Light and Color
• Light : physical– Light is a electromagnetic wave– Physically, there is no concept of “color”
(distribution with respect to the wavelength)
• color : psychological– One aspect of perception of the light– Relative intensity of three ranges of
wavelength
To learn about color, we must learn about human
eyeball• diameter
24mm
• Flexible lens (crystalline)
• Iris = aperture
• Focal length = 17mm
• Retina : film or CCD
Fovea
Retina
• Two types of photo receptor– Rod :
monochromatic, high response, work in dark environment
– Cone : three types (L, M, S) : colorlow response, work only at bright environment
How to identify the color perception?
How to measure the relationships between wavelength and color perception
• Measuring signals of neurons– Not easy– Perception is not directly related to signal
• Subjective tests– Comparing very single spectral light with
additive color mixture– Ambiguity of coordinate transform remains
Color matching experiment(1)
• Adjust the levels of R, G, B so as to match to monochromatic light– R : 700nm G : 546.1nm B : 435.8nm
Negative response
Color matching (2)
• Negative value means the light at opposite side
All in positive ith negative values
Why we have “negative values”?
• No negative response at our retina
wavelength
sensitivity
wavelength
intensity
L(λ)M(λ)S(λ)
change
i(λ)
×L
S=∫S(λ) ・ i(λ)dλ
Mλ
Smooth curve in positive region
Actual spectral response(unknown)
Sample stimulus
• R>0, G=B=0 when i = 700nm(R)– RGB space is smaller than the original space
with our actual sensitivity. Therefore, between the wavelength of B and G, R should be negative
L
S
Mλi
i=B
i=G
i=R
B
G
R
Why we have “negative values”?
rg chromaticity coordinate
• rg : chromaticity : Relative values of RGBr = R/(R+G+B), g = G/(R+G+B)
Single wavelength passes three points (r,g)=(0,0), (0,1), (1,0)
L
S
Mλ
i=B
i=G
i=R
B
G
R
R
B
G
rg
Linear trransform
rg chromaticity and RGB color matching curve
• All three values have negative regions
XYZ color space• To avoid the negative
values of RGB color space
New coordinate system which includes the spectral curve in positive areaThree points, X, Y, Z, is outside of spectral curve, so, it does not physically exist called as”imaginary color”
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
B
G
R
Z
Y
X
5943.50565.00000.0
0601.05907.40000.1
1302.17517.17689.2
XYZ color matching function
0
0.5
1
1.5
2
380410440470500530560590620650680710740770Wavelength (nm)
x_bar(l)y_bar(l)z_bar(l)
CIE1931 XYZ color matching function
xy chromaticity• Relative value
of XYZ• x = X/(X+Y+Z),
y = Y/(X+Y+Z)• Black curve :
black body radiation (related to the color temperature)
xy chromaticity and brightness
• Reflectance is limited to 1.0 or below– White is brightest– Intensity of the boundary
of spectral curve is 0– Called MacAdam limit
White light source
intensity
Object with various color
Color reproduction and gamut (1)
• Range of additive color is limited in the triangle which verteces are primal colors
• Called gamut• left figure indicates
the range of RGB tristimulus
Display and color reproduction
s
• Range of the color depends on the primal colors
• “RGB” of PC is not CIE RGB
• Wrong use of color space causes the color mismatch
Printing and color
• Printing is subtractive color (CMY)
• Inside the convex hull which defined by 6 points of C, M, Y, CM,CY, MY
• RGB and CMY have different gamut
• Convex hull of 6 primal colors
White material (paper)
cyan=G+B
magenta=R+B
yellow=R+G yellow=R+G
cyan green black blue magenta red yerrow white
・ spectral reflectance of green yellow ≒ ・ cyan → spectral reflectance of green is linearly independentfrom yellow and cyan
・ represented by halftone dot → mixture of 8 colors above
Halftone dot
Color space matched for perception
• HSB color space– Polar coordinate– HSB (Hue, Saturation,
Brightness)
• xy color space– Perceptually not
uniform– MacAdam ellipse
L*a*b* color space
• Perceptually uniform color space by nonlinear transform ⎥
⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
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⎞⎜⎜⎝
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⎠
⎞⎜⎜⎝
⎛=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛=
−⎟⎟⎠
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3
1
3
1
3
1
3
1
3
1
200*,500*
16116*
nnnn
n
Z
Z
Y
Yb
Y
Y
X
Xa
Y
YL
`erception R
`erception G
Perception B
Metamerism
• Visually same color but different spectral curve
• Depends on not only the object but also the light source
Light 1 Object 1× Perception R
Perception G
Perception BLight 2 Object 2×
same
same
same
Spectral sensitivity and evaluation of color
• If the spectral sensitivity of the sensor is different from the human beings, color matching fails
• If the spectral curve of light source is special, color matching fails (object with different colors seems same)
• ( fluorescent light is not good as light bulb)