CMYK color model

Cyan, magenta, yellow, and key (black)

CMYK (or sometimes YMCK) is a subtractive color model used in color printing. This color model is based on mixing pigments of the following colors in order to make other colors:

• C=Cyan
• M=Magenta
• Y=Yellow
• K=Key (black).

The mixture of ideal CMY colors is subtractive (Cyan, Magenta and Yellow printed together on white result to black). CMYK works through light absorption. The colors that are seen are from the part of light that is not absorbed. In CMYK magenta plus yellow produces red, magenta plus cyan makes blue, cyan plus yellow generates green and the combination of cyan, magenta and yellow form black.

Because the 'black' generated by mixing the subtractive primaries is not as dense as that of a genuine black ink (one that absorbs throughout the visible spectrum), four-color printing uses a fourth, black, ink in addition to the subtractive primaries yellow, magenta and cyan.

Use of four-color printing generates a superior final printed result with greater contrast. However the color a person sees on a computer screen is often slightly different from the color of the same object on a printout since CMYK and the RGB color model used in computer monitors have different gamuts. RGB color is made by the emission of light (additive color) whereas CMYK works by the absorption of it (subtractive color).

Converting between RGB and CMYK

To convert between RGB and CMYK, an intermediate CMY value is used. Color values are represented as a vector, with each color component varying from 0.0 (no color) to 1.0 (fully saturated color).

<math>t_{CMYK}<math> = [0,1]⁴ is the CMYK quadruple;

likewise,

<math>t_{CMY}<math> = [0,1]³ is the CMY triple,

and

<math>t_{RGB}<math> = [0, 1]³ is the RGB triple.

Actually, RGB is most oftenly expressed as a [0,255]³ vector, i.e. in 3 bytes or 24-bit colour. E.g. pure white is specified as either rgb(255,255,255) or as #FFFFFF.

Converting CMYK to RGB

To convert, we first convert CMYK to CMY, then convert the CMY value to RGB

Converting now:

<math>t_{CMYK} = (c, m, y, k)<math>

then:

<math>t_{CMY} = (c', m', y') = (c (1-k)+k, m (1-k)+k, y (1-k)+k )<math>

and:

<math>t_{RGB} = (r, g, b) = ((1 - c'), (1-m'), (1-y'))<math>

Converting RGB to CMYK

Converting RGB → CMY, with the same color vectors as before:

<math>t_{RGB} = (r, g, b)<math>

converting to CMY:

<math>t_{CMY} = (c', m', y') = (1-r, 1-g, 1-b)<math>

and then to CMYK:

<math>K = \mathrm{min}(c', m', y')<math>

if <math>K == 1<math> then <math>t_{CMYK} = (0, 0, 0, 1)<math>, else

<math>t_{CMYK} = (c, m, y, k) = ((c' - K)/(1 - K), (m' - K)/(1 - K), (y' - K)/(1 - K), K )<math>

where min(x, y, z) is the minimum of those three values.

External links

• A song about YMCK, to the tune of 'YMCA' (http://www.bookbuilders.org/news/9701/ymck.htm)
• Lists the CMYK values for hundreds of colors (http://www.december.com/html/spec/colorcmyk.html)
• Convert CMYK to RGB and back (http://www.forret.com/projects/hizmo/cmyk_rgb.asp)

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