# Color value

The color value is the absolute value of the vector for a color location .

## Explanation

A three-dimensional color valence can be assigned to every color stimulus , i.e. every stimulus that triggers color perception . This three-dimensionality is based on Graßmann's First Law ; This means that color spaces can be represented with three coordinates, except for special requirements. So three values ​​are sufficient to describe a color in its perception.

Spectral distribution of the standard color values (
tristimulus curve)

The three coordinates of such a measuring space can be determined by three calibration valences (suitable basic values); these can in turn be converted into basic colors using three suitable light emitters . All colors can be generated by additive color mixing of these three (initially theoretically determined) calibration valences .

Such additive color mixing follows the rules of vector addition , which is why Schrödinger introduced vector representation in color measurement . The color vectors are pointers in the coordinate system with a defined direction and a certain value. In the standard valence system , the basic directions are the vectors of the calibration valences X, Y, Z. These are also referred to as tristimulus values and are chosen so that only positive color values ​​occur.

In such a color system , the black point necessarily lies at the coordinate origin {0,0,0}, i.e. neither red nor green nor blue. The color valence determines the position vector (i.e. the connecting line in a three-dimensional space) from this black point to the color location . The direction of this position vector is the chrominance , and the length of this vector is the color value.

## Standard color values

The standard color values X, Y, Z are internationally agreed as basic calibration values in the standard color system .

Y is also defined in such a way that it is also a measure of the brightness of the color . For body colors , this value should better be referred to as the lightness reference value  A = Y, since the relative brightness has an effect here.

In the case of light sources , the standard color values ​​are determined from the standard spectral value functions and the spectral properties of the lamps. For standard illuminants , the standard spectral values ​​are recorded in tables.

## Standard color value proportions

Standard color value components x, y, z are standardized sizes of the standard color values ​​related to the sum of X + Y + Z for the representation of the color location in the standard color table :

${\ displaystyle x = {\ frac {X} {X + Y + Z}}}$
${\ displaystyle y = {\ frac {Y} {X + Y + Z}}}$
${\ displaystyle z = {\ frac {Z} {X + Y + Z}}}$
${\ displaystyle \ Rightarrow x + y + z = 1}$

It is therefore sufficient to specify x and y, since z results arithmetically. With these two values ​​(as part of the color valence) the color type is determined.

## literature

• Manfred Richter: Introduction to colorimetry. Walter de Gruyter, Berlin 1981