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Color model

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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. 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 a color space. This section describes ways in which human color vision can be modeled.

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Tristimulus color space

3D representation of the human color space.

The human 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 above.

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.

CIE XYZ color space

CIE1931 Standard Colorimetric Observer functions between 380 nm and 780 nm (at 5 nm intervals).
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CIE1931 Standard Colorimetric Observer functions between 380 nm and 780 nm (at 5 nm intervals).

Main article: CIE 1931 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. 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.

It must be noted 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.

CIE 1931 chromaticity diagram
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CIE 1931 chromaticity diagram

The figure on the left 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).

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. 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.

With some forms of "red-green color blindness" the green is very slightly brighter than the blue, and the red is so dark it can barely be made out. Red traffic lights in bright daylight appear broken (no light). The green traffic light appears dirty white and hard to distinduish from night street lights.

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.

RGB color space

Main article: 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. 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.

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.

HLS color space

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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.

HSV color space

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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 (angular 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.

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.

Other uses of "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 the Young-Helmholtz's tri-pigments model and Herring's Opponent processes model. Now, the popular model is the zone model, which is used to unify the above two models. According to a zone model, color signals exist in form of tri-pigments in visual cones, but in the form of opponent colors in ganglion cells.

image:colorevolution.gif

Illustration of color evolution and color blindness.

There are a few different versions of the zone model. Some models use G and R to produce red-green opponent color signals; yet some models use B, G, and R to produce red-green signals (see Problems and way out of zone model). Most models use arithmetic operations; yet, the decoding model, as a particular version of the zone model, uses logical operations. The picture shows color evolution according the decoding model. For details of the decoding model, see Chenguang Lu's research on color vision.

See also

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