Unique hue data for the calculation of hue quadrature

	Red	Yellow	Green	Blue	Red
	1	2	3	4	5
	20.14	90.00	164.25	237.53	380.14
	0.8	0.7	1.0	1.2	0.8
	0.0	100.0	200.0	300.0	400.0

The achromatic response is:

(4.48)

The lightness is:

(4.49)

The brightness is:

(4.50)

The chroma is:

(4.51)

here

(4.52)

The colorfulness is:

(4.53)

The saturation is:

. (4.54)

CIECAM02 includes three attributes in relation to the chromatic content: chroma (C), colorfulness (M) and saturation (s). These attributes together with lightness (J) and hue angle (h) can form three colour spaces , where

CIECAM02 chromaticity diagram

CIECAM02 chromaticity diagram is presented in Figures 4.1, 4.2 and 4.3 [4.6]. The figures demonstrate the dependence of colour appearance on adaptation level L_A and relative luminance level Y. It is seen from this figures that a variation of adapting luminance level may lead to significant colorfulness variation, and that variation of colorfulness increases with stimulus relative luminance growth.

Inverse conversion equations

First it’s necessary to compute surround-dependent parameters and achromatic response for reference white by using forward conversion. Lightness value can be obtained from brightness by using the following equation:

(4.55)

The chroma is:

(4.56)

If starting from lightness, the brightness can be calculated:

(4.57)

If saturation is known the chroma is defined as follows:

(4.58)

If hue quadrature data is available the hue angle can be calculated using unique hue data for the calculation of hue quadrature as:

(4.59)

here , if , otherwise

(4.60)

The eccentricity factor is:

(4.61)

The achromatic response is:

(4.62)

The following relationships are used for obtaining and values:

(4.63)

(4.64)

(4.65)

(4.66)

if , then:

(4.67)

(4.68)

(4.69)

if , then:

(4.70)

(4.71)

(4.72)

The cone responses are:

(4.73)

(4.74)

If any of the values of are negative, then the corresponding value must be negative.

(4.75)

(4.76)

(4.77)

Tristimulus values of the sample then are:

(4.78)

4.5 Modification of ciecam02 by Luo et al.

All the colorimetric assessments based on CIECAM02 are usually expressed in or spaces. As it was shown [4.7 et al.], usage of ‒space gives more accurate predictions of color appearance. The following modifications of this space for large (CAM02-LCD), small (CAM02-SCD) and both small and large (CAM02-UCS) color differences (see Section 6) were proposed:

(4.79)

(4.80)

(4.81)

The coefficients for each version of UCS based upon CIECAM02 are the following:

Version of space	CAM02-LCD	CAM02-SCD	CAM02-UCS
	0,77	1,24	1,00
	0,007	0,007	0,007
	0,0053	0,0363	0,0228

Correlation of values , is presented on Figures 4.4 and 4.5.

As follows from published results of studies [4.7 et al.], the estimations got with the use of these modifications show the best correlation with all available data on colour appearance and can be considered as basis for the further studies directed to progress of the television and related video applications and to progress colour appearance models for their use as part of the systems of image quality evaluation, in particular, evaluation of colorimetric quality.

It should be noted necessity of further colorimetric studies, related to the television specific taking into account characteristics of capture and reproduction, influencing on image quality, conditions of scenes capture and reproduction etc.

The results of testing published have shown that predictions obtained by using CIECAM02-based color spaces best match all available color appearance data and can be considered to become a base for further research work on development of TV and related video systems and on development of color appearance models for implementation them as the part of image quality assessment systems, particularly colorimetric quality assessment.

It should be noted, that there’s a need in further colorimetric research according to television specificity with taking into account the specific features of TV image capture and reproduction, influencing quality, the conditions of scene capture and reproduction and so on.

CAM02-UCS ( ) chromaticity diagram

CAM02-UCS ( ) chromaticity diagram [4.6] is presented in Figures 4.6, 4.7 and 4.8. The figures demonstrate the dependence of colour appearance on adaptation level L_A and relative luminance level Y in Luo et al. colour space.

In Table 4.1 the values of lightness of spectral color samples with given reference luminance for different adapting luminance levels are presented. The Table shows in what degree perceived lightness depends on sample colours. It also shows that the dependence of on is insignificant.