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Color Science

Uniform Color Spaces (Chapter 4)

1- Uniform Chromaticity Diagrams, 3- CIE Uniform Color Spaces 5- Comparing CIELAB and CIELUV Color Spaces, 7- Color Difference Equations Based on CIELAB 2- Uniform Lightness Scales (ULS), 4- Correlates Perceived Attributes 6- Converting of Color Difference,

and Measurement and Calculation of Colorimetric Values (Chapter 5)

1- Direct Measurement of Tristimulus values 3- General Conditions for Measurement 5- Colorimetric Values in CIELAB and CIELUV Uniform Color Spaces 2- Spectral Colorimetry

4- Calculation of Colorimetric Values

1

Color Science

The Most Important Drawback of CIEXYZ: "The system is not uniform!"

Equal distances in xy diagram do not mean equal perception for observers. Non uniform chromaticity diagram

Colors at the two ends are perceptually same

2

Color Science

Non Uniform Chromaticity Diagram

Wright experiment

(pairs have same perceived difference)

Just noticeable difference

Just noticeable difference in the wavelength of monochromatic light

3

Color Science

MacAdam's ellipses

(10 times magnification)

MacAdam's ellipses show:

MacAdam ellipses are far from being uniform Small difference of chromaticity coordinates is perceptible for bluepurple colors, while a difference in chromaticity coordinates of about 10 times that is hardly perceived for the green colors

Ideally the MacAdam ellipses should all be circles of same radius in the chromaticity diagram

4

Color Science

Totally the non uniformity of xy chromaticity diagram means:

Such space can not be directly employed for presentation the color differences between the samples

To change ellipses to circles

Stretching the CIEXYZ system

Squeezing the CIEXYZ System

Hence

Different mathematical conversions have been introduced to change CIExy to more uniform systems. Such systems are called

Uniform Color System, i.e. UCS

5

Color Science

CIE 1960 UCS Diagram

u= 4x 4X = (- 2x + 12 y + 3) (X + 15Y + 3Z) 6y 6Y v= = (- 2x + 12 y + 3) (X + 15Y + 3Z)

(A linear transformation), while Y is kept

And the shapes of ellipses

(Chromaticity diagram)

It seems that the ellipses become a bit closer to circles!

6

Color Science

CIE 1976 UCS Diagram

u = 4x 4X = (- 2x + 12 y + 3) (X + 15Y + 3Z) 9y 9Y = v = (- 2x + 12 y + 3) (X + 15Y + 3Z)

(A linear transformation), again Y is kept

And the shapes of ellipses

(Chromaticity diagram)

Still better but not good enough

7

Color Science

Uniform Lightness Scales (ULS)

Lightness is relative brightness, so

Brightness Lightness = Brightness ( White)

Lightness approximately could be expressed by "Y" And non pleasant fact: Y does not also have a uniform scale with respect to lightness

Munsell Value and Y

The figure shows the non uniformity of Y

8

Color Science

Conversion of Y and V

A fifth-order polynomial can estimate Y from Munsell value, V:

Y = 1.2219V - 0.23111V 2 + 0.23951V3 - 0.021009V 4 + 0.0008404V5

9

Color Science

Weber's Law

I = constant I

The equation is hold when a small change " I " in the intensity " I " of a stimulus is just noticeable Weber law could be improved to:

I S = k I

Where

S is the change in sensation and k is another constant

Weber-Fechner Law

I I

By integrating from S = k

I S = k log I 0

where I 0 is the minimum detectable stimulus value

10

Color Science

Weber-Fechner Law in luminance

11

Color Science

CIE Uniform Color Spaces

Uniformity in the chromaticity diagram, i.e. uv and u'v' systems, Uniformity in the lightness, Now, look for the

Uniformity in 3 dimensional color space

12

Color Science

There Are Several Types of UCS

They could be divided to

Linear and non linear transformation of CIEXYZ system The Genealogy of such transformation

13

Color Science

The Most Welcomed UCSs are:

CIE 1976 L*a*b* color space (abbreviated by CIELAB), and CIE 1976 L*u*v* color space (abbreviated by CIELUV)

Both are non linear transformation of CIEXYZ color space. (Neither them nor others satisfy perfect uniform chromaticity diagram)

14

Color Science

CIE 1976 L*a*b* color space

Its three-dimensional orthogonal coordinates are:

Y L* = 116 Y n

* 1

3

- 16

3

X a = 500 X n Y b = 200 Yn

*

1

Y - Y n Z - Z n

1

3

1

3

1

3

(Abbreviated by CIELAB)

841 X = 108 X n 841 Y = 108 Y n 841 Z = 108 Z n 16 + 116 16 + 116 16 + 116

Dark colors in CIEL*a*b* color space

When:

X Y Z 0.008856 , 0.008856 and 0.008856 (dark samples), then Xn Yn Zn

X f X n

Y L* = 116 f Y - 16 n X Y - f a * = 500 f Y n Xn b * = 200 Y f Y n - Z f Z n

While

Y f Y n Z f Z n

Where

XYZ: The tristimulus values of object

XnYnZn: The tristimulus values of source,

Hence, system is normalized to the employed light source

15

Color Science

CIELAB (CIEL*a*b*) View

Two important features of CIELAB system

Color opponencies

, .

Simple color adaptation

16

Color Science

CIE 1976 L*u*v* color space

Its three-dimensional orthogonal coordinates are:

Y 3 L = 116 Y - 16 n u * = 13L* (u - u n )

*

1

v = 13L (v - vn )

* *

While,

u =

4x 4X = (- 2x + 12 y + 3) (X + 15Y + 3Z) 9y 9Y = v = (- 2x + 12 y + 3) (X + 15Y + 3Z)

(Abbreviated by CIELUV)

17

Color Science

CIELAB Color System Is Usually Used for

Surface color

while

CIELUV Color System Is More Practical in

Colored lights, such as TVs, monitors, illuminations

18

Color Science

Color Difference Formula (CIELAB)

The most generally accepted color difference formula (also the base for several new color difference formulas)

E

* ab

= (L *) + (a *) + (b *)

2 2

{

2 1/ 2

}

L* = L* - L*2 1

where,

* a * = a 1 - a * 2

b =

*

* b1

- b* 2

Color Difference Formula (CIELUV)

E

* uv

= (L *) + (u *) + (v *)

2 2

{

2 1/ 2

}

where

L* = L* - L*2 1

* u * = u1 - u * 2

v =

*

* v1

- v* 2

19

Color Science

CIE 1976 Lightness

Y L* = 116 Y n

1/ 3

- 16

for non dark samples

Y 841 X 903.3 L* = 116 Y for dark samples 108 X n n

20

Color Science

CIELAB Metric Chroma, C*

Metric distance from origin in a*b* chromaticity diagram:

C = a

* ab

{(

* 2

) + (b ) }

* 2

1

2

CIELAB Hue Angle, ho

b* h ab = tan -1 * a

21

Color Science

In Three Dimensional Space

22

Color Science

CIELAB Metric Hue, H*

H = 2 C

* ab

(

* ab ,1

C

* ab , 2

)

1

2

h sin ab 2

* If E ab would be available:

H = E

* ab

{(

* 2 ab

) - (L ) - (C ) }

* 2 * 2 ab 1 2

Its sign is positive if hoab is positive and negative if hoab is negative

23

Color Science

Color Difference Formulas

CIELAB color difference formula can be written as

E = L

*

{(

* 2

) + (C ) + (H ) }

* 2 * 2

1

2

, too.

* * However, the values of L , C and H* are not equal for normal

observers. They could be weighted, by different weights:

L* 2 C* 2 H * 2 * + + E = l c h

1 2

24

Color Science

Small Color Difference Formulae Based on CIELAAB

Different weights have been applied to improve the CIELAB color difference formula. The general form of such formulas is:

L* 2 C* 2 H* 2 ab ab E = k S +k S +k S L L C C H C

1/ 2

This type of formula could be applied when two sample have small color difference value.

25

Color Science

CIE94 Color Difference Formula

The values of constants in this formula are:

SL = 1

SC = 1 + 0.045C* , and, ab

SH = 1 + 0.015C* ab

Where the values of

KL , KC

and

KH

depend to the nature of samples as well

as the types of evaluation, i.e. perceptibility or acceptability criteria.

26

Color Science

Uniformity of CIELAB and CIELUV Color Spaces

Both are absolutely better than CIEXYZ color space.

The uniformity of them were approved by plotting the MacAdam ellipses in a*b* as well as u*v* chromaticity diagrams

.

Uniformity of ellipses in a*b* diagram

Uniformity of ellipses in u*v* diagram

27

Color Science

Uniformity of Munsell Chips in a*b* Diagram

Munsell samples of value 5

Uniformity of Munsell Chips in u*v* Diagram

Munsell samples of value 5

28

Color Science

Measurement and Calculation of Colorimetric Values

Definition of color measurement,

Measurement is possible:

Directly by Colorimeters, Indirectly by Spectrophotometers and Spectroradiometers

To measure:

Tristimulus values, chromaticity coordinates, ...

29

Color Science

Direct Measurement of Tristimulus Values

Luther condition?

Luther condition can be provided by: 1- Template method 2- Optical filter method

Indirect Measurement

Spectral colorimetry

30

Color Science

Template Method

Using 3 different templates placing in spectrum

31

Color Science

Optical Filter Method

Duplication of color matching functions Serial arrangement Parallel Arrangement

32

Color Science

Spectral Colorimetry

Spectrophotometers for indirect measurement

33

Color Science

Radiance Factor, Reflectance Factor and Reflectance

34

Color Science

Geometrical Conditions for Measurement

35

Color Science

Standard CIE Geometrical Condition for Measurement of Reflecting Objects

36

Color Science

Standard CIE Geometrical Condition for Measurement of Transmitting Objects

37

Color Science

Calculation of Colorimetric Values

XYZ Tristimulus values Dominant wavelength and excitation purity CIELAB and CIELUV tristimulus values Metric chroma (C*), hue angle (ho) and Metric Hue (H*) Color difference value

38

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