Color model

A colour model is an abstract mathematical model describing the way colours can be represented as tuples of numbers, typically as three or four values or colour 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 colours is called "colour space." This section describes ways in which human colour vision can be modeled.

Tristimulus colour space

3D representation of the human colour 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) light 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 colour temperature or white balance as desired or as available from ambient lighting. The human colour 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 colour receptors will be saturated or even be damaged at extremely high light intensities, but such behavior is not part of the CIE colour space and neither is the changing colour perception at low light levels (see: Kruithof curve). The most saturated colours are located at the outer rim of the region, with brighter colours 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 colour 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 colour constancy.

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

CIE XYZ colour space

Main article: CIE 1931 color space

CIE 1931 Standard colourimetric Observer functions between 380 nm and 780 nm (at 5 nm intervals).

One of the first mathematically defined colour spaces is the CIE XYZ colour space (also known as CIE 1931 colour 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 function (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 colours. Along the same lines, the relative magnitudes of the X, Y, and Z curves are arbitrarily chosen to produce equal areas under the curves. One could as well define a valid colour space with an X sensitivity curve that has twice the amplitude. This new colour space would have a different shape. The sensitivity curves in the CIE 1931 and 1964 xyz colour space are scaled to have equal areas under the curves.

Sometimes XYZ colours are represented by the luminance, Y, and chromaticity coordinates x and y, defined by:

$x={\frac {X}{X+Y+Z}}$ and $y={\frac {Y}{X+Y+Z}}$

Mathematically, x and y are projective coordinates and the colours 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 colour-matching functions.

Additive and subtractive colour models

RYB colour model

Main article: RYB color model

RGB colour model

Main article: RGB color model

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

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

CMY and CMYK colour models

Main articles: CMY color model and CMYK color model

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

The cyan ink absorbs red light but reflects green and blue, the magenta ink absorbs green light but reflects red and blue, and the yellow ink absorbs blue light but reflects 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 colour, making a deep and neutral black impossible, the K (black ink) component, usually printed last, is needed to compensate for their deficiencies. Use of a separate black ink is also economically driven when a lot of black content is expected, e.g. in text media, to reduce simultaneous use of the three coloured inks. The dyes used in traditional colour photographic prints and slides are much more perfectly transparent, so a K component is normally not needed or used in those media.

Cylindrical-coordinate colour models

A number of colour models exist in which colours are fit into conic, cylindrical or spherical shapes, with neutrals running from black to white along a central axis, and hues corresponding to angles around the perimeter. Arrangements of this type date back to the 18th century, and continue to be developed in the most modern and scientific models.

Background

Philipp Otto Runge’s Farbenkugel (color sphere), 1810, showing the outer surface of the sphere (top two images), and horizontal and vertical cross sections (bottom two images).

Color sphere of Johannes Itten, 1919-20

See also: Color solid

Different colour theorists have each designed unique colour solids. Many are in the shape of a sphere, whereas others are warped three-dimensional ellipsoid figures—these variations being designed to express some aspect of the relationship of the colours more clearly. The colour spheres conceived by Phillip Otto Runge and Johannes Itten are typical examples and prototypes for many other colour solid schematics. The models of Runge and Itten are basically identical, and form the basis for the description below.

Pure, saturated hues of equal brightness are located around the equator at the periphery of the colour sphere. As in the colour wheel, contrasting (or complementary) hues are located opposite each other. Moving toward the center of the colour sphere on the equatorial plane, colours become less and less saturated, until all colours meet at the central axis as a neutral gray. Moving vertically in the colour sphere, colours become lighter (toward the top) and darker (toward the bottom). At the upper pole, all hues meet in white; at the bottom pole, all hues meet in black.

The vertical axis of the colour sphere, then, is gray all along its length, varying from black at the bottom to white at the top. All pure (saturated) hues are located on the surface of the sphere, varying from light to dark down the colour sphere. All impure (unsaturated hues, created by mixing contrasting colours) comprise the sphere's interior, likewise varying in brightness from top to bottom.

HSL and HSV

Main article: HSL and HSV

Painters long mixed colors by combining relatively bright pigments with black and white. Mixtures with white are called tints, mixtures with black are called shades, and mixtures with both are called tones. See Tints and shades.

The RGB gamut can be arranged in a cube. The RGB model is not very intuitive to artists used to using traditional models based on tints, shades and tones. The HSL and HSV color models were designed to fix this.

HSL cylinder

HSV cylinder

HSL and HSV are both cylindrical geometries, with hue, their angular dimension, starting at the red primary at 0°, passing through the green primary at 120° and the blue primary at 240°, and then wrapping back to red at 360°. In each geometry, the central vertical axis comprises the neutral, achromatic, or gray colours, ranging from black at lightness 0 or value 0, the bottom, to white at lightness 1 or value 1, the top.

Most televisions, computer displays, and projectors produce colours by combining red, green, and blue light in varying intensities—the so-called RGB additive primary colours. However, the relationship between the constituent amounts of red, green, and blue light and the resulting colour is unintuitive, especially for inexperienced users, and for users familiar with subtractive colour mixing of paints or traditional artists’ models based on tints and shades.

In an attempt to accommodate more traditional and intuitive colour mixing models, computer graphics pioneers at PARC and NYIT developed the HSV model in the mid-1970s, formally described by Alvy Ray Smith in the August 1978 issue of Computer Graphics. In the same issue, Joblove and Greenberg described the HSL model—whose dimensions they labeled hue, relative chroma, and intensity—and compared it to HSV. Their model was based more upon how colours are organized and conceptualized in human vision in terms of other colour-making attributes, such as hue, lightness, and chroma; as well as upon traditional colour mixing methods—e.g., in painting—that involve mixing brightly coloured pigments with black or white to achieve lighter, darker, or less colourful colours.

The following year, 1979, at SIGGRAPH, Tektronix introduced graphics terminals using HSL for colour designation, and the Computer Graphics Standards Committee recommended it in their annual status report. These models were useful not only because they were more intuitive than raw RGB values, but also because the conversions to and from RGB were extremely fast to compute: they could run in real time on the hardware of the 1970s. Consequently, these models and similar ones have become ubiquitous throughout image editing and graphics software since then.

Munsell colour system

Munsell’s color sphere, 1900. Later, Munsell discovered that if hue, value, and chroma were to be kept perceptually uniform, achievable surface colors could not be forced into a regular shape.

Three-dimensional representation of the 1943 Munsell renotations. Notice the irregularity of the shape when compared to Munsell's earlier color sphere, at left.

Main article: Munsell color system

Another influential older cylindrical colour model is the early-20th-century Munsell colour system. Albert Munsell began with a spherical arrangement in his 1905 book A colour Notation, but he wished to properly separate colour-making attributes into separate dimensions, which he called hue, value, and chroma, and after taking careful measurements of perceptual responses, he realized that no symmetrical shape would do, so he reorganized his system into a lumpy blob.

Munsell's system became extremely popular, the de facto reference for American colour standards—used not only for specifying the colour of paints and crayons, but also, e.g., electrical wire, beer, and soil colour—because it was organized based on perceptual measurements, specified colours via an easily learned and systematic triple of numbers, because the colour chips sold in the Munsell Book of colour covered a wide gamut and remained stable over time (rather than fading), and because it was effectively marketed by Munsell's Company. In the 1940s, the Optical Society of America made extensive measurements, and adjusted the arrangement of Munsell colours, issuing a set of "renotations". The trouble with the Munsell system for computer graphics applications is that its colours are not specified via any set of simple equations, but only via its foundational measurements: effectively a lookup table. Converting from RGB ↔ Munsell requires interpolating between that table's entries, and is extremely computationally expensive in comparison with converting from RGB ↔ HSL or RGB ↔ HSV which only requires a few simple arithmetic operations.

Natural colour System

Main article: Natural Color System

A three-dimensional drawing of the Ostwald color system. First described in Wilhelm Ostwald (1916).

Animation showing the NCS 1950 standard color samples in the NCS color circle and hue triangles.

The Swedish Natural colour System (NCS), widely used in Europe, takes a similar approach to the Ostwald bicone at right. Because it attempts to fit colour into a familiarly shaped solid based on "phenomenological" instead of photometric or psychological characteristics, it suffers from some of the same disadvantages as HSL and HSV: in particular, its lightness dimension differs from perceived lightness, because it forces colourful yellow, red, green, and blue into a plane.

Preucil hue circle

In densitometry, a model quite similar to the hue defined above is used for describing colours of CMYK process inks. In 1953, Frank Preucil developed two geometric arrangements of hue, the "Preucil hue circle" and the "Preucil hue hexagon", analogous to our H and H₂, respectively, but defined relative to idealized cyan, yellow, and magenta ink colours. The "Preucil hue error" of an ink indicates the difference in the "hue circle" between its colour and the hue of the corresponding idealized ink colour. The grayness of an ink is m/M, where m and M are the minimum and maximum among the amounts of idealized cyan, magenta, and yellow in a density measurement.

CIELCH_uv and CIELCH_ab

The visible gamut under Illuminant D65 plotted within the CIELCH_uv (left) and CIELCH_ab (right) color spaces. Lightness (L) is the vertical axis; Chroma (C) is the cylinder radius; Hue (H) is the angle around the circumference.

The International Commission on Illumination (CIE) developed the XYZ model for describing the colours of light spectra in 1931, but its goal was to match human visual metamerism, rather than to be perceptually uniform, geometrically. In the 1960s and 1970s, attempts were made to transform XYZ colours into a more relevant geometry, influenced by the Munsell system. These efforts culminated in the 1976 CIELUV and CIELAB models. The dimensions of these models—(L*, u*, v*) and (L*, a*, b*), respectively—are cartesian, based on the opponent process theory of colour, but both are also often described using polar coordinates—(L*, C*_uv, h*_uv) and (L*, C*_ab, h*_ab), respectively—where L* is lightness, C* is chroma, and h* is hue angle. Officially, both CIELAB and CIELUV were created for their colour difference metrics ∆E*_ab and ∆E*_uv, particularly for use defining colour tolerances, but both have become widely used as colour order systems and colour appearance models, including in computer graphics and computer vision. For example, gamut mapping in ICC colour management is usually performed in CIELAB space, and Adobe Photoshop includes a CIELAB mode for editing images. CIELAB and CIELUV geometries are much more perceptually relevant than many others such as RGB, HSL, HSV, YUV/YIQ/YCbCr or XYZ, but are not perceptually perfect, and in particular have trouble adapting to unusual lighting conditions.

The HCL colour space seems to be synonymous with CIELCH.

CIECAM02

The CIE's most recent model, CIECAM02 (CAM stands for "colour appearance model"), is more theoretically sophisticated and computationally complex than earlier models. Its aims are to fix several of the problems with models such as CIELAB and CIELUV, and to explain not only responses in carefully controlled experimental environments, but also to model the colour appearance of real-world scenes. Its dimensions J (lightness), C (chroma), and h (hue) define a polar-coordinate geometry.

colour systems

There are various types of colour systems that classify colour and analyse their effects. The American Munsell colour system devised by Albert H. Munsell is a famous classification that organises various colours into a colour solid based on hue, saturation and value. Other important colour systems include the Swedish Natural colour System (NCS), the Optical Society of America's Uniform colour Space (OSA-UCS), and the Hungarian colouroid system developed by Antal Nemcsics from the Budapest University of Technology and Economics. Of those, the NCS is based on the opponent-process colour model, while the Munsell, the OSA-UCS and the colouroid attempt to model colour uniformity. The American Pantone and the German RAL commercial colour-matching systems differ from the previous ones in that their colour spaces are not based on an underlying colour model.

Other uses of "colour model"

Models of mechanism of colour vision

We also use "colour model" to indicate a model or mechanism of colour vision for explaining how colour signals are processed from visual cones to ganglion cells. For simplicity, we call these models colour mechanism models. The classical colour mechanism models are Young–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 colour opponency receive signals from the three types of cones and process them at a more complex level. A widely accepted model is called the zone model. A symmetrical zone model compatible with the trichromatic theory, the opponent theory, and Smith's colour transform model is called the decoding model

Vertebrate evolution of colour vision

Main article: 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, amphibians, reptiles and birds are all tetrachromatic. Placental mammals lost both the mid and short wavelength cones. Thus, most mammals do not have complex colour vision—they are dichromatic but they are sensitive to ultraviolet light, though they cannot see its colours. Human trichromatic colour vision is a recent evolutionary novelty that first evolved in the common ancestor of the Old World Primates. Our trichromatic colour vision evolved by duplication of the long wavelength sensitive opsin, 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 colour 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.

See also

• colour appearance model
• Comparison of colour models in computer graphics
• RGBW colour model
• RGBY colour model

Bibliography

• Fairchild, Mark D. (2005). Color Appearance Models (2nd ed.). Addison-Wesley. This book doesn't discuss HSL or HSV specifically, but is one of the most readable and precise resources about current colour science.
• Joblove, George H.; Greenberg, Donald (August 1978). "Color spaces for computer graphics". Computer Graphics. 12 (3): 20–25. CiteSeerX 10.1.1.413.9004. doi:10.1145/965139.807362. Joblove and Greenberg's paper was the first describing the HSL model, which it compares to HSV.
• Kuehni, Rolf G. (2003). Color Space and Its Divisions: Color Order from Antiquity to the present. New York: Wiley. ISBN 978-0-471-32670-0. This book only briefly mentions HSL and HSV, but is a comprehensive description of colour order systems through history.
• Levkowitz, Haim; Herman, Gabor T. (1993). "GLHS: A Generalized Lightness, Hue and Saturation Color Model". CVGIP: Graphical Models and Image Processing. 55 (4): 271–285. doi:10.1006/cgip.1993.1019. This paper explains how both HSL and HSV, as well as other similar models, can be thought of as specific variants of a more general "GLHS" model. Levkowitz and Herman provide pseudocode for converting from RGB to GLHS and back.
• MacEvoy, Bruce (January 2010). "Color Vision". handprint.com.. Especially the sections about "Modern colour Models" and "Modern colour Theory". MacEvoy's extensive site about colour science and paint mixing is one of the best resources on the web. On this page, he explains the colour-making attributes, and the general goals and history of colour order systems—including HSL and HSV—and their practical relevance to painters.
• Smith, Alvy Ray (August 1978). "Color gamut transform pairs". Computer Graphics. 12 (3): 12–19. doi:10.1145/965139.807361. This is the original paper describing the "hexcone" model, HSV. Smith was a researcher at NYIT’s Computer Graphics Lab. He describes HSV's use in an early digital painting program.

External links

• Illustrations and summaries of RGB, CMYK, LAB, HSV, HSL, and NCS
• Demonstrative colour conversion applet
• HSV colours by Hector Zenil, The Wolfram Demonstrations Project.
• HSV to RGB by CodeBeautify.