CIE color difference formula

Color difference refers to the concept of three dimensional space in uniform color space. The perceptual color difference between two colors can be calculated by CIE color difference formula, that is, the distance between two color points in color space. Color difference has important industrial significance. For example, in the printing and dyeing industry, in order to quantitatively evaluate the color quality of products, people want to measure the color difference with a simple quantity value. Because of the characteristics of color, it must be comprehensively evaluated with three color attributes. The establishment of uniform color space makes the instrument measurement of color closely linked with visual color difference.

In 1976, CIE recommended two color difference formulas that are equivalent in representing color difference perception: CIE LAB color difference formula and CIE LUV color difference formula.
CIE LAB color difference formula
CIE 1976 (L * a * b *) color difference formula, or CIE LAB color difference formula：

LAB color difference formula

Where are the lightness and chromaticity indexes of samples 1 and 2 respectively, which can be determined by the formula：

Calculated, where X, Y, Z are the tristimulus values of the sample color; It refers to the tristimulus value obtained by the human eye after the fully diffuse reflective object surface passes through the CIE standard illuminant.
CIE 1976 (L * u * v *) color difference formula, or CIE LUV color difference formula：

LUV color difference formula

In the CIE L * u * v * uniform color space , the vertical axis is lightness L *, and the chromaticity indexes u * and v * are on the horizontal plane and perpendicular to each other. The relationship between the hue index u * and v * values and the hue angle and position in the figure. The surface with constant chromaticity angle is the vertical plane with L * as the side; The surface with constant chromaticity is a cylinder with L * as the central axis; If we consider the color of a single hue angle, they will be on the same plane, sensitive above and dark below; The low chromaticity color is close to the L * axis, and the high chromaticity color is far away from the L * axis.

Therefore, the definition of hue angle is as follows:
and：
Therefore, the hue angle can also be defined as:

The measurement chromaticity is defined as follows:

The total color difference of CIE LUV system can also be calculated by the difference of lightness L *, chroma and hue:

Comparison between CIE 1976 (L * a * b *) system and (L * u * v *) system
The two uniform color spaces L * a * b * and L * u * v * recommended by CIE in 1976 and the corresponding color difference formula did not specify where these two systems should be applied. However, because people have been familiar with and used to the AN LAB system in dyeing, painting, plastics and other industries involving colorants, they hope that the color difference data obtained can be compared with the original AN LAB system. Therefore, it is more appropriate for people to choose CIE LAB system.

On the other hand, industries using additive color mixing technology, such as television industry, hope to have a space related to chromaticity map. For example, it is very simple to use additive color mixing in TV display devices. On the x-y chromaticity diagram, it is easy to calculate the color mixing effect by using the characteristics that the mixed color obtained by adding two colors must be on the line between the two colors. Therefore, CIE LUV system is selected.
Manufacturers can select suitable systems for use according to their different fields.

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