4.2 Cielab Model

Forward conversion equations

Input data:

– CIE 1931 tristimulus values of the sample;

– CIE 1931 tristimulus values for reference white_.

The lightness of stimulus is defined as follows:

(4.1)

Opponent axes:

(4.2)

where

(4.3)

(4.4)

(4.5)

Chroma:

(4.6)

Hue:

(4.7)

Inverse conversion equations

Input data:

– stimulus coordinates in CIELAB system or

– lightness, chroma and hue of stimulus in CIELAB system

– CIE 1931 tristimulus values for reference white.

In case when the hue and chroma are specified stimulus coordinates in system are defined as:

(4.8)

To obtain values it is necessary to use the following equations:

(4.9)

(4.10)

(4.11)

(4.12)

(4.13)

(4.14)

4.3 Cieluv Model

Forward conversion equations

Input data:

– CIE 1931 tristimulus values of the sample;

– CIE 1931 tristimulus values for reference white_.

Stimulus lightness is defined as follows:

(4.15)

(4.16)

Opponent axes:

; (4.17)

Chroma:

(4.18)

Hue:

(4.19)

Inverse conversion equations

Input data:

– stimulus coordinates in CIELUV system or

– lightness, saturation and hue of stimulus in CIELUV system

– CIE 1931 tristimulus values for reference white.

In case when the hue and saturation are specified stimulus coordinates in system are defined as:

_(4.20)

For stimulus color coordinates calculation in CIE 1931 it is necessary at first to calculate the values of reference white in system using the following equations:

(4.21)

(4.22)

(4.23)

(4.24)

(4.25)

4.4 Ciecam02 Model

Forward conversion equations

Input data:

– CIE 1931 tristimulus values of the sample_;

– CIE 1931 tristimulus values for reference white;

_{, – surround white luminance;}

_{, – reproduced image white luminance;}

_{, –} adapting luminance. If data on adapting luminance are not available it is recommended be taken to be equal to_:

(4.26)

_{– surround impact factor}

_{– chromatic induction factor}

_{– factor for degree of adaptation}

_{– relative luminance of the background. If the value of this parameter is unavailable it can be adopted to be equal to:}

(4.27)

If data on , and are unavailable they can be chosen as follows.

Categorical viewing conditions settings for the model

Viewing condition
Average surround	0.69	1.0	1.0
Dim surround	0.59	0.9	0.9
Dark surround	0.525	0.8	0.8

Surround type may be defined via such a relationship:

(4.28)

The value corresponds to dark surround, to dim one and to average one.

The cone responses are:

(4.29)

here

(4.30)

The degree of viewer’s adaptation:

(4.31)

The adaptation transform is:

(4.32)

(4.33)

(4.34)

(4.35)

(4.36)

(4.37)

The transformation to Hunt-Pointer-Estevez cone responses is conducted as follows

(4.38)

(4.39)

(4.40)

The nonlinear response compression transform is:

(4.41)

If any of values of are negative then their absolute values are used and then the corresponding quotient term in Equations (4.41) must be multiplied by a negative 1 before adding the value 0.1.

Opponent axes:

(4.42)

Hue angle:

(4.43)

(4.44)

(4.45)

Eccentricity factor:

(4.46)

Color quadrature may be obtained via linear interpolation method:

(4.47)

using the values of unique hues shown in Table below. Here if , and else wise.