CIE 1931 color space

The CIE standard colorimetric system or the CIE standard color system was developed by the International Commission on Illumination (CIE - Commission Internationale de l' eclairage ) defined to establish a relation between the human perception of color (color) and the physical causes of the color stimulus ( color valency ). It captures the totality of perceptible colors. Using the color space coordinates is also the name Yxy color space or CIE Yxy use, and primarily in the English section also tristimulus color space.

• 2.1 The construction principle
• 2.2 metamerism
• 2.3 Practical considerations

The CIE standard observer from 1931 and 1964

In the 1931 CIE standard colorimetric system developed (CIE 1931) measured values ​​were assumed, which are based on a standard observer. This " average " observer looks at an area with a field of view of 2 ° centered to the main viewing direction. This field is about the size of a one euro coin, which one holds with his outstretched arm in front of him. This limitation was derived from the size of the zone of the highest density of the color sensitive photo- receptors in the eye. The cones are concentrated on the retina in the best color vision. The normal field of view of human perception, however, is larger than 2 ° range. Therefore, in 1964, the system for a normal observer with 10 ° field of view was introduced. The CIE (1964) color system based on the "wide angle " field of view of the people, this is the size of an A4 sheet in a normal viewing distance of 30 cm. In the 10 ° - edge region, the number of cones per area increases since clearly, the reference values ​​are correspondingly different.

As a method, the visual color matching was used by observers, which should provide a predetermined color space according to their individual impression on "equal". The mixture experiments were carried out by W. David Wright (1928) and John Guild ( 1931). For these physiological considerations they had chosen the 2 ° - viewing area. There was a split screen used on the A- side of a certain color was projected. On the B-side three emitters were projected in the colors red, green and blue. This overlapped and illuminated each in a color. The brightness of each color radiator was adjustable while its wavelength was determined by defined filters.

Wright and Guild selected for 546.1 nm ( green) and 435.8 nm ( blue), because these spectral lines can be easily produced by mercury vapor lamps and separated by interference filters. For 700 nm ( red) light bulbs have been used with a simple color filter at the end of the 1920s due to lack of strong spectral colors because making in the red zone small deviations of the wavelength is less noticeable in the results.

The observer should adjust a respectively predetermined color impression of the A-side of his subjective feelings out by changing the brightness of the three available light sources (B-side ). The underlying trichromatic theory was introduced at this time and said with three suitable light sources can represent every light impression. Were determined at the three light sources of the B-side setting values ​​for green, blue, red, could be used as a measure of the specified on the A- side of light color. For some given test colors in the green - blue settings from the observer, however, could not be reached due to its setting ( on the B- side) to ensure full compliance. The observer had therefore on the A- side ( ie on the set ), nor "to regulate " red light. Such a scale value was entered in the result sheet as a negative red value. Inflicting on the B - side corresponded to a " removal of red light " on the A side. In this way, the entire region of human-discernible color stimuli was recorded numerically.

To date, the CIE chromaticity diagram is from 1931, the most widely used perceptual color description system. As the CIE system nor the 2 -degree field of view system is also now assumed unless otherwise specified. The shape of the color stimulus area in the standard color charts of the two systems (2 ° -/10 ° observer ) is slightly different.

The lower picture shows the weights of the three primary colors for the saturated colors along the outer edge of the chromaticity diagram. Since no color screen or projector can produce red color with negative intensity, colors can be displayed in green - turquoise only unsaturated, so too pale in the area. If you choose other colors, shifts the color triangle and it comes to color distortion. For every choice there is in nature colors that lie outside the triangle and therefore in principle can not be represented (gamut ).

Tristimulus

Especially in the English-speaking world, the three fundamental values ​​of X, Y and Z are called tristimulus. In this sense they are the three components of ( this ) defined standardized colors. Each color can be characterized with such a triple of numbers. Accordingly, it is common for the CIE tristimulus system, the designation system. The 1931 measured curves are also called Tristimuluskurven. An emerald green then has the tristimulus values ​​{ X, Y, Z } = { 22.7; 39.1; 31.0 }. To 10 nm, 5 nm, or 1 nm for each wavelength interval of 20 nm, the tabulated values ​​of x, y, z of the spectral energy that is emitted from the light source multiplied. These values ​​are multiplied at each wavelength with the position of the reflectance of the sample. This remission is measured against a perfect reflecting diffuser. Usually it involves the BaSO4 standard, sometimes to a more stable against signs of polytetrafluoroethylene ( Teflon) standard. The reflectance of this diffuser is placed at each sampled wavelength at 100. Finally, the sums of all three series of values ​​are summed and divided by the sum of the spectral energies y, because Y must be less than perfect white by definition equal to 100. The CIE Publication 15.2 from 1986 contains the relevant information about the XYZ color scale and function of the CIE standard observer.

Due to the measurement technology from the early 20th century color were also introduced the imaginary colors as design thinking in the cognitive process used to describe the phenomenon.

The standard color chart

In order to display the perceived by the viewer three dimensional color space clearer ( the type of color ), the two-dimensional CIE chromaticity diagram was developed. The third component Z (in the case of the right diagram shown opposite blue) for each point on the chromaticity diagram calculated from the other two by the relation x y z = 1 is determined. The horseshoe-shaped area of possible colors in the CIE chromaticity diagram plotted on a coordinate system where the x-and y -component ( the CIE standardized theoretical background colors X ( red ), Y ( green) and Z ( blue) (see CIE XYZ color space) ) of any color P can be read off directly. By the fundamental condition x y z = 1 can be the z -component (z = 1 - x - y) respectively determined by calculation. The totality of possible colors ( without regard to the light-dark variants) are bordered by the horseshoe bounding Spektralfarblinie ( spectrally pure colors) as well as the bottom line of purples.

The central focus of the panel is the key in every color measurement situation white point W. The point on the graph W end is the one theoretical white point of all three colors, each 1/3 ( x, y, and z = 0.333 ... ) represents. Depending on the lighting situation, the white point can be located within the horseshoe virtually anywhere. Of significance in only the black body curve. In the course of the colors are given as temperature of an ideal radiator (black body ) in Kelvin. Starting from the white point can all be read as color shade perceived colors on a line through the point P. About the used color space addition ( here the Adobe RGB color space is shown), the appropriate for the specific situation spectral be read on the Spektralfarblinie (P '). On the exact opposite side of W complementary colors can be read on the extended line WQ. The point Q ' in this case represents the extreme ( pure ) complementary color, which is in this case defined by the intersection with the line of purples.

The CIE color system is precisely defined simply by initially experimentally determined relative sensitivities of the three color receptors of the human perception of color system ( the so-called ' Standard Observer ) for each visible spectral color. The sensitivity curves are subject to variation from person to person, defined as mean values ​​, however, as so-called standard observer (CIE Standard Observer ).

From the measurement of the spectral sensitivity of the three human pin a physiological color space can be determined by the same template. The three pins are named according to their sensitivity peak as L, M, S cones, for long -middle -short. The color space is formed therefrom, which can represent all perceivable colors is LMS color space. With appropriate normalization can also specify this a Farbarttafel. Is normalized by dividing by the sum L M S. Thus, for this purpose, the values ​​l = L / (L M S), m = M / (L M S), s = S / (L M S), the relation l m s = 1 meet.

The construction principle

On the edge of this surface ( spectral color ), the "pure" colors are the highest saturation. The connecting line between violet ( ≤ 420 nm ) and red ( ≥ 680 nm ) is called the purple line. A further trend is the color thermal radiation sources. It begins with saturated reds for low temperatures around 900 K, increases for temperatures 5000-6500 K at a largely white color and is used for even higher temperatures bluish ( but never a pure blue ).

A period ( therefore, a color tone ) of the CIE color space is determined by the color point of a straight line is placed from the neutral point W. The ratio of the white point chromaticity coordinate distance (WF ), and white point distance outer edge (WP) is a measure of the saturation. Each color point on the Spektralfarbzug Thus, the saturation of 1 (corresponding to 100 %).

Is expressed as a dominant wavelength: The straight line from the white point (W) on the color locus (F) to the edge of Spektralzuges (P) ends at this wavelength. Purple shades will be referred to by the wavelength at contrary extension of the straight line through the white point.

The xy chromaticity species level is only the projection of belonging to the system color solid according to Rösch. The third size necessary for the definition of a color is the lightness value of A, this is the same size and the same by definition with the brightness parameter Y. This also resulted in the designation as Yxy color space.

The psychological and artistic class object color ( complementary color ) is achieved by determining the color coordinates in the xy amount by mirroring the white point W the color locus of the complementary color. By the same method to obtain the saturation and the dominant wavelength.

Metamerism

Painters had long known that it is possible colors mixing to three components. The theory presented on this Hermann von Helmholtz and Thomas Young on:

• Each color impression can be made of three primary color beams ( additive color mixing ) can be achieved and
• Different spectral composition can be perceived as equally ( metamers ).

Developed by Helmholtz and Young from the practical experience trichromatic theory requires that in the human eye three different color receptors are present. They must also have a certain absorption spectrum. For the discharge of this is on the other hand, the spectral sensitivity of the subject. Each absorption spectrum has a maximum at a certain wavelength. The visual perception is made up of three components. Therefore any perceptible color impression will ermischt from the corresponding spectral maximum sensation. General Hermann Günther Grassmann formulated in his First Grassmann's law that every color is uniquely described by three ( sufficiently independent ) variables. This can be, for example:

• Brightness, hue and saturation or
• Intensity of red, green and blue.

The "eye " (and the following perceptual apparatus ) assigns any "complex" light spectra by " few " parameters. Lights having different spectra ( with suitable - just metameric - intensity) thereby producing the same color impression. The color stimuli of the continuous visible spectrum from 380 nm to 780 nm are mapped to the perception of the size of the three valences.

All perceivable colors can thus be represented as position vectors in a three dimensional color space. The three coordinates of each point in the color space are the measure of the intensity of the color components red (R ), green ( G) and blue (B). The length of a vector is determined, the total intensity of the light, while its spatial direction represents the mixing ratio of three primary colors. The intensity is allowed to ignore, then all possible color effects can be provided on a triangular area F in the space, for every point on the R G B = 1. Projecting this on the surface, which is spanned by the axes for red and green, so there is a simple way to represent the ratios of the three color values ​​graphically: The Red ( = X) - and green ( = Y ) components are directly to read, while the blue ( = Z ) component according to B = 1 - R - G is computable.

When trying to enter all existing valences of spectral colors on the thus resulting graph (dashed line BGR - cut with our line in P ') falls - regardless of the Spektralfarbtrio - on that ( pure ) spectral components outside each of the possible relationships subject.

It had negative setting values ​​for almost all spectral except for the system-defined primary colors. To select from the three primary colors a spectral cyan (C) to produce 'to apply described valences in:

The numerical values ​​of the coordinates, ie, the absolute amounts of Farbortvektors in this color space can be transformed mathematically correct.

So the request, " blue " from the and the "green" arises omit ( in the required intensity) something " red" light in order to obtain the desired Cyan For practical use. With such transformations it is possible to arrange all of the colors in an (initially theoretical ) color space. This about an arbitrary RGB color space moves easily into the interior of such a complete color space.

Practical Considerations

The international CIE standard colorimetric system introduced is the basis of most modern color measurement and reproductive systems. On it rests also in computer graphics widely used standard - Lab color space. This is logarithmic and parametrically from the XYZ color space to L * a * b * distorted by reasons of physiology of perception, the discernment of different color stimuli is better represented.

The German implementation of the international CIE standard is defined in DIN 5033-3.

The XYZ system was created in the years up to 1931. The then precision for accurate scientific purposes is inadequate under present technical possibilities. The underlying sensitivity curves are the result of measurement protocols whose permission may be questioned. To average the data values ​​were used from different sources, these were also extrapolated and smoothed ( because of inadequate computer technology ) with a soft-focus filter. Thus, errors in the brightness curve Vλ may have occurred. The error could even be in the order of 10 at a wavelength below 400 nm. In any case, the tabulated curves are to be used with caution, because today the wavelengths in 1- nm steps are given and the abscissa values ​​in several decimal places. However, the original data were specified with a value in an interval of about 10 nm. To work around suspected inaccuracies of the numerical values ​​numerous color spaces were provided with mathematical conversions and tricks, but the XYZ values ​​are still based.

The standard lighting

The CIE standard colorimetric system was originally developed in terms of lighting issues. The system allows, in principle any possible combination of X, Y and Z values. In order to achieve a standardized overview of the colors neutral white standard light colors have been defined. For the sake of color perception they are on the black body curve, as these are associated with a color temperature lighting.

Before today's development of the computer technology a representation of the values ​​was necessary as a table. To make them comparable, the intensity values ​​Sλ the standard light types were normalized to S560 nm = 100 %, which is why an appropriate recalculation is necessary for colorimetric calculations.

Conversion of color spaces

As with the installation of the CIE color space perception "Color" is numerically detected to color stimuli can be described also in other color spaces such as by conversion to the corresponding matrix operations.

Example is the conversion of the coordinates of the sRGB color space into the Tristimuluskoordinaten X, Y, Z is given.