210810 'HAND' http://farbe.li.tu-berlin.de/CEA_S.HTM or http://color.li.tu-berlin.de/CEA_S.HTM.

For links to the chapter A Colour Image Technology and Colour Management, 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 content part AEAI of 26 parts AEAI to AEZI: AEAI in English or AGAI in German.
Example images part AEAS of 26 parts AEAS to AEZS: AEAS in English or AGAS in German.

For links to the chapter B Colour Vision and Colorimetry, 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 content part BEAI of 26 parts BEAI to BEZI: BEAI in English or BGAI in German.
Example images part BEAS of 26 parts BEAS to BEZS: BEAS in English or BGAS in German.

For links to the chapter C Colour Spaces, Colour Differences, and Line Elements, under work, see
Content list of chapter C: CEA_I in English or CGA_I in German.
Summary of chapter C: CEA_S in English or CGA_S in German.
Example content part CEAI of 26 parts CEAI to CEZI: CEAI in English or CGAI in German.
Example images part CEAS of 26 parts CEAS to CEZS: CEAS in English or CGAS in German.

For links to the chapter D Colour Appearance, Elementary Colours, and Metrics, under work, see
Content list of chapter D: DEA_I in English or DGA_I in German.
Summary of chapter D: DEA_S in English or DGA_S in German.
Example content part DEAI of 26 parts DEAI to DEZI: DEAI in English or DGAI in German.
Example images part DEAS of 26 parts DEAS to DEZS: DEAS in English or DGAS in German.

Project title: Colour and colour vision with Ostwald, device, and elementary colours -
Antagonistic colour-vision model and properties for many applications

Chapter C: Colour Spaces, Colour differences, and Line Elementes, Main part CEA_S, under work

Mathematical relations of spaces and differences in both directions;
Threshold colour differences for different viewing situations;
Line elements for different viewing situations;
Colour spaces for different viewing situations;
Modifications of the CIELAB colour space and the CIELAB colour difference for different viewing situations and applications.

1. Introduction and goals.
2. Colour differnce formula LABJND of CIE 230:2019 based on threshold data delta_Y.
3. Contrast and thresholds as function of the luminance L, and of the tristimulus value Y.
4. Colour line elements and derivations for the description of colour differences of adjacent and separate colours.

The following pages of the chapter Colour spaces, colour differences, and line elementes
give an introduction with special images.

1. Introduction and goals

This part shows the relations of colour spaces and colour differences with line elements.
to be developed.

2. Colour difference formula LABJND of CIE 230:2019 based on threshold data delta_Y

This part includes information on threshold data delta_Y. These data are used as basis for the colour difference formula LABJND of CIE 230:2019.


Figure 1: Visual threshold delta_Y of achromatic samples in a grey surround with a white frame.
For the download of this figure in the VG-PDF format, see CEA10-1N.PDF.

The figure shows that the threshold delta_Y increases linear with Y. Therefore the so called Weber-Fechner ratio Y/delta_Y is constant within the range 10 <= Y <= 100.


Figure 2: Visual threhold delta_Y of achromatic and chromatic samples in a grey surround with a white frame.
For the download of this figure in the VG-PDF format, see CEA01-3N.PDF.

The figure shows that the threshold delta_Y increases approximately linear with Y. Therefore the so called Weber-Fechner ratio Y/delta_Y is approximately constant within the range 10 <= Y <= 100. For the tristimulus values Y < 0,4 it is valid delta_Y=0,012. For all values Y < 0,4 the two central field colours appear as a uniform deep black.

The results in Fig. 2 are the basis of the colour-difference formula LABJND for Just Noticeable Differences (JNDs) in CIE230:2019. The performance of LABJND_PF is calculated in Table 9 and 11 of CIE 230 for the scope range 0 <= delta_E*ab <=2 of the CIELAB colour-difference formula, and for the 8 available CIE datasets, see
http://files.cie.co.at/TC181_Datasets.zip.

The LABJND_PF colour difference formula shows the best performance for 5 out of 8 CIE datasets. CIELAB_PF, CMC_PF, and CIEDE2000_PF show the best performance for one dataset. The abbreviation "_PF" stands for a "power function correction". This correction is given for the five colour difference formulae CIELAB, CMC, CIE94, CIEDE2000 and LABJND. The values of the calculated colour differences decrease by the PF exponent for larger colour differences. This increases the performance of each formula.

The comparison of the five formulae for large (LCD) and extra large (ELCD) colour differences shows about the same performance for all formulae, see
YE370-7N.PDF.
It is recommended to compare the results for the scope range 5 < delta_E*ab < 199 of the CIE committee TC1-63. In 2016 the CIE TC1-63 members could not agree to proceed with the draft WD11 for this CIE report on large colour differences, for example based on this (unexpected?) result.

6. Contrast and threshold as function of luminance L and tristimulus value Y.

This part includes information on the display or scene contrast between white and black. This contrast is described by a ratio of the two reflections, or the two tristimulus values, or the two luminance of white and black, for example YW:YN=25:1.

The threshold contrast for just noticeable differences is described by the ratio R/delta_R, or Y/delta_Y, or Ldelta_L.

oder Ldelta_L beschrieben.

The luminance L is proportional to the tristimulus value Y. For surface colours the scene contrast YW:YN is often similar to the visual threshold contrast Yu/delta_Yu (u=grey surround, German: Umfeld), for example 25:1. The maximum visual threshold contrast is near 100:1. This contrast decreases with the age of the observer. The reason is the increasing stray light on the retina.


Figure 3: Contrast L/delta_L of achromatic samples for five surround luminance.
For the download of this figure in the VG-PDF format, see CEA10-7N.PDF.

Experimental results of Lingelbach [3] show the visual threshold contrast for five different surround luminance. In a standard office the luminance is 142 cd/m^2 for the standard illumination 500 lux, and for the standard White with the reflection R=0,90.

Fig. 3 shows approximately the contrast L/deltaL=25:1. In the experimental case for surround with the luminance Lu=100 appears white. The data describe the threshold for a long time adaptation (t > 600s) on a surround luminance Lu and the short time presentation (t=0,1s) of a central field difference delta_L. The curve shape is approximately a Gauß function. The difference delta_L decreases for smaller and larger central field luminance compared to the surround luminance.

However, if the presentation time increases to about t=2s, then the Weber-Fechner ratio
L/delta_L is approximately constant according to the Weber-Fechner law.

This ratio still decreases to both sides of the surround luminance and more towards black. However, it is approximately constant for achromatic surface colours in the tristimulus value range 0,2Yu <= Y <= 5Yu.


Figure 4: Contrast values L/delta_L and three other plot possibilities as function of L.
For the download of this figure in the VG-PDF format, see CEA01-7N.PDF.

In Fig. 4 the central field lightness L* is calculated from experimental threshold results delta_L by integration. According to Schroedinger and Stiles [1] the function L* is called the line element of the achromatic colour vision. The experimental threshold results can be calculated from L* by derivation.


Figure 5: Ratio L/delta_L as function of L for the lightness L*CIELAB and L*th (schematic).
For the download of this figure in the VG-PDF format, see CEA10-8N.PDF.

In Fig. 5 the derivation of the lightness L*CIELAB gives the function L/delta_L (in white). This is very different to the approximately constant Weber-Fechner ratio L/delta_L (in black). The normalisation of the lightness L*JND for adjacent samples from the Weber-Fechner ratio will be described further with Fig. 16.

In a vision model Richter (2006) shows many connections for scaling of separated colours according to the Stevens law, and the threshold (JND) for adjacent colours according to the Weber-Fechner law on a grey surround, see BAMAT.PDF.


Figure 6: Viewing situtations of adjacent and separated samples.
For the download of this figure in the VG-PDF format, see CEA10-3N.

In Fig. 6 grey samples are shown as two adjacent (top) or separated (botom) samples. For surface colours in the range 4 < Y < 100 the tristimulus-value differences delta_Y or the luminance differences delta_L depend on the black, or the grey, or the white surround.

The following Fig. 17 shows a larger dependance of the threshold on the distance or the separation of the two samples. This separation effect is for example applied in the automotive industry. Different parts of a car which may be painted at different locations are often separated by small gaps of for example 2 mm. Then the visual detection of small colour differences is reduced by about a factor 3.


Figure 7: Colour difference in the lightness direction as function of the sample distance.
For the download of this figure in the VG-PDF format, see CEA10-5N.PDF.

The figure shows six different colours with their CIELAB data L*a*b*. The threshold was measured for adjacent and separated samples. One sample was lighter. The threshold increases with the sample distance or the gap between the samples. Already a gap of 2 mm in a viewing distance of 50 cm increases the colour difference at threshold by about a factor 3. For larger sample gaps the colour difference is constant.

The CIELAB lightness L* is not directly normalised to describe the threshold of separated colours. However, in many applications a lightness difference of delta_L*=1 is assumed as the threshold for separated colours on a grey surround. Then the threshold is by a factor 3 smaller for adjacent compared to separated colours on the same grey background. This is also shown in Fig. 15

The L* functions and the derivation functions can be normalised with the experimental results of Fig. 17. In Fig. 15 both delta_Y threshold values are normalised at the surround luminance Lu. This delta_Yu-threshold value is by about a factor 3 smaller for separated colours compared to adjacent colours.

Several available datasets of CIE TC1-81 have shown approximately a threshold delta_L*JND=0,30 for adjacent colours. However, Members of CIE TC1-81 could not agree to recommend this threshold for adjacent colours. Therefore in CIE 230:2019 further research is recommended. However, in addition for example Fig. 17 shows that the threshold is by a factor three smaller for adjacent colours compared to separated colours.

References:
[1] Stiles, W. S. (and E Schroedinger) (1972), The line element in colour theory: a historical review, p. 1-25, in Color metrics, AIC/Holland, TNO Soesterberg.
[2] Seim, T. and A. Valberg (2015), A neurophysiological based analysis of lightness and brightness perception, CR&A, 26 pages, This paper includes important threshold data for adjacent colours, and for different presentation times, and different adaptation luminance for improved colour vision models.
[3] Haberich, F. J. and B. Lingelbach, Psychophysical measurement concerning the range of visual perception, Pflügers Archiv 1980; 386, 141-146.
[4] Avramopoulos, D. (1989), Leuchtdichte-Unterscheidungsvermögen von unbunten und bunten Infeldfarben für kurz- und langzeitige Leuchtdichte-Unterschiede (Luminance discrimination of achromatic and chromatic central fields for short and long term luminance differences], see UE.HTM.
[5] Richter, K., (1996), Computergrafik und Farbmetrik [computer graphic and colorimetry], VDE-Verlag, Berlin - Offenbach, 288 pages, see BUA4BF.PDF.
[6] Richter, K., (2012), Colour and colour vision - Elementary colours in colour image technology, 72 pages, Berlin University of technology, section lighting technology, with about 100 colour figures, see http://standards.iso.org/iso/9241/306/ed-2/index.html.
[7] CIE 230:219, Validity of formulae for prediction small colour differences, developed by CIE TC1-81 with the chairman: Klaus Richter, see for a summary at
http://www.cie.co.at/publications/validity-formulae-predicting-small-colour-differences.

Summary of this part
The luminance range in offices with paper and display applications is similar according to ISO 9241-306. In this luminance range with 0,2Lu < L < 5Lu the Weber-Fechner ratio L/delta_L is approximately constant. This range corresponds to the normalised reflection range 0,2 < R1 < 5,0 in Fig. 9 or the reflection 0,04 < R <1,00 in Fig. 2. In this range the threshold is by a factor 3 smaller for adjacent colours compared to separated colours, see figures 16 and 17.

4. Colour line elements and deviations for the description of colour differences of adjacent and separated colours


Figure 8: Approximation of the lightness L*CIELAB by L*Z for a grey surround; Lightness L*W for a white and L*N for a black surround.
For the download of this figure in the VG-PDF format, see CEA10-4N.PDF.

The figure shows different scaling funktions for the surrounds White W, mean Grey Z, and Black N. Power functions with different exponents between 0,5 < k < 0,33 are used in applications.

Often separated colours are viewed on a grey surround. They appear equally spaced in lightness, if the differences delta_L* are equal. This is for example fulfilled for a 16 step grey scale with the lightness L*CIELAB=15, 20, 25, ..., 85, 90. In Figure 17 the calculated colour difference is about three times smaller for adjacent compared to separated colours.


Figure 9: Viewing situations of adjacent and separated colours.
For the download of this figure in the VG-PDF format, see CEA10-3N.PDF.

This figure shows in all smaller figures a mean grey surround. The figures 1A to 3A show adjacent samples and the figures 1B to 3B separated samples. There are three possibilities to specified the grey samples. One can use: the reflection R, the tristimulus value Y, or the luminance L. Most of the users prefer for grey colours the reflection R, which is also preferred in the following.


Figure 10: Lightness L*Z of separated greys in a main grey surround Z
For the download of this figure in the VG-PDF format, see CEA11-1N.PDF.

The figure uses the lightness L*Z of the sRGB colour space according to IEC 61966-2-1, compare L*Z in Fig. 40. Two normalisation of the reflection are given in equation [1] and [2] in the Fig. 42. The first one is widely used in colorimetry. However, the second one is preferred in the following and based on colour physiology. The antagonistic colour vision model is based on antagonistic signals White W and Black N with Grey Z in the middle.

One must consider that mean grey is defined by the logarithmic mean of the Reflection RW=0,9 of White and RN=0,036 of Black. If the reflection is normalised to R1 = R/0,20 then R1W is five times larger compared to R1Z and R1N is five times smaller compared to R1Z.

Therefore the logarithmic values are:
log(R1W) = log 5
log(R1Z) = 0
log(R1N) = log (1/5) = - log 5.

The logarithmic mean is:

log R1Z = 0,5 [ log(R1W) + log(R1N) = 0,5 [ log 5 + (- log 5)] = 0.

Equation [4] in the Fig. 42 describes the experimental result of Fig. 12. It is approximately valid for adjacent samples:
delta_R/R^0,14 = const.

This is approximately the Weber-Fechner ratio: delta_R/R = const.


Figure 11: Lightness L*JND of adjacent greys in a main grey surround Z
For the download of this figure in the VG-PDF format, see CEA11-2N.PDF.

This figure uses the experimental exponent k=0,14 which is by a factor three different to the exponent k=0,42 in Figure 10. Therefore the lightness for adjacent colours is different to the lightness of separated colours.

Mathematically the slope is defined by different exponents of the L* functions. Further the L* functions differ by different scaling constants. In experiments for the surround the slope can be determined by a normalisation to the surround values. The scaling constant can be determined by an appropriate normalisation to the reflection threshold at the surround.

The lightness function L* is called the line element of the lightness differences at threshold. Equation [4] in Fig. 11 defines the values delta_R as function of R. The values delta_R can be measured in visual threshold experiments with the viewing situation 1A in Fig. 9. With these experimental values a function for the lightness L* can be determined.


Figure 12: Line element and derivation of the lightness formula L*IECsRGB

For the download of this figure in the VG-PDF format, see CEA11-6N.PDF.

The lightness L*IECsRGB is an approximation of the lightness L*CIELAB, compare Fig. 8. This lightness is intended for separated samples on a mean grey surround.


Figure 13: Lightness L*LABJND of adjacent greys in a mean grey surround Z; Use in the colour difference formula LABJND of CIE 230
For the download of this figure in the VG-PDF format, see CEA11-8N.PDF.

The lightness formula L*LABJND in Fig. 13 describes the threshold for adjacent greys on a mean grey surround Z. This lightness formula uses three constants A0, A1 and A2. The formula was developed by integration of threshold results.

A BAM-research report of Richter (1985) describes the experimental thresholds delta_Y as function of Y for achromatic and special chromatic colour series. These BAM results are shown in Fig. 2.

The LABJND colour-difference formula of 1985 uses these results with the constants A0, A1, and A2. The LABJND colour difference formula is used in CIE 230:2019. The performance of the five colour difference formulae CIELAB, CMC, CIE94, CIEDE2000, and LABJND is evaluated.

According to Table 9 and 11 of CIE 230, the LABJND_PF formula shows the best performance for 5 out of 8 CIE datasets. CIELAB_PF, CMC_PF, and CIEDE2000_PF gives the best performance for one of the 8 datasets, see the datasets
TC181_datasets.zip

The best performance of the five colour difference formulae is one advantage of LABJND. The probably more important advantage is the line element L*LABJND as function of Y. This is the calculated lightness in Fig. 13 by integration of the threshold results.

If this integration is also possible for the antagonistic directions R-G and Y-B with the BAM and other data, then probably two new colour spaces for colour appearance are created. The two exponents k=0,42 and k=0,14 for separated and adjacent colours in Fig. 10 and 11 may be used to calculate the thresholds for these two viewing situations.

Other constants A0, A1, and A2 may be needed:
1. for black and white surrounds, compare Fig. 6 and 8,
2. different luminance adaptations, compare Fig. 4, and
3. different viewing times, compare Fig. 5, and
4. different chromatic adaptations, compare left and right in BGH5L0NP.PDF.

It is intended to reach some of these goals by integration of threshold data in a new
Part C: Colour Appearance, Elemenmtary Colours, and Colour Differences.

Further remarks
CIE 230:219 includes only the threshold function delta_Y as function of Y for the definition of the LABJND-colour difference formula. CIE 230 includes NOT the corresponding line element L*JND of Fig. 13. For this unanimity was required by all TC1-81 members, and this was not possible.

The missing corresponding colour appearance space is a larger disadvantage of the colour difference formulae CMC, CIE94, and CIEDE2000. This advantage of the CIELAB space may be reached also with LAB2JND by integration of the BAM and other threshold results.

For more equations calculated from the lightness L*LABJND, see for example
BEU41-7N.PDF.

In CIE 230 the chromatic values (A, B) of LABJND have been used. In future calculations with the more visual chromatic values (A2, B2) of LAB2JND may lead to an increase of the performance.


Figure 14: Line element and derivation of the lightness L*IECsRGBJND
For the download of this figure in the VG-PDF format, see
CEA11-7N.PDF.

The lightness L*IECsRGBJND is intended to describe the threshold for adjacent samples on a mean grey surround. For this aim the constants of the lightness L*IECsRGB for separated samples are modified for adjacent samples.


Figure 15: Colour attribute chromaticness C* and achromaticness A*
For the download of this figure in the VG-PDF format, see CEA11-5N.PDF.

The lightness L*CIELAB is intended to describe the threshold for separated samples on a mean grey surround. The slope mu=0,33 shows some difference compared to the slope mu=0,42 of the lightness L*IECsRGB.

Summary of this part:
The lightness is for separated and adjacent samples different. It is usually valid
1. the lightness differences can be calculated from the lightness function by mathematical derivation.
2. the lightness function can be calculated from the lightness differences by mathematical integration.
3. For surface colours logarithmic properties of the lightness functions can be approximated by exponential functions in the limited range of R, Y or L.

This web site is under work since 2021.
In future the figures and the text will be improved depending on new results.


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