1.1 Spectral versus non-spectral colors

Most light sources are not pure spectral sources; rather they are created from mixtures of various wavelengths and intensities of light. To the human eye, however, there is a wide class of mixed-spectrum light that is perceived the same as a pure spectral color. In the table above, for instance, the "orange" patch is not emitting pure light at a fixed wavelength of around 600 nm. Rather, it is emitting a mixture of about two parts red to one part green light. We cannot see the difference, and the reason has to do with the pigments that make up our color vision cells (see below).

A useful quantification of this property is the dominant wavelength, which matches a wavelength of spectral light to a non-spectral source that evokes the same color perception. Dominant wavelength is the formal background for the popular concept of hue.

In addition to the many light sources that can appear to be pure spectral colors but are actually mixtures, there are many color perceptions that by definition cannot be pure spectral colors due to desaturation or because they are purples (which do not appear in the Newtonian pure spectrum). Some examples of necessarily non-spectral colors are the achromatic colors (black, gray and white) and other colors such as pink, tan and magenta.

1.2 Color in the wave equation

The wave equation describes the behavior of light and so we should be able to describe color spectra in terms of the mathematical properties of the solutions of the wave equation. However, to understand which particular color perception will arise from a particular physical spectrum requires knowledge of the specific retinal physiology of the observer. For completeness, we include a simple equation for light traveling in a vacuum:

u_tt=c²(u_xx+u_yy+u_zz)

where the subscripts denote partial derivatives and c is the speed of light. If we fix (x,y,z) a point in space and look at the solution u(x,y,z,t) as a function of t, we obtain a signal. If we take the Fourier transform of this signal, we obtain a frequency decomposition as described above. Each frequency has an amplitude and phase. The frequency multiplied by Planck's constant h determines the energy of a photon of the relevant component. The square of the amplitude represents the intensity, which is the amount of energy transmitted per second through a unit area of a surface perpendicular to the light propagation. The phase information is much more mysterious because it is difficult to measure and observe. Humans cannot perceive phase effects of light except in special cases of interference (e.g. see thin-film optics) where phase effects lead to perceptible amplitude changes. Most light has randomly distributed phases, but lasers are more efficient when the photons all have the same phase.

2 Color vision

Although Aristotle and other ancient scientists speculated on the nature of light and color vision, it was not until Newton that light was correctly identified as the source of the color sensation. Goethe studied the theory of colors, and in 1801 Thomas Young proposed his trichromatic theory which was later refined by Hermann von Helmholtz. That theory was confirmed in the 1960s and will be described below.

The human eye contains three different types of color receptor cells, or cones. One type, relatively distinct from the other two, is most responsive to blue light with wavelengths around 420 nm (this type is sometimes called short-wavelength cones, S cones, or blue cones). The other two types are closely related genetically, and in chemistry and response, and both respond most to greenish light. One (sometimes called long-wavelength cones, L cones, or red cones) are most sensitive to yellowish-green light with wavelengths around 564 nm, the other (sometimes called middle-wavelength cones, M cones, or green cones) are most sensitive to green light with wavelengths around 534 nm. The term "red cone" for the long-wavelength cone is deprecated as this cone is actually maximally responsive to green light, albeit longer wavelength green light than that which maximally excites the mid-wavelength/green cone.

The sensitivity curves of the cones are roughly bell-shaped and overlap considerably. The incoming signal spectrum is thus reduced by the eye to three values, sometimes called tristimulus values, representing the intensity of the response of each of the cone types.

Because of the overlap between the sensitivity ranges, not all combinations of stimuli are actually possible. For example, it is not possible to stimulate only the mid-wavelength/green cones: the other cones will be stimulated to some degree at the same time. The set of all combinations of stimuli that are possible make up the human color space. It has been estimated that humans can distinguish roughly 10 million different colors, although the identification of a specific color is highly subjective, since even the two eyes of a single individual perceive colors slightly differently. This is discussed in more detail below.

2.1 Clinical issues

If one or more types of a person's color-sensing cones does not respond as normal to incoming light, that person has a smaller or skewed color space and is said to be color deficient. Another term frequently used is color blind, although this can be misleading; only a small fraction of color deficient individuals actually see completely in black and white, most simply have anomalous color perception. Other animals may have more than three different color receptors (some birds, reptiles, and fish) or fewer (most mammals).

An unusual psychological condition sometimes affecting color perception is synaesthesia.

3 Color models

A color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components. The resulting set of colors is called color space. This section describes ways in which human color vision can be modeled.

3.1 Tristimulus color space

One can picture this space as a region in three-dimensional Euclidean space if one identifies the x, y, and z axes with the stimuli for the long-wavelength (L), medium-wavelength (M), and short-wavelength (S) receptors. The origin, (S,M,L) = (0,0,0), corresponds to black. White has no definite position in this diagram; rather it is defined according to the color temperature or white balance as desired or as available from ambient lighting. The human color space is a horse-shoe-shaped cone such as shown here (see also CIE chromaticity diagram below), extending from the origin to, in principle, infinity. In practice, the human color receptors will be saturated or even be damaged at extremely-high light intensities, but such behavior is not part of the CIE color space and neither is the changing color perception at low light levels (see: Kruithof curve).

The most saturated colors are located at the outer rim of the region, with brighter colors farther removed from the origin. As far as the responses of the receptors in the eye are concerned, there is no such thing as "brown" or "gray" light. The latter color names refer to orange and white light respectively, with an intensity that is lower than the light from surrounding areas. One can observe this by watching the screen of an overhead projector during a meeting: one sees black lettering on a white background, even though the "black" has in fact not gotten darker than the white screen on which it is projected before the projector was turned on. The "black" areas have not actually become darker but appear "black" relative to the higher intensity "white" projected onto the screen around it. See also color constancy below.

The human tristimulus space has the property that additive mixing of colors corresponds to the adding of vectors in this space. This makes it easy to, for example, describe the possible colors ( gamut) that can be constructed from the red, green, and blue primaries in a computer display.

3.2 Tristimulus color space as a mathematical projection

Continuing with our mathematical description of light using the wave equation, a good model for the way our receptors work can be explained in terms of Hilbert spaces and orthogonal projections. Indeed, as mentioned previously, the light going through point (x,y,z) in space is a signal. It is useful to think of this signal as some function in L², the space of square- integrable functions. This space is a (infinite dimensional!) Hilbert space, which means that it has a useful notion of orthogonal projection.

Each receptor can be thought of as a unit vector. For instance, the red receptor would be some vector r of light, whose Fourier transform would be large in the 405 to 480 THz interval, and smaller elsewhere. If we take the Fourier transform of v and plot its absolute value, we obtain what is called the frequency response curve of the human red receptor.

Then, the amount of "red" present in any color will be the orthogonal projection onto the axis generated by the vector r. In fact, only the magnitude of the orthogonal projection onto r is measured by our receptors. There are two more vectors, one for blue and one for green. Therefore, our color perception is in fact limited to a three-dimensional subspace of the infinite dimensional space of all possible colors.

3.3 CIE XYZ color space

One of the first mathematically defined color spaces is the CIE XYZ color space (also known as CIE 1931 color space), created by the International Commission on Illumination in 1931. This color space is based on the Standard Colorimetric Observer functions. The figure shows the related chromaticity diagram with wavelengths in nanometers.

In this diagram, x and y are related to the X, Y, and Z tristimulus values under Human tristimulus color space above according to:

x = X/(X + Y + Z),

y = Y/(X + Y + Z).

The values for X, Y, and Z are obtained by integrating the product of the spectrum of a light beam and the published color-matching functions. Blue and red wavelengths do not contribute strongly to the luminosity, which is illustrated by the following example:

red

green

blue

red+green

green+blue

red+blue

red+green+blue

zero light

For someone with normal color vision, green is brighter than red, which is brighter than blue. Even though the pure blue appears to be very dark and hardly discernible from black when observed from a distance, blue has a strong coloring power when mixed with green or red.

It must be noted that the tabulated sensitivity curves have a certain amount of arbitrariness in them. The shapes of the individual S, M, and L sensitivity curves can be measured with a reasonable accuracy. However, the overall luminosity curve (which in fact is a weighted sum of these three curves) is subjective, since it involves asking a test person whether two light sources have the same brightness, even if they are in completely different colors. Along the same lines, the relative magnitudes of the S, M, and L curves are arbitrary. One could as well define a valid color space with an S sensitivity curve that has twice the amplitude. This new color space would have a different shape. The sensitivity curves in the CIE 1931 xyz color space are scaled to have equal areas under the curves. This scaling means that light with a flat energy spectrum corresponds to the point (x,y) = (0.333,0.333).

The CIE-xyz color space is a prism, as opposed to the cone-shaped tristimulus space above. In the two-dimensional xy representation, all possible additive mixtures of two colors A and B form a straight line. However, the additive mixture of two colors does generally not lie on the mid-point of this line.

4 Reproduction of color

Two different light spectra which have the same effect on the three color receptors in the human eye will be perceived as the same color. This is exemplified by the white light that is emitted by fluorescent lamps, which typically has a spectrum consisting of a few narrow bands, while daylight has a continuous spectrum. The human eye cannot tell the difference between such light spectra just by looking into the light source, although reflected colors from objects can look different.

Similarly, most human color perceptions can be generated by a mixture of three colors called primaries. This is used to reproduce color scenes in photography, printing, television, and other media.

No mixture of colors, though, can produce a fully pure color perceived as completely identical to a spectral color, although one can get very close for the longer wavelengths, where the chromaticity diagram below has a nearly straight edge. For example, mixing green light (530 nm) and blue light (460 nm) produces cyan light that is slightly desaturated, because response of the red color receptor would be greater to the green and blue light in the mixture than it would be to a pure cyan light at 485 nm that has the same intensity as the mixture of blue and green.

Because of this, and because the primaries in color reproduction systems generally are not pure themselves, the colors reproduced are never perfectly saturated colors, and so spectral colors cannot be matched exactly. However, natural scenes rarely contain fully saturated colors, thus such scenes can usually be approximated well by these systems. The range of colors that can be reproduced with a given color reproduction system is called the gamut. The CIE chromaticity diagram can be used to describe the gamut.

Another problem with color reproduction systems is connected with the acquisition devices, like cameras or scanners. The characteristics of the color sensors in the devices are often very far from the characteristics of the receptors in the human eye. In effect, acquisition of colors that have some special, often very "jagged", spectra caused for example by unusual lighting of the photographed scene can be relatively poor.

Species that have color receptors different from humans, e. g. birds that may have four receptors, can differentiate some colors that look the same to a human. In such cases, a color reproduction system `tuned' to a human with normal color vision may give very inaccurate results for the other observers.

4.1 Pigments and reflective media

When producing a color print or painting a surface, the applied paint changes the surface; if the surface is then illuminated with white light (which consists of equal intensities of all visible wavelengths), the reflected light will have a spectrum corresponding to the desired color.

4.2 RGB color space

Media that transmit light (such as television) use additive color mixing with primary colors of red, green, and blue, each of which stimulates one of the three types of the eye's color receptors with as little stimulation as possible of the other two. This is called " RGB" color space—see also RGB color model. Mixtures of light of these primary colors cover a large part of the human color space and thus produce a large part of human color experiences. This is why color television sets or color computer monitors need only produce mixtures of red, green and blue light.

Other primary colors could in principle be used, but with red, green and blue the largest portion of the human color space can be captured. Unfortunately there is no exact consensus as to what loci in the chromaticity diagram the red, green, and blue colors should have, so the same RGB values can give rise to slightly different colors on different screens.

4.3 CMYK color model

It is possible to achieve a large range of colors seen by humans by combining cyan, magenta, and yellow transparent dyes/inks on a white substrate. These are the subtractive primary colors. Often a fourth black is added to improve reproduction of some dark colors. This is called "CMY" or " CMYK" color space.

The cyan ink will reflect all but the red light, the yellow ink will reflect all but the blue light and the magenta ink will reflect all but the green light. This is because cyan light is an equal mixture of green and blue, yellow is an equal mixture of red and green, and magenta light is an equal mixture of red and blue.

4.4 HSV color space

The RGB and CMYK color spaces are most useful for technical reproduction of color scenes. A color space used in computer graphics that more closely models the human experience is the HSV color space which arranges colors in a cylinder, somewhat similar to the CIE-xyz space discussed above. The cross-section of the cylinder is a color wheel, but instead of pure spectral colors, the edge consists of additive mixtures of red, green, and blue. In the HSV color space, every color is specified by its hue (position on the circle), saturation (distance from the circle's center) and value (luminosity). The basic idea of the HSV color space was already used by 19th century physiologist Ewald Hering, although the modern definition dates from the 1970s. The HSV color space is also sometimes referred to as the HSB (hue-saturation-brightness) color space.

4.5 HLS color space

The HLS color space, also called HSL, stands for "Hue, Saturation, Lightness". While HSV (Hue, Saturation, Value) can be viewed graphically as a color cone or hexcone, HSL is drawn as a double cone or double hexcone. Both systems are non-linear deformations of the RGB color cube. The two apexes of the HLS double hexcone correspond to black and white. The angular parameter corresponds to hue, distance from the axis corresponds to saturation, and distance along the black-white axis corresponds to lightness.

See also: Color space.

5 Color perception

There is an interesting phenomenon which occurs when an artist uses a limited color palette: the eye tends to compensate by seeing any grey or neutral color as the color which is missing from the color wheel. E.g.: in a limited palette consisting of red, yellow, black, and white, a mixture of yellow and black will appear as a variety of green, a mixture of red and black will appear as a variety of purple, and pure grey will appear bluish.

When the eye shifts attention after viewing a color for some time, then the complement of that color (the color opposite to it in the color wheel) is perceived by the eye for some time wherever it moves. This effect of color perception was utilised by Vincent van Gogh, a Post-Impressionist painter.

5.1 Effect of luminosity

Note that the color experience of a given light mixture may vary with absolute luminosity, because both rods and cones are active at once in the eye, with each having different color curves, and rods taking over gradually from cones as the brightness of the scene is reduced. This effect leads to a change in color rendition with absolute illumination levels that can be summarised in the " Kruithof curve".

5.2 Cultural influences

Different cultures have different terms for colors, and may also assign some color names to slightly different parts of the spectrum, or have a different color ontology: for instance, the Japanese color aoi can be interpreted as meaning something between the Western color terms of "blue" and "green": green is regarded as a shade of aoi.

Some argue that color terms evolve. There are a limited number of universal "basic color terms" which begin to be used by individual cultures in a relatively fixed order. For example, a culture would start with only two terms, equivalent to black and white or dark and light, before adding subsequent colors closely in the order of red; green and yellow; blue; brown; and orange, pink, purple, and gray. Older arguments for this theory also stipulated that the acquisition and use of basic color terms further along the evolutionary order indicated a more complex culture with more highly developed technology.

A somewhat recent example of a universal color categories theory is Basic Color Terms: Their Universality and Evolution (1969) by Brent Berlin and Paul Kay. A example of a linguistic determinism theory is Is color categorisation universal? New evidence from a stone-age culture (1999) by Jules Davidoff et al. Language, Thought, and Reality by (1956) Benjamin Lee Whorf. The idea of linguistically determined color categories is often used as evidence for the Sapir-Whorf hypothesis.

5.3 Color constancy

The trichromatric theory discussed above is strictly true only if the whole scene seen by the eye is of one and the same color, which of course is unrealistic. In reality, the brain compares the various colors in a scene, in order to eliminate the effects of the illumination. If a scene is illuminated with one light, and then with another, its colors will nevertheless appear constant to us. This was discovered by Edwin Land in the 1970s and led to his retinex theory of color constancy.

6 Miscellaneous

6.1 Structural color

Structural color is a property of some surfaces that are scored with fine parallel lines, formed of many thin parallel layers, or otherwise composed of periodic microstructures on the scale of the color's wavelength, to make a diffraction grating. The grating reflects some wavelengths more than others due to interference phenomena, causing white light to be reflected as colored light. Variations in the pattern's spacing often give rise to an iridescent effect, as seen in peacock feathers, films of oil, and mother of pearl, because the reflected color depends upon the viewing angle.

Structural color is studied in the field of thin-film optics. A layman's term that describes particularly the most ordered structural colors is iridescence.

6.2 Associations

Different colors are often associated with different emotional states, values or groups, but these associations can vary between cultures. In one system, red is considered to motivate action; orange and purple are related to spirituality; yellow cheers; green creates cosiness and warmth; blue relaxes; and white is associated with either purity or death. These associations are described more fully in the individual color pages, and under color psychology.

see also: National colors

6.3 Color systems

There are various types of color systems that classify color and analyse their effects. The Munsell color system is a famous classification that organises various colors into a color solid based on hue, saturation and value.

6.4 Contrast

Compare the visibility of the RGB primary and secondary colors against a white background:

red

green

blue

red+green

green+blue

red+blue

red+green+blue

zero light

Again, compare variations on gray backgrounds—#7f7f7f, #5f5f5f & #9f9f9f—the eight RGB primaries are equidistant from #7f7f7f in a 3-d geometrical representation of RGB color space—a reminder of the importance of background color for color perception.

Background = #7f7f7f

red

green

blue

red+green

green+blue

red+blue

red+green+blue

zero light

And let's look at black again, for completeness. (Note that your monitor background probably isn't perfectly black. Turn it off and see for yourself.)

Background = #00000

red

green

blue

red+green

green+blue

red+blue

red+green+blue

zero light

7 See also

• Metamerism
• List of colors
• Qualia
• Color temperature
• Color wheel
• Colors and emblems for parties
• Sporting colours
• Color psychology
• Web colors—Since HTML 3.2 was released—in early 1996—the W3C HTML standards have provided for the use of #rrggbb to identify text / foreground & background colors, where rr, gg & bb are 2-digit hexadecimal numbers in decimal numbers, from 0 to 255, representing the intensity of the red, green and blue light respectively. In earlier years of the Internet browser card computer screens, web designers were encouraged to limit use of screen colors to the 216 colors defined by the Netscape color cube (see Web-safe colors).
• The International Commission on Illumination defines colors and color spaces

8 External links

• Kruithof curve citation
• Article by technical lighting manufacturer on rod/cone vision, with cites to literature
• http://www.web-hog.com/tool/ez_cube.html

Color Computer vision Vision

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