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Color Representation
Lecture 3
CIEXYZ Color SpaceCIE Chromaticity SpaceHSL,HSV,LUV,CIELab
X
Z
Y
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CIEXYZ Color Coordinate System
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
1931 – The Commission International de l’Eclairage (CIE)Defined a standard system for color representation.
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400 500 600 7000
20
40
60
80
Wavelength (nm)
Every color can be represented by 3 values.
Space of visible colors is 3 Dimensional.
“tri”=three “chroma”=color
Trichromatic Color Theory
e1
e2
e3
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David Wright 1928-1929, 1929-1930 & John Guild 193117 observers responses to Monochromatic lights between 400-700nm using viewing field of 2 deg angular subtense.
Primaries are monochromatic : 435.8 546.1 700 nm2 deg field.
These were defined as CIE-RGB primaries and CMF.
XYZ are a linear transformation away from the observed data.
r(λ)
g(λ)b(λ)
400 500 600 700
0
1
2
3
Wavelength (nm)
Prim
ary
Inte
nsity
Calculating the CIEXYZ Color Coordinate System
CIE-RGB
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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 ateach wavelength).
3) The y color matching function is defined to matchthe luminous-efficiency function of the human eye.
4) Primaries are as ‘tight’ as possible around theset of possible colors (Maxwell triangle Projectsto equilateral in XYZ space).
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Wavelength (nm)
Lum
inous
Eff
icie
ncy
400 500 600 700
0.2
0.6
1
Luminous-Efficiency function of the human eye
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X
Z
Y
CIEXYZ Color Coordinate System
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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.
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CIE RGB space to XYZ space. Map Cb Cg Cr to x=(0,0) y=(0,1) z=(1,0)
CIE-RGB to CIE-XYZ
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CIE Color Standard - 1931
Wavelength (nm)
Trist
imulu
svalu
es
400 500 600 700
0.2
0.6
1
1.4
1.8
z(λ)
y(λ)
x(λ)
• 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.
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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
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Colorimeters
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Color matching functions vsLMS - cone photoreceptor responses
Wavelength (nm)
Rela
tive
sensiti
vity
Cone Spectral Sensitivity
Wavelength (nm)
Tristim
ulu
svalu
es
XYZ Tristimulus System
z(λ)y(λ)x(λ)
400 500 600 700
0.2
0.6
1
1.4
1.8
400 500 600 7000
0.25
0.5
0.75
1LMS
The cone responses form a 3D linear system.Cone responses are equivalent for metamers.
thus
The cone spectral sensitivities and the XYZ colormatching functions are related by a 3 x 3 linear transformation.
1.9023 -1.4000 0.35440.6371 0.3933 -0.00930.0007 0.0033 1.7462
LMS
=XYZ
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CIE – RGBPrimaries are monochromatic : 435.8 546.1 700 nm
1.9023 -1.4000 0.35440.6371 0.3933 -0.00930.0007 0.0033 1.7462
RGB
=XYZ
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Wavelength (nm)
Trist
imulu
sva
lues
400 500 600 700
0.2
0.6
1
1.4
1.8
z(λ)
y(λ)
x(λ)
CIEXYZ Color Coordinate System
x y z Color Matching Functions
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X
Z
Y
CIEXYZ Color Coordinate System
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CIE Chromaticity Diagram
YX+Y+Z
Y= y
XX+Y+Z
X= x
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
x+y+z = 1
A common representative of color signal: [x,y,Y]
ZX+Y+Z
Z= z
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X
Z
Y
(ax,ay,az)
CIE Chromaticity Diagram
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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
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CIE-RGB Primaries
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0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
C
BA
D65
20000
10000
8000
7000
60005000
400030002000
E
Blackbody Radiators andCIE standard Illuminants
CIE Standard Illuminants:A - tungsten lightB - Sunset C - blue skyD65 - Average daylightE - Equal energy white (x=y=z=1/3)
x
y
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Blackbody Radiators
Wavelength (nm)
Rel
ativ
e en
erg
y
3000K
3500K
9000K
http://www.olympusmicro.com/primer/java/colortemperature/index.html
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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
CIE Chromaticity + Gamut applet :http://www.cs.rit.edu/~ncs/color/a_chroma.html
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Signal Lights
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XYZ Color Space
Hue vs Saturation
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0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
Referencewhite
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.
550
630490
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0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
Referencewhite
Chromaticity in Polar Coordinates
Given a reference white.
Complementary Wavelength –wavelength of the spectral color which addedto the given color, produces the reference white.
570
485
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Chromaticity in Polar Coordinates
Given a reference white.
Purity –the ratio of the lengths between the given color andreference white and between the dominant wavelengthand reference white. Ranges between 0 .. 1.
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
Referencewhite
0.2
0.4
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0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
C
S1
D1
S2
D1‘
D2
S
Dominant Wavelength of color S1 is D1
of color S2 is D2.
Excitation Purity of S1 is the ratio CS1/CD1
of S2 is the ratio CS2/CD2
of S3 is the ratio CS3/CD3
EXAMPLE:
Reference white is CIE standard illuminant - C.
Complementary Wavelength of color S1 is D1.S2 does not have a complimentary wavelength.
‘
S3
D3
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Chromaticity in Polar Coordinates
0 0.2 0.4 0.6 0.80
0.2
0.4
0.6
0.8
reference white
purity
Dominant/complimentary Wavelength
X
Y
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Hue
Saturation
Brightness
Black
White
RG
B
Color Description
Hue (red, green, yelow, blue ...)
Saturation (pink,bright red, ....)
Lightness (black, grey, white ....)(Value)
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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 (neutral ... saturated)Value: i0 ... 10 (dark ... pure white)
/2 /4 /6 /8/10
1/
5/
10/
Valu
e
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
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Munsell Book of Colors
Atlas of thr Munsell Color System (1915)
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Color Polytopes
Applets:http://www.cs.rit.edu/~ncs/color/a_spaces.htmlhttp://www.nacs.uci.edu/~wiedeman/cspace/me/rgbhsv.html
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MayuraDraw
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PowerPoint
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Photoshop
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Color Picker
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Color Space Summary
Spectral Power Distribution (SPD) – High Dimensional
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.
3 Dimensional Spaces:
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