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V'(l) V(l)
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wavelength (nm)
Con
e r
esp
on
se
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.
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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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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Log Spatial Frequency (cpd)
Con
tras
t Sen
siti
vity
Luminance
Red-Green
Blue-Yellow
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)
Primarylights
Test light
Bipartitewhitescreen
Surround field
Test light Primary lights
Subject
Surround light
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”)
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
Primarylights
Test light
Bipartitewhitescreen
Surround field
Test light Primary lights
Subject
Surround light
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)
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)