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V'(l) V(l)
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wavelength (nm)
Con
e r
esp
on
se
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Trichromacy
• Helmholtz thought three separate images went forward, R, G, B.
• Wrong because retinal processing combines them in opponent channels.
• Hering proposed opponent models, close to right.
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Opponent Models
• Three channels leave the retina:– Red-Green (L-M+S = L-(M-S))– Yellow-Blue(L+M-S)– Achromatic (L+M+S)
• Note that chromatic channels can have negative response (inhibition). This is difficult to model with light.
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wavelength (nm)
RedGreen L-M+S BlueYellow L+M-S
Achromatic L+M+.05*S
Schematic color opponent response
+- +
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-0.5
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V(l)
wavelength (nm)
RedGreen L-M+S BlueYellow L+M-S
Achromatic L+M+.05*S
Schematic color opponent response
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-1 0 1 2
Log Spatial Frequency (cpd)
Con
tras
t Sen
siti
vity
Luminance
Red-Green
Blue-Yellow
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Color matching
• Grassman laws of linearity:()(l(l(l
ll• Hence for any stimulus s(l) and response
r(l), total response is integral of s(l) r(l), taken over all l or approximately s(l)r(l)
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Primarylights
Test light
Bipartitewhitescreen
Surround field
Test light Primary lights
Subject
Surround light
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Color Matching
• Spectra of primary lights s1(l), s2(l), s3(l)
• Subject’s task: find c1, c2, c3, such thatc1s1(l)+c2s2(l)+c3s3(l)
matches test light.
• Problems (depending on si(l))
– [c1,c2,c3] is not unique (“metamer”)
– may require some ci<0 (“negative power”)
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Color matching
• What about three monochromatic lights?• M(l) = R*R(l) + G*G(l) + B*B(l)• Metamers possible• good: RGB functions are like cone
response• bad: Can’t match all visible lights with any
triple of monochromatic lights. Need to add some of primaries to the matched light
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Primarylights
Test light
Bipartitewhitescreen
Surround field
Test light Primary lights
Subject
Surround light
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Color matching
• Solution: CIE XYZ basis functions
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z
y x
CIE 1931 standard colorimetric observer color matching functions
Tris
timul
us v
alue
wavelength (nm)
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Color matching
• Note Y is V(l)
• None of these are lights
• Euclidean distance in RGB and in XYZ is not perceptually useful.
• Nothing about color appearance
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3.5Stiles and Burch 1959 10-degree bipartite field color matching functions
primary lights at 645.2 nm 525.3 nmand 444.4 nm
b10(l) g10(l)
r10(l)