230201 1L2L0X0B_(I), http://farbe.li.tu-berlin.de/BEEI.HTM or http://color.li.tu-berlin.de/BEEI.HTM

For this main page with general information and special images
of the corresponding image page with 10 colour series, see BEEI in English, BGEI in German.
For the previous main page, see BEDI in English, BGDI in German.
For the next main page, see BEFI in English, BGFI in German.

For links to the chapter B Colour Vision and Colorimetry (2020), see
Content list of chapter B: BEA_I in English or BGA_I in German.
Summary of chapter B: BEA_S in English or BGA_S in German.
Example image part of 26 parts BEAS to BEZS: BEAS in English or BGAS in German.

Chapter B: Colour Vision and Colorimetry (2020), Main part BEEI

1. Introduction and Goals
In many applications the question arises, if these visual attributes can be calculated. For this the CIE XYZ tristimulus values of colorimetry shall be used. In the following instead of the CIE XYZ tristimulus values the relative spectral reflectances 0 < R < 1 are used.


Figure 1: Additive colour mixture of Ostwald-optimal colours
For the download of this figure in the VG-PDF format, see BEE20-7N.PDF.

The spectral mixture to the optimal colours of Ostwald leads to basic data for an antagonistic model of colour vision.

The figure shows reflection factors between 0,035 and 0,865. The contrast is C=25:1 which is identical to the ratio 0,865:0,035. Most surface colours have similar reflections with minimum values near 0,04 and maximum values near 0,90.


Figure 2: Additive colour mixture of Ostwald-optimal colours
For the download of this figure in the VG-PDF format, see BEE20-3N.PDF.

This figure shows the refection factor R1=R/0,2 between the R1-values 0,2 and 5 for R=0,04 and R=1,00. Figure 2 shows no change of the contrast C=25:1 compared to Figure 1. The minimum reflection values are R1=0,2, and R=0,04.


Figure 3: Antagonistic signals for the green Ostwald colour G
For the download of this figure in the VG-PDF format, see BEE91-3A.PDF.

The first two arrows shows the reflection factor of two green colours Gn and G. A blackish green Gn is located in the middle between black N and the green Ostwald colour G.

The next two arrows shows the reflection factor of two green colours Gw and G. A whitish (w) green Gw is located in the middle between white W and the green Ostwald colour G.
The figure ordinate uses the coordinate R2=log[R/0,2]. This coordinate R2 is intended to be proportional to the triangle lightness t*. For achromatic colours the triangle lightness is proportional to the CIELAB lightness L*. For the contrast ratio C=8:1 and for the achromatic colours the triangle lightness t* is asumed to be equal to the CIELAB lightness L*.

For the three reflection factors R=0,071, 0,200, and 0,564 the three CIE tristimulus values Y are 7,1, 20,0 and 56,4. According to the CIELAB formula

L* = 116 (Y/100) ^ (1/3) - 16

the three CIELAB lightness values are L*=32,03, 51,84, and 79,84.


Figure 4: Antagonistic signals for the magenat-red Ostwald colour M
For the download of this figure in the VG-PDF format, see BEE91-6A.PDF.

The first two arrows show now the reflection factor of two magenta-red colours Mn and M, and the next two the magenta-red colours Mw and M. A blackish magenta-red Mn is located in the middle between black N and the magenta-red Ostwald colour M. Similar a whitish magenta-red Mw is located in the middle between white W and the magenta-red Ostwald colour M.


Figure 5: Relation between reflection, log[reflection], and triangle lightness t*
For the download of this figure in the VG-PDF format, see BEE91-8A.PDF.

The figure shows three different reflections R, R1, and R2. The calculation of the contrast C is shown.


Figure 6: Antagonistic signals for six chromatic Ostwald colours and white for the contrast C=8:1.
For the download of this figure in the VG-PDF format, see BEE91-7N.PDF.

For the description compare the text for the figures 3 to 5.


Figure 7: Ostwald-hue circle for two contrast values
For the download of this figure in the VG-PDF format, see BEE61-8N.PDF.

The colorimetric chromatic values A2 and B2 of the Ostwald-hue circle are approximately on a circle. All antichromatic colours have equal absolute chromatic values |A2| and |B2|.

The circle diameter reduces for the two contrasts from C>288:1 (black lines) to C=2:1 (chromatic lines) by a factor two. In the colour space L*AB2JND this is similar for the three devices:
sRGB, see BEE3L0NP.PDF,
WCGa, see BEE4L0NP.PDF,
and Ostw, see BEE6L0NP.PDF.

The three images for sRGB, WCGa, and Ostw show in addition the CIELAB-chroma values a* and b*. Because for example the antagonistic colours G and M mix to the achromatic white W, equal absolute chroma values |a*| and |b*| are expected for all antogonistic colours.

For the three devices many CIELAB-chroma values are different by a factor two. Therefore for the antagonistic colours the CIELAB-colour space does NOT include the expected visual property.

This is a difficulty of the present CIE colorimetry for many applications. Usually on the displays three antagonistic colours pairs R - C, Y - B and G - M are used. The colours of any pair are mixed to white.

In addition the different colour difference formulae, for example CMC, CIE94, and CIEDE2000 are based on transformations of the CIELAB values. This seems to be similar for the colour appearance models CIECAM02 and CIECAM16 (2021 under vote).

This indicates, that improved colour-difference formulae and colour-appearance models are needed for many applications. The antagonistic colour vision model seems an alternative new starting point.

The antagonistic colour space LABJND is used in:
CIE 230:2019, Validity of formulae for prediction small colour differences, with the chairman: Richter, Klaus, see for a summary at
http://www.cie.co.at/publications /validity-formulae-predicting-small-colour-differences.

For small CIELAB-colour differences delta E*ab <= 2 and for six out of eight CIE-datasets, the colour difference formula LABJND_PF produces the best performance. On displays often relative CIELAB-colour differences delta E*ab smaller 2 are produced. Therefore on displays they may be more important compared to surface colours.

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