230201 1L2L0X0A_(I), http://farbe.li.tu-berlin.de/AEGI.HTM or http://color.li.tu-berlin.de/AEGI.HTM

For this main page with general information and special images
of the corresponding image page with 10 colour series, see AEGI in English, AGGI in German.
For the previous main page, see AEFI in English, AGFI in German.
For the next main page, see AEHI in English, AGHI in German.

For links to the chapter A Colour Image TechnoloGL and Colour Management (2019), see
Content list of chapter A: AEA_I in English or AGA_I in German.
Summary of chapter A: AEA_S in English or AGA_S in German.
Example image part of 26 parts AEAS to AEZS: AEAS in English or AGAS in German.

Chapter A: Colour Image Technology and Colour Management (2019), Main part AEGI

1. Introduction and goals.

There are transfers from coordinates rgb* to other coordinates, for example nicwde*. The equations will be shown with examples.

Any colour circle includes the four elementary hues RYGBe. However, for the four elementary hues both the CIE lightness and chroma are different in any hue circle.

For example in photography there is often the wish to make th sky more blue or all colours more chromatic. In an extrem case all colours shall look achromatic. The different tasks can be solved by different transfers of chroma c*.

Finally the ISO-colour loop is shown and discussed. Proposals for a revision of standard documents are given. Often the display and the print output considers not the requirements of ergonomics and colorimetry. Proposals how to solve this user requirements are given.

2. Transfer of rgb* to nicwde* coordinates.

There are transfers from coordinates rgb* to other coordinates, for example nicwde*. The letters stand for n*=blackness, i*=brillantness, c*=chromaticness, w*=whiteness, d*=deepness, and e=elementary hue.

All are relative coordinates in the range 0 to 1 compared to the CIELAB coordinates Lab* or LCh*. Therefore often lab* may be used instead of Lab*. Often lch* may be used instead of LCh* depending on the application.


Fig. 1 - Transfer from rgb* to nicwde* coordinates
For the download of this Figure in the VG-PDF format, see AEG00-1N.PDF.

The figure includes the equations for the transfer of the rgb* data to the other data nicwde*. For example the coordinates i*=brillantness and c*=chromaticness=chroma are used within the series AEG1 to AEG7.

Many transfers of the chromaticness or chroma c* to new values c*' are shown in the series AEG1 to AEG7. The series AEG8 transfer rgb* data to rgb*' data by an exponential function r*' = r*(n) with the exponent n and similar for g*' and b*'.

3. CIELAB data of elementary hue circles of Miescher, offset OLS18, display TLS18, and the CIE test colours no. 9 to 12 according to publication CIE 13.3.

Any colour circle includes the four elementary hues RYGBe. However, for the four elementary hues both the CIE lightness L* and chroma C*ab are different in any hue circle. According to CIE R1-47:2009 the CIE-test colours no. 9 to 12 define the CIELAB hue angles. According to the publication CIE 13.3 for colour rendering the CIE-test colours no. 9 to 12 have the CIELAB hue angles hab=26, 92, 162, and 272. These four elementary hue angles are used in DIN 33872-1 to 6:2010 and ISO 9241-306:2018.


Fig. 2 - CIELAB LCh* data of CIE test cholours no. 9 to 12 according to CIE 13.3.
For the download of this Figure in the VG-PDF format, see
AEG01-2N.PDF.

In this hue circle the lightness L* reaches a maximum for yellow Ye and a minimum for blue Be. The chroma is for Green Ge and Blue Be by a factor of about 0,7 smaler compared to Red Re and Yellow Ye.

4. rgb* colour data for six colours RYGCBM with transfer of the relative chroma c*.

For example in photography there is often the wish to make th sky more blue or all colours more chromatic. In an extrem case all colours shall look achromatic. This different tasks can be solved by different transfers of the relative chroma c*.


Fig. 3 - Transfer of the relative chroma c* by a function c*(n) with an exponent n.
For the download of this Figure in the VG-PDF format, see
AEG10-6N.PDF.

In this figure the relative chroma c*=0,25 is transfered by the exponential function square root to a larger value c*'=0,50. Similar a change to larger values appear for c*=0,5 and c*=0,75. No change is produced for c*=1,00. Therefore all chromatic steps appear more chromatic exept for red with c*=1,00.

There are eight separate example transfers in any of six device hues RYGCBM within the series AEG1 to AEG6. In addition the six device hues are shown in one file of the series AEG7.

5. rgb* colour data for six colours RYGCBM with the transfer rgb*(n) with the exponent n.

For example for 9 or 16 equally spaced grey steps the rgb* data between r*=g*=b*=0 and r*=g*=b*=1 are equally spaced. In this case the lightness L* is equally spaced between 0 and 100. This is true in a dark room without a reflection of the ambient light on the display. For only 2,5% reflection compared to the white display the lightness of black increases fromL*=0 to L*=18. Therefore the lightness range decreases by about 20%.

Visually it is important that the spacing of the 16 steps changes from the constant value delta L*=6,7 to a value of delta L*=2,0 near black and a value of delta L*=10,0 near white. Therefore the difference between the first two and the last two grey steps is by a factor 3. For different display reflections the changes of spacing are shown in Fig. X of ISO 9241-306:2018.


Fig. 4 - CIELAB LCh* data of CIE test cholours no. 9 to 12 according to CIE 13.3.
For the download of this Figure in the VG-PDF format, see
AEG80-6N.PDF.

In the figure the spacing increases between black N and the next grey or the dark red step. However, for 2,5% reflection the spacing decreases. Therefore for these colours and the exponential transfer compensates this decrease. Depending on the amount of reflection a special exponent n produces again 16 equal visual steps. In an extrem case of equal luminance of a data projector and the room luminance on the projector screen, the equal step difference delta L*=6,7 in a dark room is approximately reduced to L*=1,7.

6. Affine ergonomic colour-space metric, standardization with the ISO-colour loop for output and input.

A ISO-colour loop: ISO-file - print or display output - scan or photographic input - back to the ISO-colour file is an important part of colour comumnication. In applications the colour device copier is used for input and output. The colour device display and printer (or print) is used for output. The colour device scanner or camera is used for input.

Up to now many standard documents are made by device specific ISO commitees, for example ISO/IEC JTC1/SC28 Office Systems, ISO TC42 Photography, and ISO 130 Graphic Technology. There is no ISO committee which covers all the sections of the colour loop. Therefore the ergonomic colour requirements, for example defined in ISO 9241-306:2018, are usually not considered.


Fig. 5 - ISO-colour loop and ergonomic requirements for colour output
For the download of this Figure in the VG-PDF format, see
AEG90-3N.PDF.

Ergonomics and colorimetry require an improved standardization for the display and prin(ter) output, see the three rectangles on the left side in the Bild.

CIE R8-09:2015 (CIE internal) and a paper with the same technical content describes the OLM16 method for output linearization on displays, on printers, and in offset print. This OLM16 method has been used to produce the analog ISO/IEC test charts according to ISO/IEC 15775:2000&2005 and ISO 9241-306:2018 in offset print (D65, 3600 dpi).

The quality is defined by the regularity index g*. This index has the value g*=100, if the 16 grey steps have equal lightness differences delta L* between Black N and White W. This index has the value g*=0 if two of the 16 steps have the lightness differences delta L*=0. Below delta L*=1 two steps are usually not distinguishable.


Fig. 6 - Relation of many standard documents for the colour devices copier, scanner, printer, and display
For the download of this Figure in the VG-PDF format, see
AEG90-7N.PDF.

This figure shows the relation of different ISO/IEC and CIE standard documents and national standards of DIN in Germany and JIS in Japan. ISO/IEC TR 24705 has been withdrawn in 2019. This TR was based on a failed ISO DIS 19839-1 to 4:2003. For free download of the content of all documents see remark 3). All these standard documents may be usefull for new standard documents and may contribute to realize the ISO-colour loop.

One reason for the failure of ISO DIS 19839-X was the missing computer power for colorimetric transformations in 2003. The necessary computing power is now included in most office computers. Now the 729 colours of the analog ISO-test chart AE49 according to ISO 9241-306:2018 can be measured within minutes.


Fig. 7 - Equally spaced colour steps in hue planes for offset with rgb* and CIELAB LCh* values
For the download of this Figure in the VG-PDF format, see
AEG91-7N.PDF.

The figure includes colour samples in hue planes with the coordinates L*C*ab. The elementary hue planes Yellow Ye and Green Ge for standard offset are shown.

If an LCh*-value set is given, then for example the four most adjacent LCh* values can be determined, see top right. Then the rgb* values for the intended LCh* output values can be calculated by interpolation. Fast calculation methods were described by Witt (2008), see
http://farbe.li.tu-berlin.de/A/WITT08.PDF.
They were used by Richter (2016) in CIE R8-09:2015, see with the same technical content
http://farbe.li.tu-berlin.de/OUTLIN16_01.PDF.

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For the archive information (2000-2009) of the BAM server "www.ps.bam.de" (2000-2018)
about colour test charts, colorimetric calculations, standards, and publications, see
indexAE.html in English, indexAG.html in German.

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