The International Commission on Illumination (CIE) is the body responsible for international color standards. In 1931, CIE first recommended the CIEXYZ tristimulus color system as an international standard. Although the system was revised after the launch of the system, a new system was introduced, but the basic principles have not changed. Based on the CIEXYZ tristimulus color system, more than 40 color difference formulas have been proposed with the goal of providing an objective color decision-making for the industry. In addition to the above objectives, the color difference formula can also provide the basis for accurate color inconstancy evaluation, meta tamerism evaluation, shade sorting, and fastness testing. The ideal color difference formula is a pass/fail decision for any color with a single color value. The latest CIE recommended CIEDE2000 color difference formula is very close to this ideal state. This article reviews the history of the earliest color difference formula from 1936 to the current CIEDE2000.
The experimental database is extremely important for the development of color formulas because the essential color difference formula is used to accurately describe these experimental data. Many experimental databases are obtained under different conditions, including different viewing conditions, materials, scaling techniques, and physical size of samples, which also leads to many color difference formulas. Suitable for some experimental databases. The figure below lists the vast majority of experimental databases. All databases are divided into two categories, namely perceptibility and acceptability. Perceptibility means that the observer can judge the difference between the two colors or the visual chromatic aberration between the two colors, and also the minimum noticeable difference (JND); the acceptability indicates whether the observer can accept the observation. The difference in color. Industry is more interested in acceptability because it can be used for standards of pass/fail in the quality control process. Perceptibility data is used in all CIE-recommended color difference formulas because acceptability data often includes some commercial considerations, such as production costs.
Early experimental data, such as MacAdam and Munsell data, showed that the original CIEXYZ color space was uneven. The figure below shows the distribution of Munsell color swatches in the CIE xy space, where each circle represents a color swatch with the same Munsell chroma, and each line represents a color swatch with the same Munsell hue. Because the Munsell color samples are based on the same visual differences. For an ideal color space, all circles should be round, and the circle and the circle are equally spaced, and all lines should be straight. The length of one chroma step in the blue area in the figure below is at least five times shorter than the length of one chroma step in the green area.
The figure below shows 25 MacAdam ellipses on the CIE xy chromaticity diagram. Each ellipse represents the same visual chromatic aberration from the center of the ellipse to the elliptical boundary. For an ideal color space, all ellipse should be a circle of equal diameter, which is obviously inconsistent with the following figure. The elliptical size of the distinct green area is at least 10 times larger than the ellipse of the blue area.
Usually a color difference formula is proposed to accurately match a certain set of experimental data, such as Munsell or MacAdam data, so the performance of the color difference formula depends significantly on the reliability and reproducibility of the experimental data. Since the first color difference formula (Nickerson's index of fading) was proposed in 1936, more than 40 color difference formulas have been proposed. The development of these color difference formulas can be roughly divided into three periods, before 1976, after 1976 and after 1976. The figure below shows the most important color difference formulas that have been important in the development process so far. Due to the limited space of the WeChat public account, the commonly used color difference formula is introduced.
Color difference formula before 1976
At this stage, more than 20 color difference formulas were introduced, which can be roughly divided into three categories, 1 based on MacAdam ellipse derivation, 2 based on Munsell data derivation, and 3 based on linear transformation of CIEXYZ color space. Since the color difference formula introduced at this stage has been outdated so far, it will not be introduced.
1976 color difference formula
At this stage, CIE recommends two uniform color spaces (UCS) CIELAB (or CIEL*a*b*) and CIELUV (or CIE L*u*v*) for subtractive mixture respectively. Additive mixture with colored light. Both color spaces contain the same brightness scale L*, and the oppo nent colouraxes generally represent redness-greenness and yellowness-blueness.
CIE L*a*b* color difference formula (CIELAB)
Where X, Y, Z are the tristimulus values â€‹â€‹of the test color, and Xn, Yn, and Zn are the tristimulus values â€‹â€‹that the CIE standard illuminator illuminates on the fully diffuse reflector to reflect into the observer's eye, where Yn = 100.
In addition to L*, a*, b*, chroma C*ab and hue angle hab are often used to characterize colors as they correspond to visual perception, and chroma and hue angles can be calculated using the following formula:
The CIELAB color difference formula is as follows:
In the middle
The subscripts 1, 2 represent the target and test color samples, respectively.
Although the CIELAB color difference space and the color difference formula have a certain distance from the ideal uniform color space (see the circle in the next two figures is an ellipse instead of a circle of equal diameter), it is widely used in industry, mainly due to the color space and color difference. The formula is intuitive and simple to calculate.
Luo & Rigg experimental data ellipse on a*b* map
RIT Dupont experimental data ellipse on a*b* map
CIE L*u*v* color difference formula (CIELUV)
Where u', v', Y are the parameters of the test color sample, and u'n, v'n, and Yn are completely diffuse reflector parameters.
The CIELUV color difference formula is as follows:
In the middle
It should be noted that CIELAB and CIELUV contain both color space and color difference formulas. Most of the color difference formulas after 1976 have no corresponding color space. The color space and color difference formulas are different. The color space typically has three axes, such as a lightness axis, a redness-greenness, and a yellowness-blueness. Two different color swatches can be represented by two points in the color space, and the geometric distance between the two points represents the chromatic aberration between the two color swatches. Most of the color difference formulas after 1976 are optimized or modified based on the CIELAB color space, and generally do not have corresponding color space.
Color difference formula after 1976
The color difference formula before 1976 is basically based on the Munsell and MacAdam databases. The observation conditions for obtaining these databases are very different from those commonly used in the industry. For example, in the Munsell system, the CIELAB color difference unit between two adjacent color samples can reach 5 -10, which is about 10 times larger than the typical color difference in the industry, and the physical size of the Munsell color sample is generally smaller than the size of the industrial color sample; while the experimental data of the MacAdams is based on visual matching, the observer has only one, and the observation conditions are also Very special.
After 1976, many new experimental databases were published and the experimental setups used typical industrial observation conditions. Typical examples are the OSA database of the Optical Society of America and the DIN database of the German Standards Institute. Based on the above two databases, the FCM, LABHN, ATD, SVF and Oleari color difference formulas are successively proposed. In addition to the above two databases, there are also McDonald, Luo & Rig, RIT-Dupont, Kim and Nobbs, Witt, Chou and Cui databases, which are used to develop more complex and accurate color difference formulas based on the CIELAB color difference formula, such as CMC (l:c), BFD (l:c), CIE94, LCD, and finally CIEDE2000 color difference formula. This is an introduction to CMC (l:c), CIE94, and CIEDE2000.
CMC (l:c) and JPC79 color difference formula
Coats' McDonald prepared 600 pairs of polyester color pairs with 55 color standards, allowing eight professional colorists to perform visual evaluation experiments. In addition, McDonald also prepared 8000 pairs of color samples for one viewer to visually evaluate. These experimental data were finally used to derive the initial JPC79 color difference formula. Later, the Colour Measurement Committee (CMC) of the Society of Dyers and Colourists (SDC) modified JPC79 to obtain the CMC (l:c) color difference formula, which is currently organized by ISO. Recommended for the color difference formula of the textile industry.
The color difference formula of CMC(l:c) is as follows:
The brightness weighting factor l and the chroma weighting factor c are used to adjust the influence of brightness and chroma on the total color difference. A large number of experimental data show that for the acceptability evaluation of the textile industry, l:c is recommended to be 2:1; The perceived color difference, l:c is recommended to be 1:1.
CIE94(KL:KC:KH) color difference formula
Roy Berns and others at Rochester Institute of Technology (RIT) conducted visual evaluation experiments using glossy paint samples. The database included 19 color centers and 156 visual color difference thresholds. Finally, a color difference formula similar to the CMC (l:c) structure is proposed, but the weight function is simpler. They think that the CMC (l:c) color difference formula is too complicated. Finally, the color difference formula was recommended by CIE in 1994 and named CIE94 color difference formula.
Usually for the textile industry, KL, KC and KH are recommended to be 2:1:1; for the non-textile industry, KL:KC:KH=1:1:1 is recommended.
CIEDE2000 (KL: KC: KH) color difference formula
Since ISO recommends CMC (l:c) as an international standard, and CIE recommends CIE94 as an international standard, CIE Technical Committee TC1-47 was established in 1998 with the goal of proposing a more reliable and applicable color difference formula to fuse these two standards. . Finally, the technical committee recommended the most up-to-date formula for the CIEDE2000 color difference formula to be recommended to the industry.
The calculation steps are as follows:
In the middle
Compared with the previous color difference evaluation model, the CIEDE2000 color difference formula focuses on the following aspects:
1. Re-scale the a* axis of the near-neutral region to improve the predictive performance of near-neutral colors;
2. Modify the brightness weight function in the CIE94 formula to a near-V shape function;
3. The effect of the hue angle is considered in the tone weight function;
4. Contains an elliptical rotation term that reflects the case where the color difference tolerance ellipse of the blue region does not point to the neutral point.
After several sets of experimental data tests, the CIEDE2000 color difference formula is the best for the matching of visual evaluation results. The figure below shows a comparison of the BFD database and the RIT-DuPont database (red) with the CIEDE2000 predicted ellipse (black). In general, the degree of coincidence between the two is high, which also indicates that the color difference formula of CIEDE2000 is reliable.
After many years of development of the color difference formula, the CIEDE2000 color difference formula is basically the color difference formula that best meets the visual evaluation. However, the study of the color difference formula has not stopped, and the future development direction is as follows:
1. So far, basically all of the color difference formulas after 1976 are based on CIELAB improvements. Therefore, the development of a new uniform color space and the development of color difference formula is the future development direction, such as CAM02-UCS.
2. We need to develop uniform color spaces for different applications, such as light stimulation in the lighting industry, HDR uniform color space in the display industry, etc.
3. All color difference formulas use only a set of fixed CIE-defined observation conditions. In the future, it is necessary to develop color difference formulas suitable for different observation conditions, such as sample size, background, and illumination.
4. Almost all color difference formulas are used to predict the color difference between pairs of individual color samples. In the future, it is necessary to develop color difference formulas such as images for more complex color samples.
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