Chromaticity defined in Polar Coordinates Given a reference white. Dominant Wavelength - wavelength of the spectral color which added to the reference white, produces the given color.
Relationship between HSV and XYZ Y vs V : Luminance (intensity) vs Brightness (Lightness)
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.
0.8 Dominant/complimentary Wavelength
0.6
Luminance
Complementary Wavelength - wavelength of the spectral color which added to the given color, produces the reference white.
∆I2 ∆I1
I1 < I2, ∆I1 = ∆I2 purity
0.4
Equal intensity steps:
reference white
0.2 Equal brightness steps:
0
I1
0
0.2
0.4
0.6
0.8
I2
Weber’s Law
Munsell lines of constant Hue and Chroma. 0.5
0.4
In general, ∆I needed for just noticable difference (JND) over background I was found to satisfy: ∆I = constant I
0.3
y 0.2
0.1
(I is intensity, ∆I is change in intensity)
Value =1/ 0
Weber’s Law: Perceived Brightness = log (I)
0
0.1
0.2
0.3
x
0.4
0.5
0.6
MacAdam Ellipses of JND (Just Noticable difference)
Perceived Brightness
0.8
0.6
y (Ellipses scaled by 10)
0.4
0.2
Intensity 0
0
0.2
0.4
x
0.6
CIE- UVW Coordinates
Munsell lines of constant hue and chroma plotted in CIE-uv coordinates:
The transformation from XYZ space to perceptual space is Non Linear:
0.4
Linear approximation defined by CIE: CIE Uniform Chromaticity Scale (UCS) : v
U= 2X 3 V=Y
=
0.66 0 0 0 1 0 -0.5 1.5 0.5
CIE-uv Chromaticity Coordinates: u=
4x -2x + 12y + 3
v=
6y -2x + 12y + 3
0.2
0.1
-X + 3Y + Z W= 2 U V W
0.3
0
X Y Z
0
Value =1/ 0.1
0.2
0.3
0.4
u
0.5
0.6
Perceptual Color Spaces
Munsell lines of constant hue and chroma plotted in CIE- L*u*v* Coordinates: 100
The transformation from XYZ space to perceptual space is Non Linear:
Value =5/ 50
CIE- L*a*b* Coordinates
v*
a* = 500 [ (X/X0) 1/3 - (Y/Y0)1/3]
0
-50
b* = 200 [ (X/X0) 1/3 - (Z/Z0)1/3] L* =
116(Y/Y0)1/3 - 16 903(Y/Y0)
for Y/Y0 > 0.01 otherwise
X0 Y0 Z0 = coordinates of reference white
-100
-150 -150
u* = 13 L*(u’-u0’)
903(Y/Y0)
0
50
100
150
u*
100
v* = 13 L*(1.5v’-v0’) L* =
-50
MacAdam Ellipses of JND plotted in CIE- L*u*v* Coordinates:
CIE- L*u*v* Coordinates
116(Y/Y0)1/3 -
-100
50
16
for Y/Y0 > 0.01 otherwise
u0 v0 Y0 = coordinates of reference white u‘ = u v‘ = 1.5 v
Ewald Hering (1905) - Pure colors R G B Y. No such colors greenish-red, yellowish-blue
S
M
L
L and M cone sensitivities are highly correlated.
0.75 0.5 0.25
Hue Cancellation Experiment
0
400
500
600
700
Wavelength (nm)
cancelling light Cone responses to several Natural SPDs :
1
0.75
+
-
S-cone absorption
+
M-cone absorption
test light
1
0.75
0.5
0.25
0.5
0.25
0.25
0.5
0.75
1
L-cone absorption
0.25
0.5
0.75
1
M-cone absorption
Opponent Color Space Decorrelation: O1 O2 = O3
0.30 0.59 0.11 0.60 -0.47 -0.22 0.21 0.52 -0.31
R G B
+ Spectral sensitivity of three decorrelating signals:
1
Blue-Yellow
-
Red-Green
+
Black-White
1.5 0 -0.5 400
500
600
700
Opponent Color Space
+ black-white
+ blue-yellow
-
+ red-green
-
YIQ - Color Space NTSC = National Television Systems Committee Y = luminance I = red-green Q = blue-yellow
Y I Q
0.177
0.813
0.011
0.246 -0.675
0.404
= 0.540 -0.263 -0.174
R G B are the CIE-RGB
R G B
Subtractive Color System - CMYK Original
Y - Blur
Printer Dyes: Cyan
= removes red
Magenta = removes green Yellow
= removes blue
blacK
= removes all
Ideal block dyes:
I - Blur
Q - Blur
magenta
yellow
transmit
cyan
B
G
R
B
G
R
B
G
R
Opponent Color Wheel
Multiplicative (Subtractive) Color System red = magenta + yellow B
magenta
*
B
G
R
B
G
R
B
G
R
G
R
yellow
= red
Additive primaries Subtractive Primaries
red = magenta + yellow green = cyan + yellow blue = magenta + cyan
R
Cyan - controls amount of red in print: low C = high R (also high G and B) high C = low R (high G and B) cyan
B
G
R G
R
B
High density cyan
R G
B
Medium density cyan
R G
B
Low density cyan
CMY + Black C + M + Y = K (black) • Using three inks for black is expensive • C+M+Y = dark brown not black • Black instead of C+M+Y is crisper with more contrast. Undercolor removal (gray component replacement)
= 100 50 70 C M Y
+ 50 K
50 0 20 C M Y
Color Spaces - Summary RGB space - Additive space used for CRT, Color Image representation CIE-XYZ Tristimulus Coordinates Device Independent, Universal standard CIE-Lab - Perceptual Space, used for image quality, Image Metric (distance measure). YIQ - Opponent Space, used for color television broadcast. HSV - Perceptual Digitized Space, used for Human Interactive Painting. CMYK - Subtractive Space used for ink and dyes (printing).
All these color spaces are 3D. There are conversions from one space to the other.
