GEK1532 Color Classification (CIE)

8/6/2019 GEK1532 Color Classification (CIE)

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GEK1532

Color (Hue) Classification Systems

Thorsten Wohland

Dep. Of ChemistryS8-03-06

Tel.: 6516 1248

E-mail: [email protected]


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remember metamerism?T.N. Cornsweet, Fig. 8.7

How to mix colors?

Can a specific color

be mixed by two other

colors?


3/37

T.N. Cornsweet, Fig. 8.8


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Lets take a look at the

Mathematics

32

32

32

32

BBB

AAA

SISID

SISID

+=+=

1

1

1

1

BB

AA

SID

SID

=

=

2AS

2BS

3AS

3BS

nI : intensity at wavelength n

nXS

: sensitivity of cone X at wavelength n

1BS

1AS


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132

132

132

132

BBB

AAA

SISISI

SISISI

=+

=+

132

2

31

13

31

BBB

A

AASISIS

S

SISI=+

2

31 31

2

A

AA

S

SISII

=

13

2

23

2

21

1331

BB

A

BA

A

BA

SISIIS

SS

IS

SS

=+

31 3

2

23

1

2

21

ISS

SSIS

S

SSB

A

BA

B

A

BA

=

13

3

2

23

1

2

21

I

SS

SS

SS

SS

I

B

A

BA

B

A

BA

=


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12

2

3

3

2

23

1

2

21

2

1

I

S

S

SS

SS

SS

SS

S

SI

A

A

B

A

BA

B

A

BA

A

A

=

2

31 31

2

A

AA

S

SISII

=

12

2

3

3

2

23

1

2

21

2

1

IS

S

SS

SS

SS

SS

S

SI

A

A

B

A

BA

B

A

BA

A

A

=

13

3

2

23

1

2

21

I

S

S

SS

SS

SS

I

B

A

BA

B

A

BA

=

13

3

2

23

1

2

21

I

SS

SS

SS

SS

I

B

A

BA

B

A

BA

=


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12

2

3

3

2

23

1

2

21

2

1

IS

S

SS

SS

SS

SS

S

SI

A

A

BA

BA

B

A

BA

A

A

=13

3

2

23

1

2

21

I

SS

SS

SS

SS

I

BA

BA

B

A

BA

=

If we put in now the numbers from the graph:

photonsII710710

13 == .

photonsII 128028112==

.

4801

.=A

S 1601

.=BS

103

.=A

S

4302

.=A

S 33002

..=B

S

3703

.=B

S

photonsI 10001 =


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Color Discrimination

1.0

0.8

wavelength

S

ensitiv

ity(pro

ba

bilityofabso

rpt

ion)

Ratio of the sensitivities is different for every wavelength. Therefore awavelength can be identified by the ratio of excitation of two different cones.

B/R = 0.33/0.03 = 11

B/R = 0.33/0.62 = 0.53

1

0.33

0.03

2

0.62


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Review: Cone Sensitivities

Assume we have an

array of cone pairs

Image

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

00.5

0.5

0.5

0.5

0.5 0.5 0.5 0.5 0.5

Ratio of excitation of

cones in a pair

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

00.5

0.5

0.5

0.5

11 11 11 11 11


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No overlap of sensitivity curves

The overlap of sensitivity curves of cones is necessary for color

discrimination. If there is no overlap the eye would work like a

monochromat in the different spectral regions.

B = 0

R > 0

B > 0

R = 0

B/R=

R/B=0

B/R=0

R/B=


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Cone sensitivity and color

For a dichromat:

In a 2D plot we can find for every

wavelength one point which represents

how much each cone is excited by light

of this wavelength. The two axisrepresent the excitation of the two cones.

The curve seen here represents the

pure spectral hues (only one

wavelength) of a standard number of

photons and how they are perceived bytwo different cones of a dichromat.

The dashed line represents light of 620 nm at different intensities.

T.N. Cornsweet, Fig. 8.12b


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Cone sensitivity and color

What happens when we have light of two wavelength?

T.N. Cornsweet, Figs. 8.13a and e


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Coming back to gamut


Note: With light of two

wavelength we can mix almost

all colors for the dichromat.


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Sensitivity Curve 2D color graph

1.0

0.8

0.6

0.4

0.2

Cone A

ConeB

0.5 1.0

0.5

1.0


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2D color graph constant

excitation

Cone A

ConeB

0.5 1.0

0.5

1.0

For the blue line the sum of

excitation of Cone A and B is

always constant (in this

example Cone A + Cone B is

always 0.5).

Along the dashed line(s) only

the intensity changes but not

the ratio of excitation of

Cone A and B.

The blue point(s)

represent a certain

color (i.e. ratio of cone

excitations) at a

constant overall

excitation (x+y)

x

y


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2D color graph constant

excitation

Since x+y=0.5 :

It follows that if we know x then we know y=0.5-x

Example: x = 0.2, then y = 0.5 - 0.2 = 0.3

Cone A

ConeB

0.5 1.0

0.5

1.0

x

y

0.2

0.3


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For a Dichromat:

T.N. Cornsweet, Fig. 8.12b

This axis

represents the

possibleexcitation

values for

cone B, i.e.

the number of

photons

absorbed.

This axis represents the possible

excitation values forcone A, i.e. the

number of photons absorbed.

This curve represents

the possible ratios a

single wavelength can

elicit in your two cone

system for a constant

number of photons.

The dashed line

represents a constantratio but different

total intensities

This line represents

a constant

number of

absorbed photons


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Sensitivity space color space

For a trichromat we can create a similar plot, but now in 3D.



19/37


Here again we see that given three wavelength (pure spectral hues) which we

can vary in intensity, we can reproduce any other color within the pyramid (thegamut) they describe with the origin.



20/37


Now let us describe planes where the sum of the absorbed photons ofall three cones is always constant.



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Constant intensity

Constant number of photons

c

hhE ==

W1210330 .=

1

10600

1031063610

9

8

346.

Light source

Light of ONE wavelength = 600 nmcomes from this light source with a

constant numbern = 106 photons per

second

The light beam has a cross section ofA = 1 mm2

AreaTime

EnergyIntensity

=

== Ahc

nI


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Constant intensity


W1210410.=

+

110400

10

10600

1010636103

9

6

9

6

348.

Light source

Light of TWO wavelength

1 = 600 nm (n1 = 0.5*106 ) 2 = 400 nm (n2 = 0.5*106)

A = 1 mm2

=

+= A

nn

nhcI

2

2

2

1

1

Note: The number of photons is constant but the intensity has changed

since the photons have different wavelength. The photons at 400 nm

have a higher energy than the photons at 600 nm and thus the intensity

has increased.


23/37

Constant intensity


Constant stimulation

Light source

What happens now in the eye? The stimulation in the eye depends on

HOW MANYPHOTONS ARE ABSORBED.

If the beam of light (A = 1 mm2) is imaged by the eye on the retina it hits

lets say, 10,000 cones (5,000 blue cones and 5,000 red cones). So

every cone receives 100 photons.

One wavelength, = 600 nmn = 1,000,000

1.0

0.8

0.9

0.2

0.9*100=90 photons absorbed (red)

0.2*100=20 photons absorbed (blue)


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Constant intensity


Constant stimulation

Light source

So we have seen the following:

1) Constant number of photons does not necessarily mean constant

intensity (only when a single wavelength is present would that be

true).

2) The stimulation in your eye depends on the number of photons

absorbed

Accordingly we have two systems of color classification systems:

1) Based on intensity (CIE, see left side)

2) Based on number of photons absorbed (physiological system, see

right side)


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For a trichromat

T.N. Cornsweet, Fig. 8.18 T.N. Cornsweet, Fig. 10.2

This curve represents the possible

ratios a single wavelength can

elicit in the three cone system for a

constant number of photons.

This plane is for a constant

stimulation, a constant number

of absorbed photons.


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All rights reserved.

Information is provided "As Is" without warranty of

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that this notice is included on such copy.


Differences:CIE is derived form color mixture data of three wavelength

Fig. on right is derived for measured sensitivities of the eye

CIE is derived for constant energy

Fig. on right is derived for constant number of photons

hc

hE ==


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For a trichromat


This plane is for a constant

stimulation, a constant number

of absorbed photons.


28/37

The normalization for the CIE color

space

We have here three different colors in the three lines. Within each line the color

does only change in brightness, that is the relative amount of red green and

blue (RGB) mixed is the same but the absolute amount differs.

R:G:B = 1 : 0.125 : 1

R:G:B = 0.125 : 1 : 1

R:G:B = 1 : 1 : 0.125


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Normalization

BGR

Bb

BGR

Gg

BGR

R

r

++=

++=

++=

1=++

++

BGR

BGR

=++ bgr

Assume you characterize a color by three intensity values for the primarycolors. The ratio of the intensity values tells you in which amount you have

to mix the three primaries to arrive at you color.

R : G : B

167 : 167 : 21

R : G : B

200 : 200 : 25

R : G : B

240 : 240 : 30

=++

+++

+++ BGR

B

BGR

G

BGR

R


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Normalization

1=++ bgr

Assume you characterize a color by three intensity values for the primarycolors. The ratio of the intensity values tells you in which amount you have

to mix the three primaries to arrive at you color.

R : G : B

167 : 167 : 21

R : G : B

200 : 200 : 25

R : G : B

240 : 240 : 30

grb

gr

=1,


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BGR

Bb

BGR

Gg

BGRRr

++=

++=

++=

058.0125.2

125.0

471.0125.2

1

471.0125.2

1

510

240

425

200

355

167

=

=

====

b

g

r

1058.0471.0471.0

1

=++

=++ bgr

Relative values

R:G:B = 1 : 1 : 0.125 167 : 167 : 21 200 : 200 : 25 240 : 240 : 30

Absolute values for R:G:B

(from Adobe Illustrator on a scale form 0-255):


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Gamut in the CIE system

Fig. 1-10 of Nassau


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Problem

All possible mixtures of these

wavelength lie within this curve.

E.g. All mixtures of blue at 380 nmand red at 780 nm lie on the

connection line of the ends of the

horseshoe, giving us purple

colors.

Within this system we can classifyall colors. And we can determine

as well the possible mixtures of

any colors in the system

In the CIE system we marked all naturally occurring wavelength on a horseshoe

shaped curve. Each point indicating the color we perceive at that wavelength. Forthis purpose we needed only 2 values (the x-y axes) since we normailzed the

system to a constant intensity.


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Color Classification Systems

Websites:

http://www.colorcube.com/articles/models/model.htmhttp://www.colorcube.com

http://www.cie.co.at/cie/

http://www.adobe.com/support/techguides/color/colormodels/

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Books:

The Physics and Chemistry of Color, Kurt Nassau, John Wiley, QC495Nas:RBR

Color Vision and Colorimetry, Daniel Malacara, SPIE press, QP483 MAL 2002 (CL)


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Early systems

Aristotle: Color Sphere

Nassau, Fig. 1.1

Blue

Green

Red

CyanYellow

Magenta

White


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Tristimulus theory

There are 3 cell types called cones in

the retina that have different

sensitivities over the electromagnetic

spectrum.

Arbitrar y

Units

Depending on the amount of

activation of these cones, different

colors will be seen.

These curves are not to scale!


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Summary

Mixing of one color with two others (see as

well Metamerism).

Discrimination of color by the eye

Chromaticity diagram (dichromat,

trichromat)

Normalization to get a 2D plot for a

trichromat

GEK1532 Color Classification (CIE)

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