Color models
Encyclopedia
A color model is an abstract mathematical model describing the way color
s can be represented as tuple
s of numbers, typically as three or four values or color components. When this model is associated with a precise description of how the components are to be interpreted (viewing conditions, etc.), the resulting set of colors is called color space
. This section describes ways in which human color vision
can be modeled.
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 become 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.
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.
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. These data were measured for human observers and a 2-degree field of view. In 1964, supplemental data for a 10-degree field of view were published.
Note that the tabulated sensitivity curves have a certain amount of arbitrariness in them. The shapes of the individual X, Y and Z 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 X, Y, and Z curves are arbitrary. One could as well define a valid color space with an X sensitivity curve that has twice the amplitude. This new color space would have a different shape. The sensitivity curves in the CIE 1931 and 1964 xyz color space are scaled to have equal areas under the curves.
Sometimes XYZ colors are represented by the luminance, Y, and chromaticity coordinates x and y, defined by:
Mathematically, x and y are projective coordinates and the colors of the chromaticity diagram occupy a region of the real projective plane
. Because the CIE sensitivity curves have equal areas under the curves, light with a flat energy spectrum corresponds to the point (x,y) = (0.333,0.333).
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.
mixing with primary color
s 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. 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. See Additive color
.
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.
.
HSV models itself on paint mixture, with its saturation and value dimensions resembling mixtures of a brightly colored paint with, respectively, white and black. HSL tries to resemble more perceptual color models such as NCS or Munsell. It places the fully saturated colors in a circle of lightness ½, so that lightness 1 always implies white, and lightness 0 always implies black.
HSV and HSL are both widely used in computer graphics, particularly as color pickers
in image editing software. The mathematical transformation from RGB to HSV or HSL could be computed in real time, even on computers of the 1970s, and there is an easy-to-understand mapping between colors in either of these spaces and their manifestation on a physical RGB device.
This written by TAD
, magenta
, and yellow
transparent dyes/inks on a white substrate. These are the subtractive
primary color
s. Often a fourth black
is added to improve reproduction of some dark colors. This is called "CMY" or "CMYK" color space.
The cyan ink absorbs red light but transmits green and blue, the magenta ink absorbs green light but transmits red and blue, and the yellow ink absorbs blue light but transmits red and green. The white substrate reflects the transmitted light back to the viewer. Because in practice the CMY inks suitable for printing also reflect a little bit of color, making a deep and neutral black impossible, the K (black ink) component, usually printed last, is needed to compensate for their deficiencies. The dyes used in traditional color photographic prints and slides are much more perfectly transparent, so a K component is normally not needed or used in those media.
devised by Albert H. Munsell
is a famous classification that organises various colors into a color solid based on hue, saturation and value. Other important color systems include the Swedish Natural Color System
(NCS) from the Scandinavian Color Institute, the Optical Society of America
's Uniform Color Space (OSA-UCS), and the Hungarian Coloroid
system developed by Antal Nemcsics from the Budapest University of Technology and Economics
. Of those, the NCS is based on the opponent-process
color model, while the Munsell, the OSA-UCS and the Coloroid attempt to model color uniformity. The American Pantone
and the German RAL
commercial color-matching systems differ from the previous ones in that their color spaces are not based on an underlying color model.
-Helmholtz
's trichromatic model
and Hering
's opponent-process model
. Though these two theories were initially thought to be at odds, it later came to be understood that the mechanisms responsible for color opponency receive signals from the three types of cones and process them at a more complex level.
, found on the X chromosome. One of these copies evolved to be sensitive to green light and constitutes our mid wavelength opsin
. At the same time, our short wavelength opsin evolved from the ultraviolet opsin of our vertebrate and mammalian ancestors.
Human red-green color blindness occurs because the two copies of the red and green opsin genes remain in close proximity on the X chromosome. Because of frequent recombination during meiosis, these gene pairs can get easily rearranged, creating versions of the genes that do not have distinct spectral sensitivities.
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...
s can be represented as tuple
Tuple
In mathematics and computer science, a tuple is an ordered list of elements. In set theory, an n-tuple is a sequence of n elements, where n is a positive integer. There is also one 0-tuple, an empty sequence. An n-tuple is defined inductively using the construction of an ordered pair...
s of numbers, typically as three or four values or color components. When this model is associated with a precise description of how the components are to be interpreted (viewing conditions, etc.), the resulting set of colors is called color space
Color space
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...
. This section describes ways in which human color vision
Color vision
Color vision is the capacity of an organism or machine to distinguish objects based on the wavelengths of the light they reflect, emit, or transmit...
can be modeled.
Tristimulus color space
One can picture this space as a region in three-dimensional Euclidean spaceEuclidean space
In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions...
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
Color temperature
Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, and other fields. The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of...
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
International Commission on Illumination
The International Commission on Illumination is the international authority on light, illumination, color, and color spaces...
color space and neither is the changing color perception at low light levels (see: Kruithof curve
Kruithof curve
Named after the Dutch physicist Arie Andries Kruithof, the Kruithof curve relates the illuminance and colour temperature of visually pleasing light sources...
).
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 become 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.
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
Gamut
In color reproduction, including computer graphics and photography, the gamut, or color gamut , is a certain complete subset of colors. The most common usage refers to the subset of colors which can be accurately represented in a given circumstance, such as within a given color space or by a...
) that can be constructed from the red, green, and blue primaries in a computer display.
CIE XYZ color space
- Main article: CIE 1931 color spaceCIE 1931 color spaceIn the study of color perception, one of the first mathematically defined color spaces is the CIE 1931 XYZ color space, created by the International Commission on Illumination in 1931....
International Commission on Illumination
The International Commission on Illumination is the international authority on light, illumination, color, and color spaces...
in 1931. These data were measured for human observers and a 2-degree field of view. In 1964, supplemental data for a 10-degree field of view were published.
Note that the tabulated sensitivity curves have a certain amount of arbitrariness in them. The shapes of the individual X, Y and Z 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 X, Y, and Z curves are arbitrary. One could as well define a valid color space with an X sensitivity curve that has twice the amplitude. This new color space would have a different shape. The sensitivity curves in the CIE 1931 and 1964 xyz color space are scaled to have equal areas under the curves.
Sometimes XYZ colors are represented by the luminance, Y, and chromaticity coordinates x and y, defined by:
Mathematically, x and y are projective coordinates and the colors of the chromaticity diagram occupy a region of the real projective plane
Projective plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines that do not intersect...
. Because the CIE sensitivity curves have equal areas under the curves, light with a flat energy spectrum corresponds to the point (x,y) = (0.333,0.333).
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.
RGB color model
Media that transmit light (such as television) use additive colorAdditive color
An additive color model involves light emitted directly from a source or illuminant of some sort. The additive reproduction process usually uses red, green and blue light to produce the other colors. Combining one of these additive primary colors with another in equal amounts produces the...
mixing with primary color
Primary color
Primary colors are sets of colors that can be combined to make a useful range of colors. For human applications, three primary colors are usually used, since human color vision is trichromatic....
s of red
Red
Red is any of a number of similar colors evoked by light consisting predominantly of the longest wavelengths of light discernible by the human eye, in the wavelength range of roughly 630–740 nm. Longer wavelengths than this are called infrared , and cannot be seen by the naked eye...
, green
Green
Green is a color, the perception of which is evoked by light having a spectrum dominated by energy with a wavelength of roughly 520–570 nanometres. In the subtractive color system, it is not a primary color, but is created out of a mixture of yellow and blue, or yellow and cyan; it is considered...
, and blue
Blue
Blue is a colour, the perception of which is evoked by light having a spectrum dominated by energy with a wavelength of roughly 440–490 nm. It is considered one of the additive primary colours. On the HSV Colour Wheel, the complement of blue is yellow; that is, a colour corresponding to an equal...
, 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. 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
Color television
Color television is part of the history of television, the technology of television and practices associated with television's transmission of moving images in color video....
sets or color computer monitors need only produce mixtures of red, green and blue light. See Additive color
Additive color
An additive color model involves light emitted directly from a source or illuminant of some sort. The additive reproduction process usually uses red, green and blue light to produce the other colors. Combining one of these additive primary colors with another in equal amounts produces the...
.
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.
HSV and HSL representations
Recognizing that the geometry of the RGB model is poorly aligned with the color-making attributes recognized by human vision, computer graphics researchers developed two alternate representations of RGB, HSV and HSL (hue, saturation, value and hue, saturation, lightness), in the late 1970s. HSV and HSL improve on the color cube representation of RGB by arranging colors of each hue in a radial slice, around a central axis of neutral colors which ranges from black at the bottom to white at the top. The fully saturated colors of each hue then lie in a circle, a color wheelColor wheel
A color wheel or color circle is an abstract illustrative organization of color hues around a circle that shows relationships between primary colors, secondary colors, complementary colors, etc....
.
HSV models itself on paint mixture, with its saturation and value dimensions resembling mixtures of a brightly colored paint with, respectively, white and black. HSL tries to resemble more perceptual color models such as NCS or Munsell. It places the fully saturated colors in a circle of lightness ½, so that lightness 1 always implies white, and lightness 0 always implies black.
HSV and HSL are both widely used in computer graphics, particularly as color pickers
Color tool
A color tool, color picker, or color chooser is a utility, usually found within graphics software or online, used to choose colors or create color schemes....
in image editing software. The mathematical transformation from RGB to HSV or HSL could be computed in real time, even on computers of the 1970s, and there is an easy-to-understand mapping between colors in either of these spaces and their manifestation on a physical RGB device.
This written by TAD
CMYK color model
It is possible to achieve a large range of colors seen by humans by combining cyanCyan
Cyan from , transliterated: kýanos, meaning "dark blue substance") may be used as the name of any of a number of colors in the blue/green range of the spectrum. In reference to the visible spectrum cyan is used to refer to the color obtained by mixing equal amounts of green and blue light or the...
, magenta
Magenta
Magenta is a color evoked by light stronger in blue and red wavelengths than in yellowish-green wavelengths . In light experiments, magenta can be produced by removing the lime-green wavelengths from white light...
, and yellow
Yellow
Yellow is the color evoked by light that stimulates both the L and M cone cells of the retina about equally, with no significant stimulation of the S cone cells. Light with a wavelength of 570–590 nm is yellow, as is light with a suitable mixture of red and green...
transparent dyes/inks on a white substrate. These are the subtractive
Subtractive color
A subtractive color model explains the mixing of paints, dyes, inks, and natural colorants to create a full range of colors, each caused by subtracting some wavelengths of light and reflecting the others...
primary color
Primary color
Primary colors are sets of colors that can be combined to make a useful range of colors. For human applications, three primary colors are usually used, since human color vision is trichromatic....
s. Often a fourth black
Black
Black is the color of objects that do not emit or reflect light in any part of the visible spectrum; they absorb all such frequencies of light...
is added to improve reproduction of some dark colors. This is called "CMY" or "CMYK" color space.
The cyan ink absorbs red light but transmits green and blue, the magenta ink absorbs green light but transmits red and blue, and the yellow ink absorbs blue light but transmits red and green. The white substrate reflects the transmitted light back to the viewer. Because in practice the CMY inks suitable for printing also reflect a little bit of color, making a deep and neutral black impossible, the K (black ink) component, usually printed last, is needed to compensate for their deficiencies. The dyes used in traditional color photographic prints and slides are much more perfectly transparent, so a K component is normally not needed or used in those media.
Color systems
There are various types of color systems that classify color and analyse their effects. The American Munsell color systemMunsell color system
In colorimetry, the Munsell color system is a color space that specifies colors based on three color dimensions: hue, value , and chroma . It was created by Professor Albert H...
devised by Albert H. Munsell
Albert Henry Munsell
Albert Henry Munsell was an American painter, teacher of art, and the inventor of the Munsell color system.He was born in Boston, Massachusetts, attended and served on the faculty of Massachusetts Normal Art School, and died in nearby Brookline.As a painter, he was noted for seascapes and...
is a famous classification that organises various colors into a color solid based on hue, saturation and value. Other important color systems include the Swedish Natural Color System
Natural Color System
The Natural Color System is a proprietary perceptual color model published by the Scandinavian Colour Institute of Stockholm, Sweden. It is based on the color opponency description of color vision, first proposed by German physiologist Ewald Hering...
(NCS) from the Scandinavian Color Institute, the Optical Society of America
Optical Society of America
The Optical Society is a scientific society dedicated to advancing the study of light—optics and photonics—in theory and application, by means of publishing, organizing conferences and exhibitions, partnership with industry, and education. The organization has members in more than 100 countries...
's Uniform Color Space (OSA-UCS), and the Hungarian Coloroid
Coloroid
The Coloroid Color System is a colour space developed between 1962 and 1980 by Prof. Antal Nemcsics at the Budapest University of Technology and Economics for use by "architects and visual constructors"...
system developed by Antal Nemcsics from the Budapest University of Technology and Economics
Budapest University of Technology and Economics
The Budapest University of Technology and Economics , in hungarian abbreviated as BME, English official abbreviation BUTE, is the most significant University of Technology in Hungary and is also one of the oldest Institutes of Technology in the world, having been founded in 1782.-History:BME is...
. Of those, the NCS is based on the opponent-process
Opponent process
The color opponent process is a color theory that states that the human visual system interprets information about color by processing signals from cones and rods in an antagonistic manner...
color model, while the Munsell, the OSA-UCS and the Coloroid attempt to model color uniformity. The American Pantone
Pantone
Pantone Inc. is a corporation headquartered in Carlstadt, New Jersey, USA. The company is best known for its Pantone Matching System , a proprietary color space...
and the German RAL
RAL (color space system)
RAL is a color matching system used in Europe. In colloquial speech RAL refers to the RAL CLASSIC system, mainly used for varnish and powder coating.- RAL CLASSIC:...
commercial color-matching systems differ from the previous ones in that their color spaces are not based on an underlying color model.
Models of mechanism of color vision
We also use "color model" to indicate a model or mechanism of color vision for explaining how color signals are processed from visual cones to ganglion cells. For simplicity, we call these models color mechanism models. The classical color mechanism models are YoungThomas Young (scientist)
Thomas Young was an English polymath. He is famous for having partly deciphered Egyptian hieroglyphics before Jean-François Champollion eventually expanded on his work...
-Helmholtz
Hermann von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz was a German physician and physicist who made significant contributions to several widely varied areas of modern science...
's trichromatic model
Young-Helmholtz theory
The Young–Helmholtz theory is a theory of trichromatic color vision – the manner in which the photoreceptor cells in the eyes of humans and other primates work to enable color vision...
and Hering
Ewald Hering
Karl Ewald Konstantin Hering was a German physiologist who did much research into color vision and spatial perception...
's opponent-process model
Opponent process
The color opponent process is a color theory that states that the human visual system interprets information about color by processing signals from cones and rods in an antagonistic manner...
. Though these two theories were initially thought to be at odds, it later came to be understood that the mechanisms responsible for color opponency receive signals from the three types of cones and process them at a more complex level.
Vertebrate evolution of color vision
Vertebrate animals were primitively tetrachromatic. They possessed four types of cones—long, mid, short wavelength cones, and ultraviolet sensitive cones. Today, fish, reptiles and birds are all tetrachromatic. Placental mammals lost both the mid and short wavelength cones. Thus, most mammals do not have complex color vision—they are dichromatic but they are sensitive to ultraviolet light, though they cannot see its colors. Human trichromatic color vision is a recent evolutionary novelty that first evolved in the common ancestor of the Old World Primates. Our trichromatic color vision evolved by duplication of the long wavelength sensitive opsinOpsin
Opsins are a group of light-sensitive 35–55 kDa membrane-bound G protein-coupled receptors of the retinylidene protein family found in photoreceptor cells of the retina. Five classical groups of opsins are involved in vision, mediating the conversion of a photon of light into an electrochemical...
, found on the X chromosome. One of these copies evolved to be sensitive to green light and constitutes our mid wavelength opsin
Opsin
Opsins are a group of light-sensitive 35–55 kDa membrane-bound G protein-coupled receptors of the retinylidene protein family found in photoreceptor cells of the retina. Five classical groups of opsins are involved in vision, mediating the conversion of a photon of light into an electrochemical...
. At the same time, our short wavelength opsin evolved from the ultraviolet opsin of our vertebrate and mammalian ancestors.
Human red-green color blindness occurs because the two copies of the red and green opsin genes remain in close proximity on the X chromosome. Because of frequent recombination during meiosis, these gene pairs can get easily rearranged, creating versions of the genes that do not have distinct spectral sensitivities.