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Psychophysical fundamentals of colorimetry

The concept of colour

Colour can be perception – psychological phenomenon colour stimulus – psychophysical

phenomenon radiometry - physics photometry – one dimension of colour

stimulus description

Colorimetry

Additive colour mixture

Colour mixing

Additiv subtractiv colour mixing

Grassmann’s lawsGrassmann’s laws

To specify a colour match three independent variables are necessary and sufficient

For additive mixture of colour stimuli, only their tristimulus values are relevant, not their spectral composition

In additive mixtures of colour stimuli, if one or more components are gradually changed, the resulting tristimulus values also change gradually

Colour equation - 1

Positive additivity C R G B B R G

Colour equation - 2

External colour mix - negative additivity C R G B R G B

Additiv colour matching

Additivity: IfC1R1(R)+G1(G)+B1(B)

C2R2(R)+G2(G)+B2(B)

thenCR(R)+G(G)+B(B),

where R= R1+ R2, G= G1+ G2, B= B1+ B2,

Additiv colour matching

ProportionalityIfC1R1(R)+G1(G)+B1(B)

thenaC1aR1(R)+aG1(G)+aB1(B)

The stronger form of trichromatic generalisation - 1

1/ symmetry law: If colour stimulus A matches colour stimulus B, then colour stimulus B matches colour stimulus A.

2/ transitivity law: If A matches B and B matches C, then A matches C

3/ proportionality law: If A matches B, then aA matches aB, where a is any positive factor.

The stronger form of trichromatic generalisation - 2

4/ additivity law: If A, B, C, D are any four colour stimuli, then if any two of the following three conceivable colour matches hold:

A B C D A C B D , , ( + ) ( + )

then so does the remaining match

C) (B D) (A

Composit spectrum - 1

Sum of colour stimuli: the power radiated in the single spectrum bands

6 0 04 0 0 5 0 0

r e l . i n t .

w a v e l e n g t h , n m7 0 0

Composed spectrum - 2

For one wavelength band

Composed colour stimulus:

Colour matching

R = SR()

G = SG()

B = SB()

drSkR )(

dgSkG )(

dbSkB )(

Colour equation

Integral form:

with three t values

Three real primaries with L = 1,000R + 4,5907G + 0,601B

T k ti i enm

780nm

d 380

( ) ,

R, G, B colour space

RGB - XYZ transformation

wavelength, nm

rel.

sen

s.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

350 400 450 500 550 600 650 700 750 800 850

x2(lambda)

y2(lambda)

z2(lambda)

A new system of colorimetry?

TC 1-36: Physiologically significant ...

-8

-7

-6

-5

-4

-3

-2

-1

0

1

350 450 550 650 750

wavelength, nm

log

co

ne

ac

tio

n s

en

sit

ivit

y

L-cone

M-cone

S-cone

Improved colorimetry?Improved colorimetry?

Luminance-brightness discrepancy

Additivity problemsNew colour matching functions?Individual variationsHighly metameric matchesColour appearance models

TC 1-36: Physiologically significant ...

L, M, S primaries based on psychophysical measurements:

König hypothesis - congenital dichromats

Photopigment spectral absorbance

Selective absorption by the lensSelective absorption by the

macular pigment

Further issues to be described

Lightness contrast

Colour contrast

Assimilation