Saturation (color theory)

From Wikipedia, the free encyclopedia

In color theory, saturation or purity is the intensity of a specific hue. A highly saturated hue has a vivid, intense color, while a less saturated hue appears more muted and grey. With no saturation at all, the hue becomes a shade of gray. Saturation is one of three components of the HSL color space and the HSV color space.

The saturation of a color is determined by a combination of light intensity and how much it is distributed across the spectrum of different wavelengths. The purest color is achieved by using just one wavelength at a high intensity such as in laser light. If the intensity drops the saturation also drops. To desaturate a color in a subtractive system (such as watercolor), the person can add white, black, gray, or the hue's complement.

1 Purity in CIE 1931 XYZ color space
2 Saturation in RGB color space
3 Chromaticity in CIE 1976 L*a*b* and L*u*v* color spaces
4 Chromaticity in color appearance models
5 See also
6 External links

[edit] Purity in CIE 1931 XYZ color space

In the CIE XYZ color space, the purity or saturation is the Euclidean distance between the position of the color <math> (x, y) </math> and the illuminant's white point <math> (x_{I}, y_{I}) </math> on the CIE xy projective plane, divided by the same distance for a pure (monochromatic, or dichromatic on the purple line) color with the same hue <math> (x_{P}, y_{P}) = \rho_\mathrm{max} (x - x_{I}, y - y_{I}) + (x_{I}, y_{I}) </math> :

and <math> \rho_\mathrm{max} </math> maximal within the boundary of the chromaticity diagram.

[edit] Saturation in RGB color space

In an RGB color space, saturation can be thought of as the standard deviation σ of the color coordinates R(red), G(green), and B(blue). Letting μ represent the brightness, then

<math> \sigma = \sqrt{ (R - \mu)^2 + (G - \mu)^2 + (B - \mu)^2 \over 3} </math>.

An example of saturation in layman's terms in the RGB color model is one in which a person has maximum saturation if he or she has 100% brightness in the red channel while having 0% brightness in the other channels; he or she would have no saturation if all the color channels were equal. Thus, saturation is the difference between the values of the channels.

In term of absolute colorimetry, this simple definition in the RGB color space exhibits several problems. The RGB color space is not an absolute colorimetric space; therefore, the value of saturation is arbitrary, depending on the choice of the color primaries and the white point illuminant. For example, the RGB colorspace does not necessarily have an unitary Jacobian in term of absolute colorimetry.

Although the above math would make a lot more sense, most (all?) software that represents a saturation value to the user returns this value:

[edit] Chromaticity in CIE 1976 Lab* and Luv* color spaces

The naïve definition of saturation does not specify its response function. In the CIE XYZ and RGB color spaces, the saturation is defined in terms of additive color mixing and has the property of being proportional to any scaling centered at white or the white point illuminant. However, neither color space is linear in term of psychovisually perceived color differences. It is also possible and sometimes desirable to define a saturation-like quantity that is linearized in term of the psychovisual perception.

In the CIE 1976 L*a*b* and L*u*v* color spaces, the unnormalized chromaticity is the radial component of the cylindrical coordinate CIE L*C*h (luminance, chromaticity, hue) representation of the L*a*b* and L*u*v* color spaces, also denoted as CIE L*C*h(a*b*) or CIE L*C*h for short and CIE L*C*h(u*v*). The transformation of <math> (a^{*}, b^{*}) </math> to <math>(C^{*}, h) </math> is given by

<math> h = \arctan \frac{b^{*}}{a^{*}} </math>

and analogously for CIE L*C*h(u*v*).

The chromaticity in the CIE L*C*h(a*b*) and CIE L*C*h(u*v*) coordinates has the advantage of being more psychovisually linear, yet they are non-linear in the in term of linear component color mixing. Therefore, chromaticity in CIE 1976 L*a*b* and L*u*v* color spaces is very different from the traditional sense of "saturation".

[edit] Chromaticity in color appearance models

Another, psychovisually even more accurate, more complex method to obtain or specify the saturation is to use the color appearance model, like CIECAM. The chromaticity component of the JCh (lightness, chromaticity, hue) coordinate and becomes a function of parameters like the chrominance and physical brightness of the illumination, or the characteristics of the emitting/reflecting surface, which is also psychovisually more sensible.