
400
500
600
Wavelength (nm)
700
CIEXYZ
Color Coordinate System
Y
X
Z
CIE Chromaticity Diagram
X
=x
X+Y+Z
Y
=y
X+Y+Z
Z
=z
X+Y+Z
X
Y
0.9
520
Z
530
540
510
550
y
505
x+y+z = 1
560
570
500
580
0.5
590
495
600
610
490
650
485
480
0.0
0.0
470
450
0.5
x
1.0
A common representative of color signal: [x,y,Y]
CIE Chromaticity Diagram
Y
(ax,ay,az)
X
Z
Color Naming
0.9
520
530
540
510
550
505
green
yellow- 570
green
580
yellow
500
y
560
0.5
590
495
orange 600
490 cyan
485
blue
480
610
white
pink
red
650
magenta
purple
470
450
0.0
x
0.5
1.0
CIE-RGB Primaries
Blackbody Radiators and
CIE standard Illuminants
CIE Standard Illuminants:
A - tungsten light
B - Sunset
C - blue sky
D65 - Average daylight
E - Equal energy white (x=y=z=1/3)
0.8
0.6
y
4000 3000
5000
2000
6000
7000
8000
A
B
10000
E
20000
C
D65
0.4
0.2
0
0
0.2
0.4
x
0.6
0.8
Blackbody Radiators
Relative energy
3000K
3500K
9000K
Wavelength (nm)
http://www.olympusmicro.com/primer/java/colortemperature/index.html
Television Primaries and Gamut
R 1G 1B1 - Primaries used for PAL
R2 G 2B 2 - Primaries used for NTSC
D65 - reference white for PAL
C - reference white for NTSC
0.8
NTSC
PAL
G2
G1
0.6
y
0.4
D65
E
R1
R2
C
0.2
0
B1
B2
0
0.2
0.4
x
0.6
CIE Chromaticity + Gamut applet :
http://www.cs.rit.edu/~ncs/color/a_chroma.html
0.8
Signal Lights
XYZ Color Space
Hue vs Saturation
Chromaticity in Polar Coordinates
Given a reference white.
Dominant Wavelength –
wavelength of the spectral color which added
to the reference white, produces the given color.
0.8
550
0.6
0.4
630
490
Reference
white
0.2
0
0
0.2
0.4
0.6
0.8
Chromaticity in Polar Coordinates
Given a reference white.
Complementary Wavelength –
wavelength of the spectral color which added
to the given color, produces the reference white.
0.8
0.6
570
0.4
485
Reference
white
0.2
0
0
0.2
0.4
0.6
0.8
Chromaticity in Polar Coordinates
Given a reference white.
Purity –
the ratio of the lengths between the given color and
reference white and between the dominant wavelength
and reference white. Ranges between 0 .. 1.
0.8
0.6
0.2
0.4
Reference
white
0.2
0
0.4
0
0.2
0.4
0.6
0.8
EXAMPLE:
Reference white is CIE standard illuminant - C.
Dominant Wavelength of color S1 is D1
of color S2 is D2.
Complementary Wavelength of color S1 is‘ D1.
S2 does not have a complimentary wavelength.
Excitation Purity of S1 is the ratio CS1/CD1
of S2 is the ratio CS2/CD2
of S3 is the ratio CS3/CD3
0.8
D2
0.6
S2
S
0.4
D1
S1
C
‘
D1
0.2
0
S3
D3
0
0.2
0.4
0.6
0.8
Chromaticity in Polar Coordinates
0.8
Dominant/complimentary
Wavelength
0.6
Y
purity
0.4
reference white
0.2
0
0
0.2
0.4
X
0.6
0.8
Color Description
Hue (red, green, yelow, blue ...)
Saturation (pink,bright red, ....)
Lightness (black, grey, white ....)
(Value)
White
G
Hue
Saturation
R
B
Brightness
Black
Munsell Color System (1915)
Equal perceptual steps in Hue Saturation Value.
Hue:
R, YR, Y, GY, G, BG, B, PB, P, RP
(each subdivided into 10)
Chroma: 0 ... 20
Value: i0 ... 10
(neutral ... saturated)
(dark ... pure white)
Value
10/
5/
5R
10R
5YR
10YR
10RP
1/
5Y
5RP
/2
/4
/6 /8
/10
10Y
10P
5P
5GY
/2
10PB
10GY
/4
5PB
10B
/6
/8
5B
5G
/10
10GB 5GB
10G
Example:
5YR 8/4
Munsell Book of Colors
Atlas of thr Munsell Color System (1915)
Color Polytopes
Applets:
http://www.cs.rit.edu/~ncs/color/a_spaces.html
http://www.nacs.uci.edu/~wiedeman/cspace/me/rgbhsv.html
MayuraDraw
PowerPoint
Photoshop
Color Picker
Color Space Summary
Spectral Power Distribution (SPD) – High Dimensional
3 Dimensional Spaces (Tristimulus Values):
LMS Human Cone responses. Given by the cone sensitivity
curves.
CIE–RGB Based on color Matching Experiments by Wright+Guild.
Defined by Primaries R G B (monochromatic
435.8 546.1 700 nm) and cmf r g b.
CIE-XYZ Standard Color space. Linear transformation of above
that confirms to set of constraints.
Defined by Primaries X Y Z (unrealizable) and cmf x y z.
Munsell Color Space –
Perceptually equally spaced samples in 3 dimensions:
Hue, Chroma, Value.