What is Color Space and the Tristimulus Values XYZ?

By Sareesh Sudhakaran

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Color Space

If a color model is a language, then think of color spaces as grammar, or as variations in a language, like British English versus American English.

The word ‘color’ is spelled ‘colour’ in British English.

Just because a word is used commonly or understood in one variation doesn’t mean a person using another variation will understand it. Some words are particular to a culture or history of a place. The same goes for idioms or phrases particular to a variation.

That’s approximately how color spaces work.

A Color Space is a mathematical model that maps the colors that can be reproduced by a device to a standard color model, usually the RGB model. It’s a complex thing that goes underneath the hood. Many people take color spaces lightly, and pay the price.
 

CIE XYZ 1931

The eye is as good as any reference when building a color space. Why? Even though we have displays that claim to show a billion colors, the eye can never see all of those colors.

One of the first mathematically determined color spaces is the CIE XYZ 1931 color space, created by CIE (International Commission on Illumination) in 1931.

It utilizes three main concepts –

  • It is based on and derived from the CIE RGB model, which was formed from actual experiments
  • It assumes Y to represent luminosity, and Cb and Cr to shoulder the burden of representing all colors. It is sometimes referred to as the CIE xyY color space
  • XYZ is not RGB. XYZ are extrapolations of RGB created mathematically to avoid negative numbers (In 1931 there weren’t any computers) and are called Tristimulus values.
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    It is not critical to understand how the values of the CIE XYZ color space are derived, but the following information is good to know:

  • A color space is actually a 3D image. Think of it as a bag containing color goodies.
  • The two-dimensional image seen here is only a cross-section of the entire color space.
  • It is called a Chromacity diagram.
  • The diagram represents all of the chromaticities visible to the average person. The color region is called the Gamut of human vision.
  • The curved edge is called the spectral locus and corresponds to monochromatic light, with wavelengths listed in nanometers.
  • The straight edge is called the line of purples. These colors have no counterpart in monochromatic light.
  • White is at the center (E).
  • There are no three points within the gamut that form a triangle that includes the entire gamut of human vision; or more simply, the gamut of human vision is not a triangle.
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    Other color spaces are also represented with similar chromacity diagrams that make it slightly easier to visualize them in comparison with each other.

    There are color spaces ‘smaller’ and ‘larger‘ in volume than CIE XYZ. Therefore, a two-dimensional diagram shouldn’t be used exclusively to compare various color spaces. It is possible for one color space to have lesser colors than another but still have colors that the “larger” color space doesn’t have.

    Common color spaces are:

  • PAL – SD PAL TV
  • NTSC – SD NTSC TV
  • sRGB – computer monitors
  • Rec. 709 (Officially ITU-R Recommendation BT.709) – HDTV
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    Your takeaway from this should be the understanding that a color space is a theoretical space. It is the limit you are imposing on a particular device. It’s like saying:

  • Let’s speak in the RGB (the color model) language
  • Let’s lay some ground rules for the language, as in grammar, etc. (the color space)
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    Does this mean that people will understand each other now? Of course not. Yeah, sorry to disappoint. The last piece in this puzzle is the color gamut.

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    December 26, 2012

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